# RAW.org

Open-source research and development in mathematics, software, electronics, fabrication, robotics, and practical tools.

## Sections
- [Open Math](https://raw.org/math/): Explore mathematics, machine learning, geometry, control theory, and technical foundations presented as durable long-form content.
- [Mathematics Book](https://raw.org/books/): Explore an open mathematics book with rigorous chapters on algebra, analysis, geometry, algorithms, numerical methods, probability, and related fields.
- [Open-Source Software](https://raw.org/software/): Browse software projects, libraries, engineering notes, and practical experiments across software and adjacent technical domains.
- [Electronics](https://raw.org/electronics/): Circuits, sensors, embedded systems, drivers, RF, displays and practical hardware engineering projects.
- [Fab](https://raw.org/fab/): Explore practical fabrication projects covering 3D printing, CNC machining, laser cutting, woodworking, mechanical design, workshop tools, and techniques.
- [Robotics](https://raw.org/robotics/): Explore robotics projects covering inverse kinematics, walking machines, Stewart platforms, robot arms, drones, control systems, and autonomous vehicles.
- [Open-Source Tools](https://raw.org/tools/): Explore calculators, generators, visualizers, and interactive tools built to solve real problems.
- [Programming Puzzle Solutions](https://raw.org/puzzles/): Read worked solutions to programming and math puzzles, with a focus on reasoning, trade-offs, and efficient implementations.
- [Mathematics Book](https://raw.org/books/): Long-form mathematical chapters.

## Content
- [About raw.org - Research, Engineering, and Collaboration](https://raw.org/about/): About raw.org: open engineering research, public technical work, collaboration, seed development, and technical partnerships.
- [Introduction to Algebraic Structures](https://raw.org/book/algebra/algebraic-structures/): A formal classification of algebraic structures, from semigroups and monoids to groups, rings, integral domains and fields.
- [Introduction to Complex Numbers](https://raw.org/book/algebra/complex-numbers/): A rigorous introduction to complex arithmetic, polar form, Euler's formula, logarithms, roots, trigonometric functions, geometry, and completeness.
- [Introduction to Number Systems](https://raw.org/book/algebra/number-systems/): A formal introduction to positional number systems, from decimal, binary, octal and hexadecimal to the general b-adic representation.
- [Introduction to Polynomials](https://raw.org/book/algebra/polynomials/): Polynomial arithmetic, division, root multiplicity, Vieta's formulas, and the Fundamental Theorem of Algebra, before specializing to quadratics and cubics.
- [Introduction to Quaternions](https://raw.org/book/algebra/quaternions/): Understand quaternion algebra, polar decomposition, logarithms and powers, and how unit quaternions represent and compose 3D rotations.
- [Solving Cubic Equations](https://raw.org/book/algebra/solving-cubic-equations/): Learn how to solve cubic equations with Cardano's method, discriminants, numerical methods, and a JavaScript solver.
- [Solving Quadratic Equations](https://raw.org/book/algebra/solving-quadratic-equations/): Solve quadratic equations with a Complex.js calculator, the sum-and-product method, factoring, completing the square, the discriminant, and pq/abc formulas.
- [Introduction to Binary Search](https://raw.org/book/algorithms/binary-search/): Derive binary search with invariants, midpoint safety, and lower bound and upper bound boundaries.
- [Introduction to Bit Manipulation Tricks](https://raw.org/book/algorithms/bit-manipulation-tricks/): Two's complement bit hacks for masks, popcount, sign tests, branch-free absolute value and negation, powers of two, and conditional bit updates.
- [Introduction to Bitwise Obfuscation Tricks](https://raw.org/book/algorithms/bitwise-obfuscation-tricks/): How complement, XOR, and mask tricks rewrite increments, equality checks, comparisons, and conditionals, with derivations and limitations.
- [Introduction to Bloomfilters](https://raw.org/book/algorithms/bloomfilter/): Introduction to Bloomfilters: false positive probabilities, optimal hash count, and practical hashing with Murmur3 and FNV.
- [Introduction to the CYK Algorithm](https://raw.org/book/algorithms/cyk-algorithm/): How the Cocke-Younger-Kasami algorithm decides context-free membership in cubic time: Chomsky normal form, the chart recurrence, ambiguity, and complexity.
- [Introduction to Exponentiation by Squaring](https://raw.org/book/algorithms/exponentiation-by-squaring/): Derives exponentiation by squaring from old peasant multiplication and applies it to modular exponentiation, matrices, and more.
- [Fast atan2 Algorithms](https://raw.org/book/algorithms/fast-atan2-algorithms/): Deriving fast atan2 approximations from the tangent subtraction and reciprocal arctangent identities.
- [Introduction to the Fisher-Yates Shuffle](https://raw.org/book/algorithms/fisher-yates-shuffle/): A formal derivation of the Fisher-Yates shuffle, proving by induction that every permutation is equally likely.
- [Introduction to Minimum Spanning Trees](https://raw.org/book/algorithms/minimum-spanning-tree/): Derive Tarjan's green and red rule framework for minimum spanning trees, then specialize it into Kruskal's, Prim's, and the reverse-delete algorithm.
- [Introduction to Needleman-Wunsch Algorithm](https://raw.org/book/algorithms/needleman-wunsch-algorithm/): Learn the Needleman-Wunsch algorithm for global sequence alignment with dynamic programming and traceback.
- [Introduction to the Quine-McCluskey Algorithm](https://raw.org/book/algorithms/quine-mccluskey-algorithm/): Derive Quine-McCluskey minimization, Petrick's method, XOR merging, disjoint factors, and Shannon XOR decomposition.
- [Second Smallest Element in an Array](https://raw.org/book/algorithms/second-smallest-element-in-array/): Derive an efficient algorithm for the second and third smallest element of an array from a simple case analysis.
- [Introduction to the Fast Inverse Square Root Algorithm](https://raw.org/book/algorithms/the-fast-inverse-square-root-algorithm/): Introduction to the fast inverse square root trick, with bit-level initialization and one Newton step.
- [Arc Length of a Function](https://raw.org/book/analysis/arc-length-of-a-function/): Derive the arc length formula for a smooth function from line-segment approximations, the mean value theorem, and a Riemann sum limit.
- [Introduction to Continuity](https://raw.org/book/analysis/continuity/): Derive the epsilon-delta definition of continuity, Lipschitz functions, the intermediate and extreme value theorems, and a full proof of the fundamental theorem of algebra.
- [Introduction to Derivatives](https://raw.org/book/analysis/derivatives/): Understand derivatives from limit definitions to rules, notation, implicit differentiation, and continuity.
- [Introduction to Extrema and the Mean Value Theorem](https://raw.org/book/analysis/extrema-and-the-mean-value-theorem/): How derivatives locate extrema: Fermat's theorem, the extreme value theorem, monotonicity, concavity, and the Mean Value Theorem.
- [Introduction to Functions](https://raw.org/book/analysis/functions/): Build a rigorous foundation for mathematical functions, including domain, codomain, image, preimage, composition, bijections, inverse functions, and graphs.
- [Introduction to the Gamma Function](https://raw.org/book/analysis/gamma-function/): Derive the Gamma function from the factorial and Gaussian integrals, including convergence, recurrence, half-integer values, and analytic continuation.
- [Introduction to Integral Calculus](https://raw.org/book/analysis/integration/): An introduction to integral calculus, from Riemann sums and antiderivatives to the Fundamental Theorem of Calculus, with an interactive Riemann-sum tool.
- [Introduction to Lambert W function](https://raw.org/book/analysis/lambert-w-function/): Introduction to the Lambert W function with branches, derivatives, numerical methods, and equation-solving examples.
- [Introduction to Limits](https://raw.org/book/analysis/limits/): Derive the algebra of limits, Bernoulli's inequality, and the squeeze theorem, extend limits to functions, and define Landau (Big-O) notation.
- [Introduction to Monotone, Bounded Variation, and Convex Functions](https://raw.org/book/analysis/monotone-bv-and-convex-functions/): Prove that monotone functions always have one-sided limits and countably many jumps, derive the Jordan decomposition for bounded variation, and characterize convexity by monotone difference quotients.
- [Introduction to Natural Numbers and Integers](https://raw.org/book/analysis/natural-numbers-and-integers/): Build the natural numbers from the Peano axioms and induction, then construct the integers as equivalence classes and derive absolute value and distance from their order.
- [Introduction to the Nth Derivative of Sine and Cosine](https://raw.org/book/analysis/nth-derivative-of-sin-and-cos/): Derive arbitrary derivatives of sine and cosine from phase shifts, with induction, frequency scaling, matrix structure, ODEs, and Taylor series.
- [Introduction to Power Series](https://raw.org/book/analysis/power-series/): Power series, the Cauchy-Hadamard and Euler radius formulas with proof, and the exponential function's key properties derived from its series.
- [Introduction to Rational Numbers](https://raw.org/book/analysis/rational-numbers/): Learn rational numbers through their formal construction, fraction arithmetic, exponent laws, lowest terms, density, and irrational square roots.
- [Introduction to Real Numbers](https://raw.org/book/analysis/real-numbers/): Develop the real numbers from field, order, and supremum axioms through inequality rules, radicals, intervals, and the existence of roots.
- [Introduction to Relations](https://raw.org/book/analysis/relations/): Learn how mathematical relations connect sets through Cartesian products, composition, inverses, equivalence relations, order relations, and functions.
- [Introduction to Sequences](https://raw.org/book/analysis/sequences/): Sequences, monotonicity, boundedness, and limits, with the Gauss pairing trick for arithmetic sums and a visual proof that odd numbers sum to a square.
- [Introduction to Series](https://raw.org/book/analysis/series/): Infinite series via partial sums and convergence criteria, plus closed forms for geometric and arithmetic series and an exponential-growth application.
- [Introduction to Sets](https://raw.org/book/analysis/sets/): Sets introduction: notation, subsets, power sets, number sets, Venn diagrams, operations, and Cartesian products with worked examples.
- [Introduction to Stirling's Approximation](https://raw.org/book/analysis/stirlings-approximation/): Deriving n!~sqrt(2 pi n)(n/e)^n from scratch via sum-to-integral comparison and Wallis' product, cross-checked with Laplace's method.
- [Introduction to Taylor Series](https://raw.org/book/analysis/taylor-series/): Introduction to Taylor series for local function approximation, truncation error control, and key expansions in analysis.
- [Introduction to Combinatorics](https://raw.org/book/combinatorics/permutations-combinations-and-variations/): Learn when to use permutations, combinations, and variations by reducing every counting problem to two yes/no questions.
- [Introduction to 2D Hit-Testing](https://raw.org/book/computer-graphics/2d-hittest/): Derive hit-tests between points, circles, arcs, line segments, rectangles and triangles, with interactive line-circle and rectangle-circle demos.
- [Introduction to Bézier Curves](https://raw.org/book/computer-graphics/bezier-curves/): Build polynomial and rational Bézier curves and surfaces; explore subdivision, derivatives, arc-length motion, bounds, intersections, offsets, and fitting.
- [Introduction to Fitting Bézier Curves to Function Graphs](https://raw.org/book/computer-graphics/fitting-bezier-curves-to-function-graphs/): Fit cubic Bézier curves to function graphs with endpoint tangents, explicit error metrics, monotonicity constraints, and an interactive solver.
- [GLSL Functions](https://raw.org/book/computer-graphics/glsl-functions/): Derive GLSL's smoothstep, mix, step, a smooth staircase, a smoothed absolute value, and boolean logic as float arithmetic.
- [Introduction to Line-Segment and Bézier-Curve Intersections](https://raw.org/book/computer-graphics/line-segment-bezier-curve-intersection/): Derive robust intersections between finite line segments and cubic Bézier curves, including tangencies, endpoint contacts, and degenerate cases.
- [Introduction to Rasterization Algorithms](https://raw.org/book/computer-graphics/rasterization-algorithms/): Derive the DDA and Bresenham line algorithms and the midpoint circle and ellipse algorithms from their implicit equations, with pixel-grid figures.
- [Introduction to PID Controllers](https://raw.org/book/control-theory/introduction-to-pid-controllers/): Derive proportional, integral, derivative, and combined PID control in continuous and sampled time, with response diagrams and implementation guidance.
- [Introduction to the First Fundamental Form](https://raw.org/book/differential-geometry/first-fundamental-form/): Derive the first fundamental form from a surface Jacobian, then use its metric tensor to measure tangent vectors, angles, curve lengths, and area.
- [Introduction to Quaternion Derivatives](https://raw.org/book/geometry/quaternion-derivatives/): Derive quaternion rates in world/body notation, state and transition matrices, exponential integration, SLERP derivatives, and SO(3) Jacobians.
- [Introduction to Rotations with Complex Numbers and Quaternions](https://raw.org/book/geometry/rotations/): Rotations built up from the plane: rotation matrices, complex rotors, reflections, why the quaternion holds half the angle, and the sandwich product.
- [Introduction to PageRank](https://raw.org/book/graph-theory/pagerank/): Derive PageRank from a recursive link-voting idea into a damped random-surfer Markov chain, with a live simulator and Perron-Frobenius convergence proof.
- [Introduction to Spectral Graph Theory](https://raw.org/book/graph-theory/spectral-graph-theory/): Learn how the eigenvalues of a graph's adjacency and Laplacian matrices reveal its connectivity, bipartiteness, chromatic number, and maximum density.
- [Introduction to Ackermann Steering](https://raw.org/book/kinematics/ackerman-steering/): How Ackermann steering angles are derived, and the forward kinematics that predict a car-like vehicle's motion.
- [Introduction to Shopping Cart Kinematics](https://raw.org/book/kinematics/rolling-shopping-cart/): Derive rigid-body velocity, ICR geometry, caster steering, wheel speeds, and exact planar motion for a four-wheel shopping cart.
- [Introduction to Wheel Loader Steering](https://raw.org/book/kinematics/wheel-loader-steering/): Derive the kinematics, curvature, turning radii, and exact motion update of a symmetric articulated wheel loader.
- [Introduction to 2D Perp Operator](https://raw.org/book/linear-algebra/2d-perp-operator/): Introduction to the 2D perp operator as a 90-degree rotation that maps vectors to perpendicular vectors.
- [Introduction to the 2D Perp Product](https://raw.org/book/linear-algebra/2d-perp-product/): Introduction to the 2D perp product as signed area, orientation test, and bridge to the 3D cross product for planar vectors.
- [Introduction to the 3D Cross Product](https://raw.org/book/linear-algebra/3d-cross-product/): Learn about the 3D cross product: coordinate formula, geometric meaning as oriented area, derivation from perpendicularity, and applications.
- [Introduction to the Bisector of Two Vectors](https://raw.org/book/linear-algebra/bisector-of-two-vectors/): Derive internal and external vector angle bisectors from normalization, rhombus geometry, dot products, weighted formulas, and degenerate cases.
- [Introduction to Dot Product](https://raw.org/book/linear-algebra/dot-product/): Understand the dot product through geometry, coordinate formula, projections, reflections, and key inequalities in linear algebra.
- [Introduction to EigenGame: PCA as a Nash Equilibrium](https://raw.org/book/linear-algebra/eigengame/): See how casting PCA as a k-player game with one utility function per eigenvector turns its unique Nash equilibrium into the true principal components, computable without ever forming the covariance matrix.
- [Introduction to Eigenvalues and Eigenvectors](https://raw.org/book/linear-algebra/eigenvalues-and-eigenvectors/): Learn eigenvalues and eigenvectors through characteristic polynomials, a worked numerical example, the Rayleigh quotient, power iteration, and Cayley-Hamilton.
- [Introduction to Gauss-Jordan Elimination](https://raw.org/book/linear-algebra/gauss-jordan-elimination/): Learn Gauss-Jordan elimination for solving linear systems, classifying solutions, computing rank, and constructing matrix inverses.
- [Introduction to Matrices](https://raw.org/book/linear-algebra/matrices/): Learn matrix notation, transpose, multiplication, determinant, inverse, and transformation matrices with clear geometric meaning.
- [Introduction to Matrix Inverse](https://raw.org/book/linear-algebra/matrix-inverse/): Learn matrix inversion with 2x2 formula, Gauss-Jordan elimination, adjugate method, and numerical stability insights.
- [Introduction to Matrix Multiplication](https://raw.org/book/linear-algebra/matrix-multiplication/): Understand matrix multiplication by dimensions, row-column products, geometric composition, and order-sensitive transforms.
- [Introduction to Principal Component Analysis](https://raw.org/book/linear-algebra/principal-component-analysis/): Derive principal component analysis from variance maximization and reconstruction-error minimization, connect it to the SVD, and learn how to read explained variance.
- [Introduction to Singular Value Decomposition](https://raw.org/book/linear-algebra/singular-value-decomposition/): Learn the singular value decomposition from first principles: derivation from eigenvalues, uniqueness, its relation to eigendecomposition, truncation, and least squares.
- [Introduction to Vectors](https://raw.org/book/linear-algebra/vectors/): Learn vectors in R^n with norm properties, affine interpolation, geometric intuition, and worked examples for core operations.
- [Introduction to k-Nearest Neighbors](https://raw.org/book/machine-learning/k-nearest-neighbor/): Learn kNN through distance geometry, classification, regression, scaling, weighted voting, model selection, dimensionality, and efficient search.
- [Introduction to Linear Discriminant Analysis](https://raw.org/book/machine-learning/linear-discriminant-analysis/): See how linear discriminant analysis turns class labels into a single best-separating axis, and why its closed-form solution can quietly fail on small samples.
- [Introduction to Regression](https://raw.org/book/machine-learning/linear-regression/): Derive least-squares regression from scratch: the model, loss, gradient descent, R², partial correlation, regression toward the mean, Anscombe's Quartet.
- [Introduction to LOESS and LOWESS](https://raw.org/book/machine-learning/loess-and-lowess/): Derive locally weighted regression from the normal equation: the tricube weight function, LOWESS vs. LOESS, robustness iterations, and a fully worked example.
- [Introduction to the Log-Sum-Exp Trick in Machine Learning](https://raw.org/book/machine-learning/log-sum-exp-trick/): A practical guide to log-sum-exp for stable machine learning and deep learning calculations in log-space.
- [Introduction to Continued Fractions](https://raw.org/book/number-theory/continued-fractions/): Continued fractions, convergents, best rational approximations, the golden ratio, and periodic expansions of square roots.
- [Introduction to Diffie-Hellman Key Exchange](https://raw.org/book/number-theory/diffie-hellman-key-exchange/): Learn the Diffie-Hellman key exchange and how modular exponentiation enables shared secrets over insecure channels.
- [Introduction to Greatest Common Divisor](https://raw.org/book/number-theory/greatest-common-divisor/): Learn GCD, Euclidean algorithm, Bézout identity, LCM relation, and modular-inverse criteria with examples.
- [Introduction to Modulo and Divisibility](https://raw.org/book/number-theory/modulo-and-divisibility/): Modulo and divisibility from first definitions to applications, now including the modular multiplication circle.
- [Introduction to Primality Testing](https://raw.org/book/number-theory/primality-testing/): From trial division to wheels, the Sieve of Eratosthenes, and Miller–Rabin: each step removes a class of impossible divisors.
- [Introduction to Prime Numbers](https://raw.org/book/number-theory/prime-numbers/): Primes from definition to Euclid's proof of infinitude, the Fundamental Theorem of Arithmetic with a full uniqueness proof, and twin primes.
- [Introduction to Newton's Method](https://raw.org/book/numerical-analysis/newtons-method/): Introduction to Newton's method for root finding and optimization, with derivations and convergence behavior.
- [Introduction to the Gauss-Newton Method](https://raw.org/book/optimization/gauss-newton-method/): Derive the Gauss-Newton method for nonlinear least squares from Newton's method, with a worked exponential-fit example.
- [Introduction to Gradient Descent](https://raw.org/book/optimization/gradient-descent/): Learn gradient descent from geometric intuition to convergence bounds, step-size stability, and practical SGD variants.
- [Introduction to Linear Programming](https://raw.org/book/optimization/linear-programming/): Learn linear programming from feasible polyhedra and standard form through the simplex method, duality, and a complete geometric example.
- [Introduction to Simulated Annealing](https://raw.org/book/optimization/simulated-annealing/): Simulated annealing explained through Metropolis acceptance, its link to hill climbing, cooling schedules, and initial temperature selection.
- [Inverse Kinematics of a 3-DOF Spider Robot Leg](https://raw.org/book/robotics/inverse-kinematics-of-a-3-dof-spider-robot-leg/): Minimal-trig inverse kinematics for a 3-DOF spider leg: computes coxa yaw, femur and tibia pitches in 3D with singularity-safe, MCU-friendly performance.
- [Introduction to the Average Filter](https://raw.org/book/signal-processing/average-filter/): Derives the recursive average filter from the batch mean, contrasts it with the exponential moving average, and analyzes its convergence.
- [Introduction to the Low-Pass Filter](https://raw.org/book/signal-processing/low-pass-filter/): Derives the first-order low-pass filter, explains why it is called exponential smoothing, connects alpha to a time constant and cutoff frequency, and covers tuning, code, and RC hardware.
- [Introduction to the Moving Average](https://raw.org/book/signal-processing/moving-average/): Derives the moving average filter's recursive update, explains why it needs a sliding window in memory, and analyzes the noise-versus-lag trade-off.
- [Efficient and Accurate Rolling Variance](https://raw.org/book/stochastics/efficient-and-accurate-rolling-variance/): Stable one-pass and rolling-window variance updates with Welford recurrences and replacement formulas.
- [Introduction to Monte Carlo integration](https://raw.org/book/stochastics/monte-carlo-integration/): Introduction to Monte Carlo integration via expectation-based estimators, error scaling, and variance reduction techniques.
- [Introduction to Uniform Random Rotations](https://raw.org/book/stochastics/uniform-random-rotations/): Derive uniformly random 3D rotations from a quaternion volume form via Hopf coordinates on the unit quaternion sphere, with interactive demos.
- [Introduction to Uniform Sampling on a Sphere](https://raw.org/book/stochastics/uniform-sampling-on-a-sphere/): Derive uniform random sampling on a sphere and on arbitrarily aimed spherical caps from the sphere's area element, with interactive 3D demos.
- [Git Cheat Sheet](https://raw.org/cheat-sheet/git/): Quick Git reference for staging, stashing, amending, branches, remotes, fork updates, squashing commits, rebasing, recovery, and safe undo operations.
- [macOS Network Cheat Sheet](https://raw.org/cheat-sheet/macos-network/): macOS networking commands for interfaces, DHCP, DNS, routes, Wi-Fi, Bonjour, sockets, packet capture, firewall, SSH, and Nmap diagnostics.
- [Ruby Code Golf Cheat Sheet](https://raw.org/cheat-sheet/ruby-code-golf/): Golf Ruby with compact syntax for strings, arrays, ranges, blocks, input, regexes, operators, implicit globals, and command-line filters.
- [SSH Cheat Sheet](https://raw.org/cheat-sheet/ssh/): SSH reference for local, reverse, and Unix-socket port forwarding, safe tunnel flags, and how ProxyJump authentication actually works.
- [3D Wire Creator](https://raw.org/demo/3d-wire-creator/): Build and animate simple 3D wireframes in an interactive canvas experiment with presets, perspective projection, and quaternion rotation.
- [Bubble Drag - Interactive Canvas Motion](https://raw.org/demo/bubble-drag/): Drag drifting bubbles with mouse or touch, recolor the canvas from a continuous RGB palette, and explore frame-rate independent motion.
- [Bubble Evolution - Draggable Magnifier](https://raw.org/demo/bubble-evolution/): Move a magnifying glass across an evolving bubble field, adjust its zoom, and explore responsive color and particle motion.
- [Catch It! HTML5 Game](https://raw.org/demo/catch-it/): Play Catch It, an early HTML5 Canvas game featured by Google as a Chrome Experiment, and explore its motion and collision mathematics.
- [Follow the Swarm](https://raw.org/demo/follow-the-swarm/): Steer a luminous particle chain through ribbon, vortex, and Lissajous motion while adjusting trail persistence in this interactive canvas demo.
- [HTML5 Boomshine](https://raw.org/demo/html5-boomshine/): Play HTML5 Boomshine, a responsive canvas game where one expanding circle must trigger a large enough chain reaction to clear each level.
- [HTML5 Particleline - An Interactive Canvas Field](https://raw.org/demo/html5-particleline/): Explore an interactive HTML5 canvas field where filled circles and rings react to radial pointer forces and return with smooth spring motion.
- [HTML5 Snake](https://raw.org/demo/html5-snake/): Play classic Snake on a responsive 45 by 30 grid with keyboard, swipe, and touch controls plus optional wall wrapping.
- [HTML 5 Tetris with AI](https://raw.org/demo/html5-tetris-with-ai/): Play customizable HTML5 Tetris in your browser, enable an AI autopilot, adjust the board and speed, and compete on the leaderboard.
- [Kinematic Clock with Nested SVG Transforms](https://raw.org/demo/kinematic-clock/): Watch a kinematic SVG clock whose minute and second hands form a nested linkage, with relative joint angles derived from local time.
- [HTML 5 Starship Shooter](https://raw.org/demo/starship-shooter/): Play Starship Shooter by aiming through two rotating ring gaps with pointer, touch, or keyboard controls before the survival timer expires.
- [Winamp Equalizer](https://raw.org/demo/winamp-equalizer/): Visualize speech with a live 18-band microphone FFT inside a vintage Winamp display, or use the animated demo signal without device access.
- [Using a Nokia 5110 Display with Arduino](https://raw.org/electronics/displays/arduino-nokia-5110-display/): Connect an 84 x 48 Nokia 5110 LCD to Arduino safely, level-shift its PCD8544 interface, and draw text, graphics, and bitmaps.
- [NEO-6M GPS Module with Arduino](https://raw.org/electronics/gps/neo-6m-gps-module-with-arduino/): Wire a NEO-6M GPS receiver safely to an Arduino Uno, verify its NMEA stream, parse valid fixes with TinyGPSPlus, and diagnose acquisition problems.
- [NEO-6M GPS Module with Raspberry Pi](https://raw.org/electronics/gps/neo-6m-gps-module-with-raspberry-pi/): Wire a NEO-6M GPS module to Raspberry Pi UART, configure Raspberry Pi OS, verify NMEA data, and parse valid fixes in Node.js with GPS.js.
- [DIY Ohmmeter to Measure Resistor Values with Arduino](https://raw.org/electronics/measurement/diy-ohmmeter-to-measure-resistor-values-with-arduino/): Build a voltage-divider Arduino ohmmeter, then learn exactly how accurate it is and how to pick the best reference resistor for your range.
- [Precise 220V AC Frequency Measurement with Arduino](https://raw.org/electronics/measurement/precise-220v-ac-frequency-measurement-with-arduino/): Measure mains AC frequency with an Arduino, an optocoupler, and a precise RTC clock, plus a derivation of how accurate the result really is.
- [Programming the ATtiny85 Using Arduino](https://raw.org/electronics/microcontrollers/programming-the-attiny85-using-arduino/): Program an ATtiny85 microcontroller with an Arduino Uno as ISP: wiring, board manager setup, bootloader, and a blink sketch.
- [Arduino PWM to 0-10 V Analog Signal Conversion for CNC and Spindle Control](https://raw.org/electronics/motor-control/arduino-pwm-to-0-10v-analog-signal-rc-filter-op-amp/): Convert an Arduino/GRBL PWM spindle output into a stable 0-10 V setpoint using a two-stage RC filter and an LM358 gain stage built for long cable runs.
- [TIP120 Arduino Motor Control](https://raw.org/electronics/motor-control/tip120-arduino-motor-control/): Drive a DC motor from Arduino with a TIP120 low-side switch, correctly sizing the base resistor, flyback diode, heat sink, wiring, and PWM code.
- [Control a Syma S107G Helicopter with Arduino](https://raw.org/electronics/remote-control/syma-s107g-arduino-controller/): Build a safe Arduino IR transmitter for the Syma S107G, understand its 32-bit control frame, and send commands with the current IRremote library.
- [Free 3D Print Files](https://raw.org/fab/3d-print-files/): Free 3D print files with previews, short notes, and direct downloads for useful parts, helpers, and experiments.
- [Cone and Frustum Papercraft Template Generator](https://raw.org/fab/templates/printable-cone-template-generator/): Generate a printable, 1:1-scale papercraft template for a cone or frustum from its radii and height, with an optional glue tab, then download it as SVG.
- [Imprint - Legal Information and Contact Details](https://raw.org/imprint/): Legal notice and contact details for XOR Ventures GmbH.
- [Calculating Exact Age Ratios Between Two People](https://raw.org/math/algebra/exploring-date-ratios/): Derive the exact moment when one person is twice as old as another, then generalize the result to any positive age ratio.
- [Simplifying and Optimizing Interval Conditions](https://raw.org/math/algebra/improving-interval-conditions/): Simplify interval tests with centered absolute values, integer endpoint shifts, unsigned subtraction, bit masks, and cyclic normalization.
- [Polynomial Square Roots](https://raw.org/math/algebra/polynomial-square-roots/): When a polynomial has a polynomial square root, how to extract it coefficient by coefficient, and how to verify the result.
- [Quaternion from Two Vectors](https://raw.org/math/algebra/quaternion-from-two-vectors/): Derive the shortest-arc quaternion between two vectors, including stable handling of parallel, antiparallel, and nearly opposite directions.
- [The square root of two is a loop](https://raw.org/math/algebra/square-root-of-two-is-a-loop/): Why cubing the square root of two and halving it returns the same number, two short proofs, and why 0 and -sqrt(2) also loop.
- [Fast Vector Rotation Using Quaternions](https://raw.org/math/algebra/vector-rotation-using-quaternions/): Derive the efficient two-cross-product formula for rotating a 3D vector with a unit quaternion, including conventions and non-unit inputs.
- [Why 0.999... Equals 1](https://raw.org/math/analysis/why-0-999-equals-1/): Prove rigorously that 0.999... equals 1 using limits, an epsilon argument, geometric series, and the non-uniqueness of decimal expansions.
- [The Mathematics of Pagination](https://raw.org/math/combinatorics/pagination-math/): Derive pagination formulas for page counts, overlapping slices, last-page size, offsets, and fixed-width windows from one interval model.
- [Approximating Bézier Curves with Circular Arcs](https://raw.org/math/computer-graphics/approximating-bezier-curves-with-circular-arcs/): Derive incenter biarcs and tolerance-controlled arc splines, with exact spiral extrema, general-cubic limits, and subdivision strategies.
- [Approximating Circular Arcs with Bézier Curves](https://raw.org/math/computer-graphics/approximating-circles-with-cubic-bezier-curves/): Derive cubic, quartic, and quintic Bézier arc approximations, including five-point quartics, contact orders, errors, and SVG conversion.
- [Mapping a Square to a Circle](https://raw.org/math/computer-graphics/how-to-map-a-square-to-a-circle/): Derive the elliptical grid mapping between a unit square and disk, prove its boundary behavior, invert it, and explore it interactively.
- [Line-Segment Ellipse Intersection](https://raw.org/math/computer-graphics/line-segment-ellipse-intersection/): Derive line-segment intersections with a translated and rotated ellipse using coordinate transforms, a stable quadratic, and Vector2.js.
- [Line-Segment Intersection](https://raw.org/math/computer-graphics/line-segment-intersection/): Derive a complete 2D line-segment intersection test using the perp product, including endpoint contact, overlap, and degenerate segments.
- [Partial polyline drawing](https://raw.org/math/computer-graphics/partial-polyline-drawing/): Derive and implement drawing only the first p percent of a polyline's arc length, and a common sign mistake in the branch-free version.
- [Converting SVG Circular Arcs to G-Code G2 and G3](https://raw.org/math/computer-graphics/svg-arc-to-gcode/): Derive exact G2/G3 center offsets from circular SVG arcs, including flag selection, radius correction, Y-axis inversion, and controller-safe output.
- [The Fascinating Geometry Behind A-Series Paper](https://raw.org/math/geometry/a-series-paper-aspect-ratio/): Why A-series paper uses the 1:sqrt(2) aspect ratio, how A0 fixes the scale, why A4 is 210 x 297 mm, and how the geometry generalizes.
- [Calculate the Intersection Points of Two Circles](https://raw.org/math/geometry/calculate-the-intersection-points-of-two-circles/): Derive the intersection points of two circles and robustly classify separate, tangent, contained, coincident, and degenerate cases.
- [Circle Through Three Points](https://raw.org/math/geometry/circle-through-three-points/): Derive the unique circle through three non-collinear points from equal distances, with a compact vector formula and robust JavaScript.
- [Drawing an Upright Star Polygon](https://raw.org/math/geometry/drawing-an-upright-star-polygon/): Derive the minimal rotation that places a regular star polygon upright, with an interactive Plot.js visualization and robust JavaScript code.
- [Intersection Area of Two Circles](https://raw.org/math/geometry/intersection-area-of-two-circles/): Derive the intersection area of two circles from sectors and triangles, including containment, tangency, and robust JavaScript code.
- [Intersection Point of Two Lines](https://raw.org/math/geometry/intersection-point-of-two-lines/): Derive the intersection of two parametric lines and distinguish unique, parallel, coincident, and invalid cases in robust JavaScript.
- [Is an Angle Between Two Other Angles?](https://raw.org/math/geometry/is-an-angle-between-two-other-angles/): A modulo-based formula to check whether an angle lies between two other angles, including the wrap-around case around 0 degrees.
- [Mathematics of a roller chain animation](https://raw.org/math/geometry/mathematics-of-a-roller-chain-animation/): Deriving the tangent lines between two circles to compute a roller chain's shape and length, with a live drag-to-resize animation.
- [Reduce the Length of a Line Segment by a Certain Amount](https://raw.org/math/geometry/reduce-the-length-of-a-line-segment-by-a-certain-amount/): Derive how to shorten a line segment at either endpoint or equally at both ends, with robust JavaScript and an interactive geometric plot.
- [Rounded Corners on Path Segments](https://raw.org/math/geometry/rounded-corners-on-path-segment/): Derive an efficient and numerically stable circular fillet for a path corner, including tangent points, radius limits, and readable JavaScript.
- [Tangent Line to a Circle](https://raw.org/math/geometry/tangent-line-to-a-circle/): Derive the tangent line at any point on a circle using perpendicular vectors, with an interactive Plot.js diagram and robust JavaScript.
- [Extracting Translation, Rotation, and Scaling from Homogeneous Transformations](https://raw.org/math/linear-algebra/extracting-translation-rotation-and-scaling-from-homogeneous-transformations/): How to recover translation, rotation, and per-axis scale from a 4x4 homogeneous transform, including a common SVD ordering bug and its fix.
- [How to plot a covariance error ellipse](https://raw.org/math/linear-algebra/how-to-plot-a-covariance-error-ellipse/): Derive how to draw a confidence ellipse for 2D Gaussian data from its covariance matrix, with Matlab and JavaScript implementations.
- [Normal Vectors of a Line Segment](https://raw.org/math/linear-algebra/normal-vector-of-a-line-segment/): Calculate the left and right normal vectors of a directed 2D line segment, including optional unit normalization and degenerate handling.
- [Plane Reflection Matrix](https://raw.org/math/linear-algebra/plane-reflection-matrix/): Deriving the matrix that reflects a ray off a plane, from decomposing it into normal and in-plane parts.
- [Shortest distance between a point and a line segment](https://raw.org/math/linear-algebra/shortest-distance-between-a-point-and-a-line-segment/): How the dot product and a clamped scalar projection give the shortest distance from a point to a line segment.
- [Determine if a number is a perfect square](https://raw.org/math/number-theory/determine-if-a-number-is-a-perfect-square/): Fast perfect-square tests using square-root checks, modular residue filters, Babylonian refinement, and efficient integer arithmetic.
- [Optimizing integer division](https://raw.org/math/number-theory/optimizing-integer-division/): Replace a constant integer division with a multiply and a shift, derived from scratch, with exact-division and Barrett-reduction extras.
- [Optimizing integer multiplication](https://raw.org/math/number-theory/optimizing-integer-multiplication/): Replace multiplication by a compile-time constant with shifts and additions, and see why the non-adjacent form gives the optimal version.
- [Why Perfect b-ary Trees Are Repunits](https://raw.org/math/number-theory/perfect-b-ary-trees-and-repunits/): Discover why counting nodes in a perfect b-ary tree produces a base-b repunit, and how both constructions follow the same simple recurrence.
- [Sum of Divisors](https://raw.org/math/number-theory/sum-of-divisors/): Derive the sum-of-divisors function from prime factorization and compute its summatory form in O(sqrt n) exact BigInt arithmetic.
- [Calculate the argmin of the sum of absolute values](https://raw.org/math/optimization/calculate-the-argmin-of-the-sum-of-absolute-values/): A short proof, with an interactive diagram, showing that the median minimizes the sum of absolute distances to a set of points.
- [Make a Fair Coin from a Biased Coin](https://raw.org/math/probability/make-a-fair-coin-from-a-biased-coin/): Derive von Neumann's exact method for extracting fair outcomes from an unknown biased coin, including assumptions, expected tosses, and code.
- [Intraday Traffic Forecasting](https://raw.org/math/statistics/intraday-traffic-forecasting/): Forecast a running day's final traffic from completed daily totals, a historical hourly profile, and observations accumulated so far.
- [Privacy Policy](https://raw.org/privacy-policy/): Privacy Policy for raw.org: data processing, cookies, Google Analytics, Cloudflare, legal bases, and your rights.
- [Acm Solution: Turn All the Lights Off](https://raw.org/puzzle/acm/turn-all-the-lights-off/): The optimal solution to the code puzzle from Acm to problem Turn All the Lights Off
- [Codesignal Solution: alienShip](https://raw.org/puzzle/codesignal/alienship/): The optimal solution to the code puzzle from Codesignal to problem alienShip
- [Codesignal Solution: Bottles_1](https://raw.org/puzzle/codesignal/bottles_1/): The optimal solution to the code puzzle from Codesignal to problem Bottles_1
- [Codesignal Solution: Bottles_2](https://raw.org/puzzle/codesignal/bottles_2/): The optimal solution to the code puzzle from Codesignal to problem Bottles_2
- [Codesignal Solution: caesarian](https://raw.org/puzzle/codesignal/caesarian/): The optimal solution to the code puzzle from Codesignal to problem caesarian
- [Codesignal Solution: circumcircle](https://raw.org/puzzle/codesignal/circumcircle/): The optimal solution to the code puzzle from Codesignal to problem circumcircle
- [Codesignal Solution: Complete the Sequence](https://raw.org/puzzle/codesignal/completethesequence/): The optimal solution to the code puzzle from Codesignal to problem Complete the Sequence
- [Codesignal Solution: Computer Units to Byte](https://raw.org/puzzle/codesignal/computerunitstobyte/): The optimal solution to the code puzzle from Codesignal to problem Computer Units to Byte
- [Codesignal Solution: extendedFibonacci](https://raw.org/puzzle/codesignal/extendedfibonacci/): The optimal solution to the code puzzle from Codesignal to problem extendedFibonacci
- [Codesignal Solution: Factorial](https://raw.org/puzzle/codesignal/factorial/): The optimal solution to the code puzzle from Codesignal to problem Factorial
- [Codesignal Solution: FaroShuffles](https://raw.org/puzzle/codesignal/faroshuffles/): The optimal solution to the code puzzle from Codesignal to problem FaroShuffles
- [Codesignal Solution: fibonacciWord](https://raw.org/puzzle/codesignal/fibonacciword/): The optimal solution to the code puzzle from Codesignal to problem fibonacciWord
- [Codesignal Solution: Grouped Bits](https://raw.org/puzzle/codesignal/groupedbits/): The optimal solution to the code puzzle from Codesignal to problem Grouped Bits
- [Codesignal Solution: Is Permutation Of](https://raw.org/puzzle/codesignal/ispermutationof/): The optimal solution to the code puzzle from Codesignal to problem Is Permutation Of
- [Codesignal Solution: isTournament](https://raw.org/puzzle/codesignal/istournament/): The optimal solution to the code puzzle from Codesignal to problem isTournament
- [Codesignal Solution: Matrix Perimeter](https://raw.org/puzzle/codesignal/matrixperimeter/): The optimal solution to the code puzzle from Codesignal to problem Matrix Perimeter
- [Codesignal Solution: maxBits](https://raw.org/puzzle/codesignal/maxbits/): The optimal solution to the code puzzle from Codesignal to problem maxBits
- [Codesignal Solution: Minimum Jump To Reach End](https://raw.org/puzzle/codesignal/minjumptoreachend/): The optimal solution to the code puzzle from Codesignal to problem Minimum Jump To Reach End
- [Codesignal Solution: monkeyBars](https://raw.org/puzzle/codesignal/monkeybars/): The optimal solution to the code puzzle from Codesignal to problem monkeyBars
- [Codesignal Solution: Near Square](https://raw.org/puzzle/codesignal/near_square/): The optimal solution to the code puzzle from Codesignal to problem Near Square
- [Codesignal Solution: nextSquare](https://raw.org/puzzle/codesignal/nextsquare/): The optimal solution to the code puzzle from Codesignal to problem nextSquare
- [Codesignal Solution: No odd Digits](https://raw.org/puzzle/codesignal/noodddigits/): The optimal solution to the code puzzle from Codesignal to problem No odd Digits
- [Codesignal Solution: nthPlace](https://raw.org/puzzle/codesignal/nthplace/): The optimal solution to the code puzzle from Codesignal to problem nthPlace
- [Codesignal Solution: offsets](https://raw.org/puzzle/codesignal/offsets/): The optimal solution to the code puzzle from Codesignal to problem offsets
- [Codesignal Solution: onesPosition](https://raw.org/puzzle/codesignal/onesposition/): The optimal solution to the code puzzle from Codesignal to problem onesPosition
- [Codesignal Solution: Only Survivor](https://raw.org/puzzle/codesignal/onlysourvivor/): The optimal solution to the code puzzle from Codesignal to problem Only Survivor
- [Codesignal Solution: Poker Chips](https://raw.org/puzzle/codesignal/pokerchips/): The optimal solution to the code puzzle from Codesignal to problem Poker Chips
- [Codesignal Solution: primeClimb](https://raw.org/puzzle/codesignal/primeclimb/): The optimal solution to the code puzzle from Codesignal to problem primeClimb
- [Codesignal Solution: reciprocal](https://raw.org/puzzle/codesignal/reciprocal/): The optimal solution to the code puzzle from Codesignal to problem reciprocal
- [Codesignal Solution: sumOdious](https://raw.org/puzzle/codesignal/sumodious/): The optimal solution to the code puzzle from Codesignal to problem sumOdious
- [Codesignal Solution: surviveIt](https://raw.org/puzzle/codesignal/surviveit/): The optimal solution to the code puzzle from Codesignal to problem surviveIt
- [Codesignal Solution: totalBinSum](https://raw.org/puzzle/codesignal/totalbinsum/): The optimal solution to the code puzzle from Codesignal to problem totalBinSum
- [Codesignal Solution: TwoFive](https://raw.org/puzzle/codesignal/twofive/): The optimal solution to the code puzzle from Codesignal to problem TwoFive
- [Codingame Solution: 1D Bush Fire](https://raw.org/puzzle/codingame/1d-bush-fire/): The optimal solution to the code puzzle from Codingame to problem 1D Bush Fire
- [Codingame Solution: ANEO Sponsored Puzzle](https://raw.org/puzzle/codingame/aneo-sponsored-puzzle/): The optimal solution to the code puzzle from Codingame to problem ANEO Sponsored Puzzle
- [Codingame Solution: Apple tree](https://raw.org/puzzle/codingame/apple-tree/): The optimal solution to the code puzzle from Codingame to problem Apple tree
- [Codingame Solution: ASCII Art](https://raw.org/puzzle/codingame/ascii-art/): The optimal solution to the code puzzle from Codingame to problem ASCII Art
- [Codingame Solution: Bag of Balls](https://raw.org/puzzle/codingame/bag-of-balls/): The optimal solution to the code puzzle from Codingame to problem Bag of Balls
- [Codingame Solution: Balanced ternary computer: encode](https://raw.org/puzzle/codingame/balanced-ternary-computer-encode/): The optimal solution to the code puzzle from Codingame to problem Balanced ternary computer: encode
- [Codingame Solution: Bank Robbers](https://raw.org/puzzle/codingame/bank-robbers/): The optimal solution to the code puzzle from Codingame to problem Bank Robbers
- [Codingame Solution: Bender - Episode 1](https://raw.org/puzzle/codingame/bender-episode-1/): The optimal solution to the code puzzle from Codingame to problem Bender - Episode 1
- [Codingame Solution: Bender - Episode 3](https://raw.org/puzzle/codingame/bender-episode-3/): The optimal solution to the code puzzle from Codingame to problem Bender - Episode 3
- [Codingame Solution: Benford's law](https://raw.org/puzzle/codingame/benfords-law/): The optimal solution to the code puzzle from Codingame to problem Benford's law
- [Codingame Solution: Binary Permutations](https://raw.org/puzzle/codingame/binary-permutations/): The optimal solution to the code puzzle from Codingame to problem Binary Permutations
- [Codingame Solution: Block Number Sequence](https://raw.org/puzzle/codingame/block-number-sequence/): The optimal solution to the code puzzle from Codingame to problem Block Number Sequence
- [Codingame Solution: Blowing Fuse](https://raw.org/puzzle/codingame/blowing-fuse/): The optimal solution to the code puzzle from Codingame to problem Blowing Fuse
- [Codingame Solution: Caesar Box](https://raw.org/puzzle/codingame/caesar-box/): The optimal solution to the code puzzle from Codingame to problem Caesar Box
- [Codingame Solution: CGFunge interpreter](https://raw.org/puzzle/codingame/cgfunge-interpreter/): The optimal solution to the code puzzle from Codingame to problem CGFunge interpreter
- [Codingame Solution: CGX Formatter](https://raw.org/puzzle/codingame/cgx-formatter/): The optimal solution to the code puzzle from Codingame to problem CGX Formatter
- [Codingame Solution: Chuck Norris](https://raw.org/puzzle/codingame/chuck-norris/): The optimal solution to the code puzzle from Codingame to problem Chuck Norris
- [Codingame Solution: Conway Sequence](https://raw.org/puzzle/codingame/conway-sequence/): The optimal solution to the code puzzle from Codingame to problem Conway Sequence
- [Codingame Solution: Create the longest sequence of 1s](https://raw.org/puzzle/codingame/create-the-longest-sequence-of-1s/): The optimal solution to the code puzzle from Codingame to problem Create the longest sequence of 1s
- [Codingame Solution: Darts](https://raw.org/puzzle/codingame/darts/): The optimal solution to the code puzzle from Codingame to problem Darts
- [Codingame Solution: Dead men's shot](https://raw.org/puzzle/codingame/dead-mens-shot/): The optimal solution to the code puzzle from Codingame to problem Dead men's shot
- [Codingame Solution: Defibrillators](https://raw.org/puzzle/codingame/defibrillators/): The optimal solution to the code puzzle from Codingame to problem Defibrillators
- [Codingame Solution: Digit sum successor](https://raw.org/puzzle/codingame/digit-sum-successor/): The optimal solution to the code puzzle from Codingame to problem Digit sum successor
- [Codingame Solution: Disks intersection](https://raw.org/puzzle/codingame/disks-intersection/): The optimal solution to the code puzzle from Codingame to problem Disks intersection
- [Codingame Solution: Divide the factorial](https://raw.org/puzzle/codingame/divide-the-factorial/): The optimal solution to the code puzzle from Codingame to problem Divide the factorial
- [Codingame Solution: Divisibility windows](https://raw.org/puzzle/codingame/divisibility-windows/): The optimal solution to the code puzzle from Codingame to problem Divisibility windows
- [Codingame Solution: Don't Panic - Episode 1](https://raw.org/puzzle/codingame/do-not-panic-episode-1/): The optimal solution to the code puzzle from Codingame to problem Don't Panic - Episode 1
- [Codingame Solution: Dwarfs standing on the shoulders of giants](https://raw.org/puzzle/codingame/dwarfs-standing-on-the-shoulders-of-giants/): The optimal solution to the code puzzle from Codingame to problem Dwarfs standing on the shoulders of giants
- [Codingame Solution: Egyptian multiplication](https://raw.org/puzzle/codingame/egyptian-multiplication/): The optimal solution to the code puzzle from Codingame to problem Egyptian multiplication
- [Codingame Solution: Execution Circle](https://raw.org/puzzle/codingame/execution-circle/): The optimal solution to the code puzzle from Codingame to problem Execution Circle
- [Codingame Solution: Expand the polynomial](https://raw.org/puzzle/codingame/expand-the-polynomial/): The optimal solution to the code puzzle from Codingame to problem Expand the polynomial
- [Codingame Solution: Factorial vs Exponential](https://raw.org/puzzle/codingame/factorial-vs-exponential/): The optimal solution to the code puzzle from Codingame to problem Factorial vs Exponential
- [CodinGame Solution: Fill the Square!](https://raw.org/puzzle/codingame/fill-the-square/): Solve CodinGame's Fill the Square optimally with GF(2), row chasing, bitmasks, and an exhaustive search over only the first row.
- [Codingame Solution: Genome Sequencing](https://raw.org/puzzle/codingame/genome-sequencing/): The optimal solution to the code puzzle from Codingame to problem Genome Sequencing
- [Codingame Solution: Goro Want Chocolate](https://raw.org/puzzle/codingame/goro-want-chocolate/): The optimal solution to the code puzzle from Codingame to problem Goro Want Chocolate
- [Codingame Solution: Highest truncated pyramid](https://raw.org/puzzle/codingame/highest-truncated-pyramid/): The optimal solution to the code puzzle from Codingame to problem Highest truncated pyramid
- [Codingame Solution: Horse-racing Duals](https://raw.org/puzzle/codingame/horse-racing-duals/): The optimal solution to the code puzzle from Codingame to problem Horse-racing Duals
- [Codingame Solution: Horse-racing Hyperduals](https://raw.org/puzzle/codingame/horse-racing-hyperduals/): The optimal solution to the code puzzle from Codingame to problem Horse-racing Hyperduals
- [Codingame Solution: ISBN Check digit](https://raw.org/puzzle/codingame/isbn-check-digit/): The optimal solution to the code puzzle from Codingame to problem ISBN Check digit
- [Codingame Solution: Lumen](https://raw.org/puzzle/codingame/lumen/): The optimal solution to the code puzzle from Codingame to problem Lumen
- [Codingame Solution: Magic count of numbers](https://raw.org/puzzle/codingame/magic-count-of-numbers/): The optimal solution to the code puzzle from Codingame to problem Magic count of numbers
- [Magic stones](https://raw.org/puzzle/codingame/magic-stones/): The optimal solution to the code puzzle from Codingame to problem Magic stones
- [Codingame Solution: Mars Lander - Episode 1](https://raw.org/puzzle/codingame/mars-lander/): The optimal solution to the code puzzle from Codingame to problem Mars Lander - Episode 1
- [Codingame Solution: Mayan Calculation](https://raw.org/puzzle/codingame/mayan-calculation/): The optimal solution to the code puzzle from Codingame to problem Mayan Calculation
- [Codingame Solution: Merlin's Magic Square](https://raw.org/puzzle/codingame/merlins-magic-square/): The optimal solution to the code puzzle from Codingame to problem Merlin's Magic Square
- [Codingame Solution: MIME Type](https://raw.org/puzzle/codingame/mime-type/): The optimal solution to the code puzzle from Codingame to problem MIME Type
- [Codingame Solution: Minimal Ball Cost](https://raw.org/puzzle/codingame/minimal-ball-cost/): The optimal solution to the code puzzle from Codingame to problem Minimal Ball Cost
- [Codingame Solution: Minimal number of swaps](https://raw.org/puzzle/codingame/minimal-number-of-swaps/): The optimal solution to the code puzzle from Codingame to problem Minimal number of swaps
- [Codingame Solution: Mystery sums](https://raw.org/puzzle/codingame/mystery-sums/): The optimal solution to the code puzzle from Codingame to problem Mystery sums
- [Codingame Solution: Network Cabling](https://raw.org/puzzle/codingame/network-cabling/): The optimal solution to the code puzzle from Codingame to problem Network Cabling
- [Codingame Solution: Next car license plate](https://raw.org/puzzle/codingame/next-car-license-plate/): The optimal solution to the code puzzle from Codingame to problem Next car license plate
- [Codingame Solution: Number of letters in a number - Binary](https://raw.org/puzzle/codingame/number-of-letters-in-a-number-binary/): The optimal solution to the code puzzle from Codingame to problem Number of letters in a number - Binary
- [Codingame Solution: Number of Network Hosts](https://raw.org/puzzle/codingame/number-of-network-hosts/): The optimal solution to the code puzzle from Codingame to problem Number of Network Hosts
- [Codingame Solution: Number staircase](https://raw.org/puzzle/codingame/number-staircase/): The optimal solution to the code puzzle from Codingame to problem Number staircase
- [Codingame Solution: Numeral system](https://raw.org/puzzle/codingame/numeral-system/): The optimal solution to the code puzzle from Codingame to problem Numeral system
- [Codingame Solution: Offset Arrays](https://raw.org/puzzle/codingame/offset-arrays/): The optimal solution to the code puzzle from Codingame to problem Offset Arrays
- [Codingame Solution: Onboarding](https://raw.org/puzzle/codingame/onboarding/): The optimal solution to the code puzzle from Codingame to problem Onboarding
- [Codingame Solution: Pirate's treasure](https://raw.org/puzzle/codingame/pirates-treasure/): The optimal solution to the code puzzle from Codingame to problem Pirate's treasure
- [Codingame Solution: Power of Thor - Episode 1](https://raw.org/puzzle/codingame/power-of-thor/): The optimal solution to the code puzzle from Codingame to problem Power of Thor - Episode 1
- [Codingame Solution: Pyramid height](https://raw.org/puzzle/codingame/pyramid-height/): The optimal solution to the code puzzle from Codingame to problem Pyramid height
- [Codingame Solution: Recurring Decimals](https://raw.org/puzzle/codingame/recurring-decimals/): The optimal solution to the code puzzle from Codingame to problem Recurring Decimals
- [Codingame Solution: Roller Coaster](https://raw.org/puzzle/codingame/roller-coaster/): The optimal solution to the code puzzle from Codingame to problem Roller Coaster
- [Codingame Solution: Rubik](https://raw.org/puzzle/codingame/rubik/): The optimal solution to the code puzzle from Codingame to problem Rubik
- [Codingame Solution: Scrabble](https://raw.org/puzzle/codingame/scrabble/): The optimal solution to the code puzzle from Codingame to problem Scrabble
- [Codingame Solution: Shadows of the Knight - Episode 1](https://raw.org/puzzle/codingame/shadows-of-the-knight-episode-1/): The optimal solution to the code puzzle from Codingame to problem Shadows of the Knight - Episode 1
- [Codingame Solution: Simple fraction to mixed number](https://raw.org/puzzle/codingame/simple-fraction-to-mixed-number/): The optimal solution to the code puzzle from Codingame to problem Simple fraction to mixed number
- [Codingame Solution: Simultaneous Ages](https://raw.org/puzzle/codingame/simultaneous-ages/): The optimal solution to the code puzzle from Codingame to problem Simultaneous Ages
- [Codingame Solution: Skynet Revolution - Episode 1](https://raw.org/puzzle/codingame/skynet-revolution-episode-1/): The optimal solution to the code puzzle from Codingame to problem Skynet Revolution - Episode 1
- [Codingame Solution: Stock Exchange Losses](https://raw.org/puzzle/codingame/stock-exchange-losses/): The optimal solution to the code puzzle from Codingame to problem Stock Exchange Losses
- [Codingame Solution: Sum of divisors](https://raw.org/puzzle/codingame/sum-of-divisors/): The optimal solution to the code puzzle from Codingame to problem Sum of divisors
- [Codingame Solution: Super Computer](https://raw.org/puzzle/codingame/super-computer/): The optimal solution to the code puzzle from Codingame to problem Super Computer
- [Codingame Solution: Surface](https://raw.org/puzzle/codingame/surface/): The optimal solution to the code puzzle from Codingame to problem Surface
- [Codingame Solution: TAN Network](https://raw.org/puzzle/codingame/tan-network/): The optimal solution to the code puzzle from Codingame to problem TAN Network
- [Codingame Solution: Teads Sponsored Contest](https://raw.org/puzzle/codingame/teads-sponsored-contest/): The optimal solution to the code puzzle from Codingame to problem Teads Sponsored Contest
- [Codingame Solution: Telephone Numbers](https://raw.org/puzzle/codingame/telephone-numbers/): The optimal solution to the code puzzle from Codingame to problem Telephone Numbers
- [Codingame Solution: Temperatures](https://raw.org/puzzle/codingame/temperatures/): The optimal solution to the code puzzle from Codingame to problem Temperatures
- [Codingame Solution: The Descent](https://raw.org/puzzle/codingame/the-descent/): The optimal solution to the code puzzle from Codingame to problem The Descent
- [Codingame Solution: The Fastest](https://raw.org/puzzle/codingame/the-fastest/): The optimal solution to the code puzzle from Codingame to problem The Fastest
- [Codingame Solution: The Gift](https://raw.org/puzzle/codingame/the-gift/): The optimal solution to the code puzzle from Codingame to problem The Gift
- [Codingame Solution: The greatest element](https://raw.org/puzzle/codingame/the-greatest-element/): The optimal solution to the code puzzle from Codingame to problem The greatest element
- [Codingame Solution: The greatest number](https://raw.org/puzzle/codingame/the-greatest-number/): The optimal solution to the code puzzle from Codingame to problem The greatest number
- [Codingame Solution: The Holy Grail](https://raw.org/puzzle/codingame/the-holy-grail/): The optimal solution to the code puzzle from Codingame to problem The Holy Grail
- [Codingame Solution: The Last Crusade - Episode 1](https://raw.org/puzzle/codingame/the-last-crusade-episode-1/): The optimal solution to the code puzzle from Codingame to problem The Last Crusade - Episode 1
- [Codingame Solution: The Resistance](https://raw.org/puzzle/codingame/the-resistance/): The optimal solution to the code puzzle from Codingame to problem The Resistance
- [Codingame Solution: The River I.](https://raw.org/puzzle/codingame/the-river-i/): The optimal solution to the code puzzle from Codingame to problem The River I.
- [Codingame Solution: The River II.](https://raw.org/puzzle/codingame/the-river-ii/): The optimal solution to the code puzzle from Codingame to problem The River II.
- [Codingame Solution: The Travelling Salesman Problem](https://raw.org/puzzle/codingame/the-travelling-salesman-problem/): The optimal solution to the code puzzle from Codingame to problem The Travelling Salesman Problem
- [Codingame Solution: Vortex](https://raw.org/puzzle/codingame/vortex/): The optimal solution to the code puzzle from Codingame to problem Vortex
- [Codingame Solution: War](https://raw.org/puzzle/codingame/war/): The optimal solution to the code puzzle from Codingame to problem War
- [Hackerrank Solution: Anti-Palindromic Strings](https://raw.org/puzzle/hackerrank/anti-palindromic-strings/): The optimal solution to the code puzzle from Hackerrank to problem Anti-Palindromic Strings
- [Hackerrank Solution: Best Divisor](https://raw.org/puzzle/hackerrank/best-divisor/): The optimal solution to the code puzzle from Hackerrank to problem Best Divisor
- [Hackerrank Solution: Circle City](https://raw.org/puzzle/hackerrank/circle-city/): The optimal solution to the code puzzle from Hackerrank to problem Circle City
- [Hackerrank Solution: Closest Number](https://raw.org/puzzle/hackerrank/closest-number/): The optimal solution to the code puzzle from Hackerrank to problem Closest Number
- [Hackerrank Solution: Connecting Towns](https://raw.org/puzzle/hackerrank/connecting-towns/): The optimal solution to the code puzzle from Hackerrank to problem Connecting Towns
- [Hackerrank Solution: Counting Valleys](https://raw.org/puzzle/hackerrank/counting-valleys/): The optimal solution to the code puzzle from Hackerrank to problem Counting Valleys
- [Hackerrank Solution: Easy GCD](https://raw.org/puzzle/hackerrank/easy-gcd/): The optimal solution to the code puzzle from Hackerrank to problem Easy GCD
- [Hackerrank Solution: Easy sum](https://raw.org/puzzle/hackerrank/easy-sum/): The optimal solution to the code puzzle from Hackerrank to problem Easy sum
- [Hackerrank Solution: Equations](https://raw.org/puzzle/hackerrank/equations/): The optimal solution to the code puzzle from Hackerrank to problem Equations
- [Hackerrank Solution: Even Odd Query](https://raw.org/puzzle/hackerrank/even-odd-query/): The optimal solution to the code puzzle from Hackerrank to problem Even Odd Query
- [Hackerrank Solution: Find the Point](https://raw.org/puzzle/hackerrank/find-the-point/): The optimal solution to the code puzzle from Hackerrank to problem Find the Point
- [Hackerrank Solution: Jumping on the Clouds](https://raw.org/puzzle/hackerrank/jumping-on-the-clouds/): The optimal solution to the code puzzle from Hackerrank to problem Jumping on the Clouds
- [Hackerrank Solution: Leonardo's Prime Factors](https://raw.org/puzzle/hackerrank/leonardos-prime-factors/): The optimal solution to the code puzzle from Hackerrank to problem Leonardo's Prime Factors
- [Hackerrank Solution: Little Gaurav and Sequence](https://raw.org/puzzle/hackerrank/little-gaurav-and-sequence/): The optimal solution to the code puzzle from Hackerrank to problem Little Gaurav and Sequence
- [Hackerrank Solution: Little Panda Power](https://raw.org/puzzle/hackerrank/little-panda-power/): The optimal solution to the code puzzle from Hackerrank to problem Little Panda Power
- [Hackerrank Solution: Manasa and Factorials](https://raw.org/puzzle/hackerrank/manasa-and-factorials/): The optimal solution to the code puzzle from Hackerrank to problem Manasa and Factorials
- [Hackerrank Solution: Maximizing XOR](https://raw.org/puzzle/hackerrank/maxmizing-xor/): The optimal solution to the code puzzle from Hackerrank to problem Maximizing XOR
- [Hackerrank Solution: Minimum Height Triangle](https://raw.org/puzzle/hackerrank/minimum-height-triangle/): The optimal solution to the code puzzle from Hackerrank to problem Minimum Height Triangle
- [Hackerrank Solution: Recursive Digit Sum](https://raw.org/puzzle/hackerrank/recursive-digit-sum/): The optimal solution to the code puzzle from Hackerrank to problem Recursive Digit Sum
- [Hackerrank Solution: Repeated String](https://raw.org/puzzle/hackerrank/repeated-string/): The optimal solution to the code puzzle from Hackerrank to problem Repeated String
- [Hackerrank Solution: Restaurant](https://raw.org/puzzle/hackerrank/restaurant/): The optimal solution to the code puzzle from Hackerrank to problem Restaurant
- [Hackerrank Solution: Sherlock and Array](https://raw.org/puzzle/hackerrank/sherlock-and-array/): The optimal solution to the code puzzle from Hackerrank to problem Sherlock and Array
- [Hackerrank Solution: Sherlock and Divisors](https://raw.org/puzzle/hackerrank/sherlock-and-divisors/): The optimal solution to the code puzzle from Hackerrank to problem Sherlock and Divisors
- [Hackerrank Solution: Sherlock and GCD](https://raw.org/puzzle/hackerrank/sherlock-and-gcd/): The optimal solution to the code puzzle from Hackerrank to problem Sherlock and GCD
- [Hackerrank Solution: Sherlock and Pairs](https://raw.org/puzzle/hackerrank/sherlock-and-pairs/): The optimal solution to the code puzzle from Hackerrank to problem Sherlock and Pairs
- [Hackerrank Solution: Sherlock and Permutations](https://raw.org/puzzle/hackerrank/sherlock-and-permutations/): The optimal solution to the code puzzle from Hackerrank to problem Sherlock and Permutations
- [Hackerrank Solution: Sherlock and Squares](https://raw.org/puzzle/hackerrank/sherlock-and-squares/): The optimal solution to the code puzzle from Hackerrank to problem Sherlock and Squares
- [Hackerrank Solution: Special Multiple](https://raw.org/puzzle/hackerrank/special-multiple/): The optimal solution to the code puzzle from Hackerrank to problem Special Multiple
- [Hackerrank Solution: Sum vs XOR](https://raw.org/puzzle/hackerrank/sum-vs-xor/): The optimal solution to the code puzzle from Hackerrank to problem Sum vs XOR
- [Hackerrank Solution: Summing the N series](https://raw.org/puzzle/hackerrank/summing-the-n-series/): The optimal solution to the code puzzle from Hackerrank to problem Summing the N series
- [Hackerrank Solution: The Great XOR](https://raw.org/puzzle/hackerrank/the-great-xor/): The optimal solution to the code puzzle from Hackerrank to problem The Great XOR
- [Advent calendar motifs](https://raw.org/puzzle/misc/advent-calendar-motifs/): The optimal solution to the code puzzle problem Advent calendar motifs
- [An interesting Limit](https://raw.org/puzzle/misc/an-interesting-limit/): The optimal solution to the code puzzle problem An interesting Limit
- [Cracking Apple Interview Question](https://raw.org/puzzle/misc/cracking-apple-interview-question/): Tackle the Cracking Apple Interview Question puzzle, a challenging problem designed to test and improve your problem-solving skills.
- [Division with remainder](https://raw.org/puzzle/misc/division-with-remainder/): The optimal solution to the code puzzle problem Division with remainder
- [Find the Parity of the Sum of floor(n/k) from k=1 to n](https://raw.org/puzzle/misc/find-the-parity-of-the-sum-of-floor/): Quickly decide whether G(n)=sum floor(n/k) is odd or even using a clean perfect-square argument and a reusable parity shortcut.
- [Inscribed Squares](https://raw.org/puzzle/misc/inscribed-squares/): The optimal solution to the code puzzle problem Inscribed Squares
- [Number Guessing](https://raw.org/puzzle/misc/number-guessing/): The optimal solution to the code puzzle problem Number Guessing
- [Pre-School Math Problem](https://raw.org/puzzle/misc/pre-school-math-problem/): The optimal solution to the code puzzle problem Pre-School Math Problem
- [Probability to win in a Tombola](https://raw.org/puzzle/misc/probability-to-win-in-a-tombola/): The optimal solution to the code puzzle problem Probability to win in a Tombola
- [Solution to the Water Jug Problem](https://raw.org/puzzle/misc/solution-to-the-water-jug-problem/): From Die Hard to number theory: Solve the Water Jug Problem with gcd feasibility checks, minimum-step BFS, and an interactive JavaScript walkthrough.
- [Solve exponential equation \(6^x + 4^x = 9^x\)](https://raw.org/puzzle/misc/solve-exponential-equation-i/): The optimal solution to the code puzzle problem Solve exponential equation \(6^x + 4^x = 9^x\)
- [Solve exponential equation \(x^y = y^x\)](https://raw.org/puzzle/misc/solve-exponential-equation-ii/): The optimal solution to the code puzzle problem Solve exponential equation \(x^y = y^x\)
- [Sum of Digit-Sums between one and a million](https://raw.org/puzzle/misc/sum-of-digit-sums-between-one-and-a-million/): The optimal solution to the code puzzle problem Sum of Digit-Sums between one and a million
- [The rope around the equator](https://raw.org/puzzle/misc/the-rope-around-the-equator/): The optimal solution to the code puzzle problem The rope around the equator
- [Three Digits Number](https://raw.org/puzzle/misc/three-digits-number/): The optimal solution to the code puzzle problem Three Digits Number
- [Tipping Point Problem](https://raw.org/puzzle/misc/tipping-point-problem/): The optimal solution to the code puzzle problem Tipping Point Problem
- [Project Euler Solution #1: Multiples of 3 and 5](https://raw.org/puzzle/project-euler/problem-1/): The optimal solution to the Project Euler Problem 1 Multiples of 3 and 5
- [Project Euler Solution #10: Summation of primes](https://raw.org/puzzle/project-euler/problem-10/): The optimal solution to the Project Euler Problem 10 Summation of primes
- [Project Euler Solution #107: Minimal network](https://raw.org/puzzle/project-euler/problem-107/): The optimal solution to the Project Euler Problem 107 Minimal network
- [Project Euler Solution #11: Largest product in a grid](https://raw.org/puzzle/project-euler/problem-11/): The optimal solution to the Project Euler Problem 11 Largest product in a grid
- [Project Euler Solution #12: Highly divisible triangular number](https://raw.org/puzzle/project-euler/problem-12/): The optimal solution to the Project Euler Problem 12 Highly divisible triangular number
- [Project Euler Solution #13: Large sum](https://raw.org/puzzle/project-euler/problem-13/): The optimal solution to the Project Euler Problem 13 Large sum
- [Project Euler Solution #14: Longest Collatz sequence](https://raw.org/puzzle/project-euler/problem-14/): The optimal solution to the Project Euler Problem 14 Longest Collatz sequence
- [Project Euler Solution #15: Lattice paths](https://raw.org/puzzle/project-euler/problem-15/): The optimal solution to the Project Euler Problem 15 Lattice paths
- [Project Euler Solution #16: Power digit sum](https://raw.org/puzzle/project-euler/problem-16/): The optimal solution to the Project Euler Problem 16 Power digit sum
- [Project Euler Solution #17: Number letter counts](https://raw.org/puzzle/project-euler/problem-17/): The optimal solution to the Project Euler Problem 17 Number letter counts
- [Project Euler Solution #18: Maximum path sum I](https://raw.org/puzzle/project-euler/problem-18/): The optimal solution to the Project Euler Problem 18 Maximum path sum I
- [Project Euler Solution #19: Counting Sundays](https://raw.org/puzzle/project-euler/problem-19/): The optimal solution to the Project Euler Problem 19 Counting Sundays
- [Project Euler Solution #2: Even Fibonacci numbers](https://raw.org/puzzle/project-euler/problem-2/): The optimal solution to the Project Euler Problem 2 Even Fibonacci numbers
- [Project Euler Solution #20: Factorial digit sum](https://raw.org/puzzle/project-euler/problem-20/): The optimal solution to the Project Euler Problem 20 Factorial digit sum
- [Project Euler Solution #21: Amicable numbers](https://raw.org/puzzle/project-euler/problem-21/): The optimal solution to the Project Euler Problem 21 Amicable numbers
- [Project Euler Solution #22: Names scores](https://raw.org/puzzle/project-euler/problem-22/): The optimal solution to the Project Euler Problem 22 Names scores
- [Project Euler Solution #23: Non-abundant sums](https://raw.org/puzzle/project-euler/problem-23/): The optimal solution to the Project Euler Problem 23 Non-abundant sums
- [Project Euler Solution #24: Lexicographic permutations](https://raw.org/puzzle/project-euler/problem-24/): The optimal solution to the Project Euler Problem 24 Lexicographic permutations
- [Project Euler Solution #25: 1000-digit Fibonacci number](https://raw.org/puzzle/project-euler/problem-25/): The optimal solution to the Project Euler Problem 25 1000-digit Fibonacci number
- [Project Euler Solution #26: Reciprocal cycles](https://raw.org/puzzle/project-euler/problem-26/): The optimal solution to the Project Euler Problem 26 Reciprocal cycles
- [Project Euler Solution #27: Quadratic primes](https://raw.org/puzzle/project-euler/problem-27/): The optimal solution to the Project Euler Problem 27 Quadratic primes
- [Project Euler Solution #28: Number spiral diagonals](https://raw.org/puzzle/project-euler/problem-28/): The optimal solution to the Project Euler Problem 28 Number spiral diagonals
- [Project Euler Solution #29: Distinct powers](https://raw.org/puzzle/project-euler/problem-29/): The optimal solution to the Project Euler Problem 29 Distinct powers
- [Project Euler Solution #3: Largest prime factor](https://raw.org/puzzle/project-euler/problem-3/): The optimal solution to the Project Euler Problem 3 Largest prime factor
- [Project Euler Solution #30: Digit fifth powers](https://raw.org/puzzle/project-euler/problem-30/): The optimal solution to the Project Euler Problem 30 Digit fifth powers
- [Project Euler Solution #31: Coin sums](https://raw.org/puzzle/project-euler/problem-31/): The optimal solution to the Project Euler Problem 31 Coin sums
- [Project Euler Solution #32: Pandigital products](https://raw.org/puzzle/project-euler/problem-32/): The optimal solution to the Project Euler Problem 32 Pandigital products
- [Project Euler Solution #33: Digit cancelling fractions](https://raw.org/puzzle/project-euler/problem-33/): The optimal solution to the Project Euler Problem 33 Digit cancelling fractions
- [Project Euler Solution #34: Digit factorials](https://raw.org/puzzle/project-euler/problem-34/): The optimal solution to the Project Euler Problem 34 Digit factorials
- [Project Euler Solution #35: Circular primes](https://raw.org/puzzle/project-euler/problem-35/): The optimal solution to the Project Euler Problem 35 Circular primes
- [Project Euler Solution #36: Double-base palindromes](https://raw.org/puzzle/project-euler/problem-36/): The optimal solution to the Project Euler Problem 36 Double-base palindromes
- [Project Euler Solution #37: Truncatable primes](https://raw.org/puzzle/project-euler/problem-37/): The optimal solution to the Project Euler Problem 37 Truncatable primes
- [Project Euler Solution #38: Pandigital multiples](https://raw.org/puzzle/project-euler/problem-38/): The optimal solution to the Project Euler Problem 38 Pandigital multiples
- [Project Euler Solution #39: Integer right triangles](https://raw.org/puzzle/project-euler/problem-39/): The optimal solution to the Project Euler Problem 39 Integer right triangles
- [Project Euler Solution #4: Largest palindrome product](https://raw.org/puzzle/project-euler/problem-4/): The optimal solution to the Project Euler Problem 4 Largest palindrome product
- [Project Euler Solution #40: Champernowne's constant](https://raw.org/puzzle/project-euler/problem-40/): The optimal solution to the Project Euler Problem 40 Champernowne's constant
- [Project Euler Solution #41: Pandigital prime](https://raw.org/puzzle/project-euler/problem-41/): The optimal solution to the Project Euler Problem 41 Pandigital prime
- [Project Euler Solution #42: Coded triangle numbers](https://raw.org/puzzle/project-euler/problem-42/): The optimal solution to the Project Euler Problem 42 Coded triangle numbers
- [Project Euler Solution #43: Sub-string divisibility](https://raw.org/puzzle/project-euler/problem-43/): The optimal solution to the Project Euler Problem 43 Sub-string divisibility
- [Project Euler Solution #44: Pentagon numbers](https://raw.org/puzzle/project-euler/problem-44/): The optimal solution to the Project Euler Problem 44 Pentagon numbers
- [Project Euler Solution #45: Triangular, pentagonal, and hexagonal](https://raw.org/puzzle/project-euler/problem-45/): The optimal solution to the Project Euler Problem 45 Triangular, pentagonal, and hexagonal
- [Project Euler Solution #46: Goldbach's other conjecture](https://raw.org/puzzle/project-euler/problem-46/): The optimal solution to the Project Euler Problem 46 Goldbach's other conjecture
- [Project Euler Solution #47: Distinct primes factors](https://raw.org/puzzle/project-euler/problem-47/): The optimal solution to the Project Euler Problem 47 Distinct primes factors
- [Project Euler Solution #48: Self powers](https://raw.org/puzzle/project-euler/problem-48/): The optimal solution to the Project Euler Problem 48 Self powers
- [Project Euler Solution #49: Prime permutations](https://raw.org/puzzle/project-euler/problem-49/): The optimal solution to the Project Euler Problem 49 Prime permutations
- [Project Euler Solution #5: Smallest multiple](https://raw.org/puzzle/project-euler/problem-5/): The optimal solution to the Project Euler Problem 5 Smallest multiple
- [Project Euler Solution #50: Consecutive prime sum](https://raw.org/puzzle/project-euler/problem-50/): The optimal solution to the Project Euler Problem 50 Consecutive prime sum
- [Project Euler Solution #52: Permuted multiples](https://raw.org/puzzle/project-euler/problem-52/): The optimal solution to the Project Euler Problem 52 Permuted multiples
- [Project Euler Solution #55: Lychrel numbers](https://raw.org/puzzle/project-euler/problem-55/): The optimal solution to the Project Euler Problem 55 Lychrel numbers
- [Project Euler Solution #56: Powerful digit sum](https://raw.org/puzzle/project-euler/problem-56/): The optimal solution to the Project Euler Problem 56 Powerful digit sum
- [Project Euler Solution #57: Square root convergents](https://raw.org/puzzle/project-euler/problem-57/): The optimal solution to the Project Euler Problem 57 Square root convergents
- [Project Euler Solution #58: Spiral primes](https://raw.org/puzzle/project-euler/problem-58/): The optimal solution to the Project Euler Problem 58 Spiral primes
- [Project Euler Solution #59: XOR decryption](https://raw.org/puzzle/project-euler/problem-59/): The optimal solution to the Project Euler Problem 59 XOR decryption
- [Project Euler Solution #6: Sum square difference](https://raw.org/puzzle/project-euler/problem-6/): The optimal solution to the Project Euler Problem 6 Sum square difference
- [Project Euler Solution #62: Cubic permutations](https://raw.org/puzzle/project-euler/problem-62/): The optimal solution to the Project Euler Problem 62 Cubic permutations
- [Project Euler Solution #63: Powerful digit counts](https://raw.org/puzzle/project-euler/problem-63/): The optimal solution to the Project Euler Problem 63 Powerful digit counts
- [Project Euler Solution #64: Odd period square roots](https://raw.org/puzzle/project-euler/problem-64/): The optimal solution to the Project Euler Problem 64 Odd period square roots
- [Project Euler Solution #67: Maximum path sum II](https://raw.org/puzzle/project-euler/problem-67/): The optimal solution to the Project Euler Problem 67 Maximum path sum II
- [Project Euler Solution #69: Totient maximum](https://raw.org/puzzle/project-euler/problem-69/): The optimal solution to the Project Euler Problem 69 Totient maximum
- [Project Euler Solution #7: 10001st prime](https://raw.org/puzzle/project-euler/problem-7/): The optimal solution to the Project Euler Problem 7 10001st prime
- [Project Euler Solution #71: Ordered fractions](https://raw.org/puzzle/project-euler/problem-71/): The optimal solution to the Project Euler Problem 71 Ordered fractions
- [Project Euler Solution #72: Counting fractions](https://raw.org/puzzle/project-euler/problem-72/): The optimal solution to the Project Euler Problem 72 Counting fractions
- [Project Euler Solution #8: Largest product in a series](https://raw.org/puzzle/project-euler/problem-8/): The optimal solution to the Project Euler Problem 8 Largest product in a series
- [Project Euler Solution #81: Path sum: two ways](https://raw.org/puzzle/project-euler/problem-81/): The optimal solution to the Project Euler Problem 81 Path sum: two ways
- [Project Euler Solution #9: Special Pythagorean triplet](https://raw.org/puzzle/project-euler/problem-9/): The optimal solution to the Project Euler Problem 9 Special Pythagorean triplet
- [Project Euler Solution #92: Square digit chains](https://raw.org/puzzle/project-euler/problem-92/): The optimal solution to the Project Euler Problem 92 Square digit chains
- [Skillvalue Solution: Cells' Division](https://raw.org/puzzle/skillvalue/cells-division/): The optimal solution to the code puzzle from Skillvalue to problem Cells' Division
- [Skillvalue Solution: Decrypt the enigma](https://raw.org/puzzle/skillvalue/encrypt-the-enigma/): The optimal solution to the code puzzle from Skillvalue to problem Decrypt the enigma
- [Skillvalue Solution: Even Position](https://raw.org/puzzle/skillvalue/even-position/): The optimal solution to the code puzzle from Skillvalue to problem Even Position
- [Skillvalue Solution: Find the Link](https://raw.org/puzzle/skillvalue/find-the-link/): The optimal solution to the code puzzle from Skillvalue to problem Find the Link
- [Skillvalue Solution: Minimum Gates](https://raw.org/puzzle/skillvalue/minimum-gates/): The optimal solution to the code puzzle from Skillvalue to problem Minimum Gates
- [Skillvalue Solution: Smaller Primes](https://raw.org/puzzle/skillvalue/smaller-primes/): The optimal solution to the code puzzle from Skillvalue to problem Smaller Primes
- [Spotify Solution: Best Before](https://raw.org/puzzle/spotify/best-before/): The optimal solution to the code puzzle from Spotify to problem Best Before
- [Spotify Solution: Reverse Number in Binary](https://raw.org/puzzle/spotify/reverse-number-in-binary/): The optimal solution to the code puzzle from Spotify to problem Reverse Number in Binary
- [Extending the Verified Range for \(A!B!=C!\) to \(B \leq 10^{1,000,000,000}\)](https://raw.org/research/extending-the-verified-range-for-the-factorial-diophantine-equation/): An exact finite-field and p-adic sieve extends the verified range for A!B!=C! to B
- [Inverse Kinematics of a Stewart Platform](https://raw.org/research/inverse-kinematics-of-a-stewart-platform/): Deriving closed-form inverse kinematics for a Stewart Platform driven by rotational servo motors, with circular and hexagonal anchor arrangements.
- [Solving Lights Out Using Linear Algebra](https://raw.org/research/solving-lightsout-using-linear-algebra/): Test and optimally solve Lights Out boards using linear algebra over GF(2), quiet patterns, row chasing, and minimum-weight solutions.
- [Add HTTP Response Headers in lighttpd](https://raw.org/software/administration/add-http-response-headers-in-lighttpd/): Add response headers to lighttpd error pages with mod_setenv or a hardened native FastCGI handler using constrained X-Sendfile delivery.
- [Combine CSS and JavaScript with lighttpd](https://raw.org/software/administration/combine-css-and-javascript-with-lighttpd/): Combine CSS and JavaScript for lighttpd with content-hashed build artifacts, long-lived caching, compression, and a safe runtime fallback.
- [Debian SysV Init Script for lighttpd](https://raw.org/software/administration/debian-lighttpd-startup-script/): A corrected Debian SysV init snippet for source-built lighttpd using start-stop-daemon, configuration validation, safe PID handling, and logrotate.
- [Generate and Cache Thumbnails on Demand with lighttpd](https://raw.org/software/administration/dynamic-thumbnail-generation-on-the-static-server/): Generate image thumbnails on demand with lighttpd, a bounded FastCGI worker, safe ImageMagick execution, atomic caching, and immutable URLs.
- [Enable Key Repeat and Disable the Accent Menu on macOS](https://raw.org/software/administration/enable-key-repeat-on-macos/): Enable traditional key repeat on macOS, disable the press-and-hold accent menu, check the active preference, and restore the default behavior.
- [Flash a Linux Image to an SD Card on macOS](https://raw.org/software/administration/flashing-linux-to-sdcard/): Safely flash a raw Linux image to an SD card on macOS using diskutil and dd, with device verification, checksums, and progress output.
- [Keep an Unlinked File Open on Unix](https://raw.org/software/administration/hiding-files-on-filesystem/): Demonstrate how a Unix file remains accessible through an open descriptor after unlink removes its final directory entry.
- [Set Up Internet Sharing on macOS from the Command Line](https://raw.org/software/administration/macos-internet-sharing-command-line/): Turn a Mac into an IPv4 router with command-line interface setup, kernel forwarding, scoped PF anchor rules, NAT, testing, and clean removal.
- [Set Up a Production Mail Server with Postfix, Dovecot, and MySQL](https://raw.org/software/administration/postfix-dovecot-mysql-mail-server/): Build a production mail server with Postfix, Dovecot, MySQL, TLS, DKIM, SPF, DMARC, virtual mailboxes, Sieve, and operational tests.
- [Face Detection with OpenCV and C++](https://raw.org/software/computer-vision/face-detection-with-opencv-cpp/): Detect faces in images with OpenCV 4 and C++, tune a Haar cascade, and export reliable bounding-box JSON with reproducible build commands.
- [Face Detection with PHP and OpenCV](https://raw.org/software/computer-vision/face-detection-with-php/): Detect faces from PHP with OpenCV Haar cascades, validate bounding boxes, annotate JPEGs safely, compare classifiers, and understand accuracy limits.
- [PHP-Facedetect: An OpenCV Face-Detection Extension](https://raw.org/software/computer-vision/php-facedetect-extension/): Build and use PHP-Facedetect, a native OpenCV cascade-classifier extension for counting faces and returning pixel bounding boxes from PHP.
- [Calculate Age Correctly in MySQL](https://raw.org/software/databases/age-calculation-with-mysql/): Calculate completed calendar years correctly in MySQL with TIMESTAMPDIFF(), including birthday boundaries, leap days, and indexed age filters.
- [Analyze User Activity Patterns with MySQL and PHP](https://raw.org/software/databases/analyze-user-activity-patterns/): Build timezone-correct hourly activity histograms in MySQL and find continuous windows across midnight with a tested PHP algorithm.
- [Avoid N+1 Queries with MySQL JSON Aggregation](https://raw.org/software/databases/avoid-n-plus-one-queries-with-mysql-json-aggregation/): Load products, favorite counts, viewer state, and bounded user previews without N+1 queries using native MySQL JSON aggregation.
- [Connect to Microsoft SQL Server with Python](https://raw.org/software/databases/connect-mssql-database-with-python/): Connect Python on a Raspberry Pi to Microsoft SQL Server through FreeTDS and pyodbc, with safe credentials and parameterized queries.
- [Efficient Pagination in MySQL](https://raw.org/software/databases/efficient-pagination-in-mysql/): Build fast, stable MySQL pagination with composite indexes, keyset cursors, reverse navigation, optional counts, and measured query plans.
- [Should MySQL VARCHAR Lengths Be Powers of Two?](https://raw.org/software/databases/field-size-as-power-of-two/): Learn why powers of two do not optimize MySQL VARCHAR columns, where length-prefix sizes change, and how to choose practical field limits.
- [Finding Friends of Friends with MySQL](https://raw.org/software/databases/find-friends-of-friends-using-mysql/): Model undirected friendships once and find friends of friends with indexed edges, two-hop joins, and cycle-safe recursive CTEs in MySQL 8.
- [Efficient Flag-Based Counts in MySQL](https://raw.org/software/databases/flag-based-count-using-mysql/): Count distinct flags per group efficiently in MySQL with compact bitmasks, BIT_OR(), and BIT_COUNT(), avoiding an expanded DISTINCT join.
- [Import Wikipedia into MySQL with MediaWiki](https://raw.org/software/databases/import-wikipedia-into-mysql/): Import a current Wikipedia XML dump into MySQL or MariaDB safely with MediaWiki, including verification, recovery, and rebuild steps.
- [Indexing Text Columns in MySQL 8.4](https://raw.org/software/databases/indexing-text-columns-in-mysql/): Design efficient MySQL text indexes by measuring prefix selectivity, respecting collation and byte limits, and validating real execution plans.
- [Mask IPv6 Addresses with MySQL](https://raw.org/software/databases/inet6-masking-with-mysql/): Mask packed IPv6 addresses in MySQL with a portable stored function that applies a bytewise AND to two 16-byte binary values.
- [Model Many-to-Many Relationships in MySQL](https://raw.org/software/databases/model-many-to-many-relationships-in-mysql/): Model indexed many-to-many relationships in MySQL, migrate legacy CSV IDs safely, and recognize when a JSON snapshot is appropriate.
- [Build a Circular Buffer in MySQL](https://raw.org/software/databases/mysql-circular-buffer/): Build a fixed-size MySQL circular buffer with constant-space writes, ordered reads, and a transaction-safe concurrent-writer pattern.
- [Full-Text Location Search with MySQL 8.4](https://raw.org/software/databases/mysql-fulltext-location-search/): Build a MySQL 8.4 location search across names, aliases, regions, and postal codes with safe prefix queries and measured relevance ranking.
- [Preserve ON UPDATE CURRENT_TIMESTAMP in MySQL](https://raw.org/software/databases/mysql-preserve-timestamp-on-update/): Preserve an auto-updated MySQL timestamp during selected UPDATE statements with self-assignment, without altering the table or adding a trigger.
- [Can MySQL Query Parsing Be Avoided?](https://raw.org/software/databases/mysql-query-parsing/): Learn where MySQL query parsing costs arise, how binary prepared statements reuse server state, and when protocol optimization actually pays off.
- [The Best SQL Mode Configuration for MySQL 8.4](https://raw.org/software/databases/mysql-sql-mode-configuration/): Choose a strict, deterministic MySQL 8.4 SQL mode configuration, understand every mode, and introduce it safely into an existing application.
- [MySQL Wishlist Revisited for MySQL 8.4](https://raw.org/software/databases/mysql-wishlist/): A 2009 MySQL wishlist revisited against MySQL 8.4, with clear status markers for triggers, generated columns, DML, MERGE, VALUES, and more.
- [Calculate the Next Birthday in MySQL](https://raw.org/software/databases/next-birthday-in-mysql/): Calculate the next birthday in MySQL from a birth date, including passed dates, today's birthday, leap days, and deterministic tests.
- [Finding People Near You with MySQL 8.4](https://raw.org/software/databases/people-near-you-with-mysql/): Find nearby people with MySQL 8.4 using WGS 84 points, an R-tree bounding-box filter, and an exact spherical distance check.
- [A Programmable Query Layer on Top of MySQL](https://raw.org/software/databases/programmable-query-layer-for-mysql/): Build a programmable SQL layer that compiles semantic markers into PDO bindings, routing metadata, and explicit shard-aware query plans.
- [Reliable Asynchronous Writes with MySQL](https://raw.org/software/databases/reliable-asynchronous-mysql-writes/): Design reliable asynchronous MySQL writes with direct commits, transactional outbox workers, idempotent retries, batching, and backpressure.
- [How It Was Possible to Get Root Access Through MySQL](https://raw.org/software/databases/root-access-through-mysql/): A historical analysis of how weak MySQL privileges let SQL access cross into native code execution, and which modern controls break the chain.
- [Running Standard Deviation in MySQL](https://raw.org/software/databases/running-standard-deviation-in-mysql/): Maintain a live standard deviation per MySQL group without storing raw rows, using sum-of-squares and Welford's algorithm.
- [Set and Clear Bit Flags Atomically in MySQL](https://raw.org/software/databases/set-and-clear-bit-flags-in-mysql/): Update selected MySQL bit flags atomically with set, clear, replacement, and branch-free Boolean assignment masks.
- [Persisting a Custom Sort Order in MySQL](https://raw.org/software/databases/sorted-array-to-mysql/): Persist drag-and-drop list order safely in MySQL 8 with JSON_TABLE(), complete ownership validation, and one atomic set-based UPDATE.
- [SQL NULL and Three-Valued Logic](https://raw.org/software/databases/sql-null-and-three-valued-logic/): Understand SQL NULL through three-valued logic, complete truth tables, MySQL examples, and practical guidance for filters, equality, and NOT IN.
- [Statistical Analysis with MySQL 8.4](https://raw.org/software/databases/statistical-analysis-with-mysql/): Calculate reliable statistics in MySQL 8.4 with native aggregates, CTEs, window functions, explicit estimators, and correct NULL handling.
- [Building a Tag Cloud with MySQL](https://raw.org/software/databases/store-a-tag-cloud-in-mysql/): Design a normalized MySQL tag system with race-safe upserts, exact usage counts, recency data, and logarithmic weights for a tag cloud.
- [Stream SQL to MySQL with Netcat](https://raw.org/software/databases/stream-sql-to-mysql-with-netcat/): Stream a SQL dump directly into MySQL with Netcat on a trusted private network, without exposing credentials or ignoring transfer failures.
- [TF-IDF Related-Article Ranking with MySQL 8.4](https://raw.org/software/databases/tf-idf-with-mysql/): Build explainable related-article rankings in MySQL 8.4 with logarithmic TF-IDF, L2 normalization, cosine similarity, and deterministic top-three selection.
- [Disable Vim Visual Mode on Mouse Selection](https://raw.org/software/development-tools/disable-vim-visual-mode-on-mouse-selection/): Disable Vim or Neovim mouse handling so terminal drag selection works again, and inspect, restore, or persist the setting safely.
- [Process JSON in the Terminal with jq](https://raw.org/software/development-tools/process-json-in-terminal-with-jq/): Practical jq snippet guide for filtering, transforming, sanitizing, and exporting JSON in terminal workflows.
- [Control a Stepper Motor with A4988 Driver and Arduino](https://raw.org/software/drivers/a4988-stepper-motor-driver-with-arduino/): Build a reliable A4988 and Arduino stepper setup with safe wiring, Vref tuning, and single or dual-motor control.
- [Arduino I2C Bus Scanner](https://raw.org/software/drivers/arduino-i2c-scanner/): Scan an Arduino I2C bus, list responding 7-bit device addresses, and diagnose wiring, pull-up, power, and bus errors.
- [Control a Stepper Motor with DRV8825 Driver and Arduino](https://raw.org/software/drivers/drv8825-stepper-motor-driver-with-arduino/): Bring up a DRV8825 with Arduino safely, tune current limit, and run single or dual-stepper control patterns.
- [Controlling DC Motors with DRV8833 Motor Driver and Arduino](https://raw.org/software/drivers/drv8833-motor-driver-with-arduino/): Wire a DRV8833 with Arduino, control two motors with PWM, and validate sleep, fault, and safe bring-up behavior.
- [Nintendo Nunchuk Driver for Arduino](https://raw.org/software/drivers/nintendo-nunchuk-driver/): Connect a Nintendo Nunchuk to Arduino, initialize I2C, decode its joystick, buttons, and 10-bit accelerometer, and troubleshoot replicas.
- [Control PH-4502C pH Sensor with Arduino](https://raw.org/software/drivers/ph-4502c-ph-sensor-with-arduino/): Control a PH-4502C with Arduino using wiring, calibration, calculator tooling, and robust pH reading sketches.
- [Circular Sectors and Annular Arcs in OpenSCAD](https://raw.org/software/graphics/circular-sector-and-arcs-with-openscad/): Create reliable circular sectors, annular arcs, rings, and extruded arc solids in OpenSCAD without oversized clipping geometry.
- [Build a 3D Advent Calendar with HTML, CSS, and JavaScript](https://raw.org/software/graphics/css-3d-advent-calendar/): Build an accessible 3D Advent calendar with CSS Grid, hinged transform doors, image tiles, vanilla JavaScript, saved state, and date-safe gifts.
- [Introduction to CSS 3D Transforms](https://raw.org/software/graphics/introduction-to-css-3d-transforms/): Learn CSS 3D transforms through perspective, cards, boxes, carousel geometry, matrices, and an interactive Trackball-powered cube designer.
- [Point Orientation Relative to a Directed Line](https://raw.org/software/graphics/is-a-point-on-the-left-or-right-side-of-a-line/): Classify a 2D point as left, right, or collinear relative to a directed line using the signed perp product in JavaScript.
- [A Simple Quaternion Game Engine](https://raw.org/software/graphics/simple-quaternion-game-engine/): Build a quaternion-only 3D game engine with camera transforms, clipping, projection, lighting, and an interactive HTML5 Canvas renderer.
- [Trackball Rotation using Quaternions](https://raw.org/software/graphics/trackball-rotation-using-quaternions/): Arcball rotation with quaternions for intuitive 3D mouse interaction with CSS transforms and JavaScript.
- [BitSet.js: Arbitrary-Size Bit Vectors](https://raw.org/software/libraries/bitset-js/): BitSet.js provides fast arbitrary-size bit vectors, Boolean set operations, ranges, serialization, and infinite complements in JavaScript.
- [Complex.js](https://raw.org/software/libraries/complex-js/): Complex.js brings immutable complex arithmetic, powers, roots, logarithms, and trigonometric functions to JavaScript.
- [dhcp.js: A DHCP client and server for Node.js](https://raw.org/software/libraries/dhcp-js/): dhcp.js provides a dependency-free DHCPv4 server, client, and traffic watcher for Node.js with TypeScript declarations.
- [Fraction.js](https://raw.org/software/libraries/fraction-js/): Fraction.js provides exact BigInt rational arithmetic, repeating-decimal parsing, immutable operations, and flexible output for JavaScript.
- [Gamecontroller.js: Read USB Controllers in Node.js](https://raw.org/software/libraries/gamecontroller-js/): Gamecontroller.js reads USB gamepads in a Node.js backend through HID and maps device reports to button, joystick, data, error, and close events.
- [GPS.js: NMEA Parser in JavaScript](https://raw.org/software/libraries/gps-js/): GPS.js parses NMEA receiver data in Node.js and browsers, with typed messages, normalized navigation state, stream handling, and geospatial helpers.
- [Intersection.js: 2D Geometry Intersection Library in JavaScript](https://raw.org/software/libraries/intersection-js/): Intersection.js finds intersections between line segments, circles, ellipses, arcs, and Bézier curves in JavaScript and TypeScript.
- [jQuery borderStyle](https://raw.org/software/libraries/jquery-borderstyle/): jQuery borderStyle reads and writes border radii, widths, styles, and colors through one compact, chainable plugin method.
- [jQuery Paging](https://raw.org/software/libraries/jquery-paging/): jQuery Paging calculates page links, slice bounds, overlaps, and navigation state while callbacks retain complete control over markup.
- [jQuery xcolor](https://raw.org/software/libraries/jquery-xcolor/): jQuery xcolor parses, converts, mixes, compares, and animates colors with an extensive API and an interactive color workbench.
- [mod_mysql_accesslog: MySQL Logging for lighttpd](https://raw.org/software/libraries/mod-mysql-accesslog/): mod_mysql_accesslog writes lighttpd request fields through prepared MySQL statements and demonstrates binlog replication for centralized access logs.
- [MySQL Infusion UDF: Native Functions for MySQL](https://raw.org/software/libraries/mysql-infusion/): MySQL Infusion UDF adds native aggregate, string, math, bit-field, and utility functions, with documented installation and deployment boundaries.
- [PHP-Defcon: Persistent Constants for PHP 5](https://raw.org/software/libraries/php-defcon/): PHP-Defcon loads typed configuration values as persistent PHP constants, with includes, substitution, concatenation, and startup-time parsing.
- [PHP-IDNA: Internationalized Domain Names for PHP](https://raw.org/software/libraries/php-idna/): PHP-IDNA converts Unicode domain names to ASCII-compatible encoding and back through a native PHP extension backed by GNU Libidn.
- [PHP-Infusion: Native Utility Functions for PHP](https://raw.org/software/libraries/php-infusion/): PHP-Infusion adds 29 native bit, numeric, string, array, duration, template, and introspection helpers to PHP through one extension.
- [PHP-Sysload: Load-Aware PHP Backends](https://raw.org/software/libraries/php-sysload/): PHP-Sysload checks Linux load averages during PHP request startup and signals overloaded backends through a configurable response header.
- [PNGlib.js: A Small JavaScript PNG Encoder](https://raw.org/software/libraries/pnglib-js/): PNGlib.js builds indexed-color PNG images in JavaScript using palettes, transparency, stored DEFLATE blocks, checksums, and Base64.
- [PolyEdge for OpenSCAD](https://raw.org/software/libraries/polyedge/): PolyEdge is a compact OpenSCAD library for polygons with independently configurable sharp, rounded, and inset corners.
- [Symbolic Quaternion Operations with SymPy](https://raw.org/software/libraries/quaternion-operations-in-sympy/): Derive and verify axis-angle rotations, Hamilton products, and symbolic rotation compositions with explicit SymPy quaternion components.
- [Read CSV Data into an Eigen Matrix](https://raw.org/software/libraries/read-csv-into-an-eigen-matrix/): Read validated, rectangular numeric CSV data into an Eigen matrix with explicit shape checks and robust field parsing.
- [Tag Cloud Plugin for Smarty](https://raw.org/software/libraries/smarty-tag-cloud-plugin/): A weighted tag-cloud plugin for Smarty, with logarithmic scaling, sorting options, legacy behavior, security limits, and a Smarty 5 migration path.
- [Compute a Symbolic Gradient with SymPy](https://raw.org/software/libraries/symbolic-gradient-with-sympy/): Compute symbolic gradients in SymPy with explicit variable order, and distinguish matrix derivatives from coordinate-system vectors.
- [Set Excel Column Width in Points with VBA](https://raw.org/software/programming/excel-column-width-in-points-with-vba/): Set an Excel column to a measured point width with VBA using bounded binary search, tolerance handling, unit conversion, and safe error recovery.
- [Forcing Garbage Collection in Node.js](https://raw.org/software/programming/forcing-garbage-collection-in-nodejs/): Learn when Node.js manual garbage collection is useful, how to expose it safely, and why most applications should let V8 manage memory.
- [Why I Didn't Get a Single New .de Domain](https://raw.org/software/programming/how-i-got-no-new-de-domain/): My failed 2009 attempt to secure a short .de domain, and the ranking heuristic I built to prioritize names before the DENIC land rush.
- [Packing Small Integers into Bit Fields](https://raw.org/software/programming/packing-small-integers-into-bit-fields/): Learn how to pack small unsigned integers into bit fields, derive masks for extraction and replacement, and implement the operations safely in C.
- [Inside an Experimental PHP 5.3 Language Fork](https://raw.org/software/programming/php-5-3-language-fork/): An archival, source-backed tour of a 2011 PHP 5.3.6 fork, its syntax and VM experiments, and the ideas that later appeared in PHP upstream.
- [Build a PHP Daemon and Run It as a Linux Service](https://raw.org/software/programming/php-daemon/): Build a resilient PHP daemon with asynchronous signals and graceful shutdowns, then run it safely under systemd or detach it with a correct double fork.
- [Pipe Data from Node.js to C](https://raw.org/software/programming/pipe-data-from-node-to-c/): Send numeric data from Node.js to C through a POSIX named pipe using explicit framing, robust parsing, and stream backpressure.
- [Write a PID File Safely in Bash](https://raw.org/software/programming/write-a-pid-file-in-bash/): Write and manage a PID file safely in Bash with $!, flock, atomic replacement, signal forwarding, cleanup, and systemd supervision.
- [Camera Access in JavaScript](https://raw.org/software/web-development/camera-access-in-javascript/): Access cameras from JavaScript with getUserMedia, switch devices, capture canvas photos, record video, handle permissions, and release media tracks.
- [Create KMZ Files with PHP](https://raw.org/software/web-development/create-kmz-files-with-php/): Create KMZ archives with PHP ZipArchive, including a generated doc.kml, bundled map icons, strict error handling, and portable paths.
- [Faster PHP behind FastCGI](https://raw.org/software/web-development/faster-php-behind-fastcgi/): Historical 2011 experiment using patched lighttpd, a PHP 5.3.6 fork, tmpfs, and X-Sendfile to reduce FastCGI response copying, with corrected code.
- [Build a Minimal GIF with PHP](https://raw.org/software/web-development/minimal-gif-with-php/): Build valid 35-byte and transparent 43-byte GIFs in PHP, understand every block, serve them safely, and implement a privacy-conscious tracking pixel.
- [Parse CSV with JavaScript](https://raw.org/software/web-development/parse-csv-with-javascript/): Parse CSV strings and browser files safely in JavaScript with multiline fields, escaped quotes, headers, type conversion, and error reporting.
- [Parse CSV with PHP](https://raw.org/software/web-development/parse-csv-with-php/): Parse multiline CSV strings and files safely in PHP 8 with fgetcsv(), RFC-compatible escaping, streaming, BOM handling, and row validation.
- [Board Cutting Optimizer](https://raw.org/tool/board-cutting-optimizer/): Free cutting list optimizer for boards, profiles, and pipe: finds the cheapest stock lengths to buy and shows the exact cutting plan, kerf included.
- [Caesar Cipher Encoder and Decoder](https://raw.org/tool/caesar-cipher/): Encode, decode, or crack Caesar cipher text with an interactive alphabet wheel, precise shift controls, and English frequency analysis.
- [Compare Two Lists Online - Find Differences](https://raw.org/tool/compare-two-lists/): Compare two lists online to find shared, unique, and combined items. Split, trim, deduplicate, sort, upload, and copy results instantly.
- [CSS Cubic Bézier Editor](https://raw.org/tool/css-cubic-bezier/): Design CSS cubic-bezier timing functions, compare live motion, use exact values and presets, then copy or save the result.
- [CYK Algorithm Visualizer](https://raw.org/tool/cyk-algorithm/): Visualize the CYK parsing algorithm step by step, validate CNF grammars, inspect chart cells, and test whether a context-free grammar accepts a word.
- [Online Graph Editor](https://raw.org/tool/graph-editor/): Draw graphs and automata in your browser, label them with LaTeX, then export them as TikZ code for your documents or as a standalone SVG file.
- [Monochrome Display Image Generator](https://raw.org/tool/lcd-image-generator/): Convert images into editable 1-bit pixel art and export byte arrays for Nokia PCD8544, SSD1306, SH1106, and other monochrome displays.
- [Linear Regression Calculator](https://raw.org/tool/linear-regression-calculator/): Fit paired data by closed-form linear regression with confidence and prediction bands, residuals, correlation, and slope inference.
- [Modular Inverse Calculator](https://raw.org/tool/modular-inverse-calculator/): Calculate modular multiplicative inverses exactly with BigInt and learn why the extended Euclidean algorithm finds the solution.
- [NE555 Astable Circuit Calculator](https://raw.org/tool/ne555-astable-circuit-calculator/): Calculate NE555 astable frequency and duty cycle, or find ranked E24 resistor and E12 capacitor values for a target oscillator design.
- [Number Series Solver for IQ Tests](https://raw.org/tool/number-sequence-solver/): Stuck on an IQ test number series? This free solver finds the pattern - arithmetic, geometric, Fibonacci, primes and more - and predicts what comes next.
- [Strong Password Generator](https://raw.org/tool/password-generator/): Generate or enter passwords locally and inspect their entropy, strength, search-space position, and estimated offline crack time.
- [Percentage Calculator](https://raw.org/tool/percentage-calculator/): Free Interactive Percentage Calculator for basic calculations and financial scenarios like inflation and stock price changes. Explanations with formulas are provided to improve intuition.
- [Quine-McCluskey Boolean Minimizer](https://raw.org/tool/quine-mccluskey-solver/): Minimize Boolean functions with Quine-McCluskey, Petrick's method, XOR/XNOR merging, and recursive XOR decomposition.
- [RREF Calculator with Steps](https://raw.org/tool/reduced-row-echelon-form-calculator/): Reduce matrices to RREF over real, rational, complex, or prime fields and inspect every Gauss-Jordan row operation step by step.
- [Regex Match Extractor](https://raw.org/tool/regex-match-extractor/): Parse raw text instantly with a live regex matcher, detailed groups, deduplication, and one-click copy for fast cleanup workflows.
- [Regex Simplifier](https://raw.org/tool/regex-simplifier/): Online regex simplifier and minimizer using Thompson, subset construction, and Hopcroft DFA minimization with multi-dialect output.
- [Rename FT232RL USB Device Online](https://raw.org/tool/rename-ft232rl-usb-device-online/): Rename an FT232RL USB adapter in the browser by safely rewriting its manufacturer, product, and serial descriptors with WebUSB.
- [Resistor Calculator](https://raw.org/tool/resistor-calculator/): Free resistor color code calculator: decode 4, 5, and 6-band resistor values instantly, or type a resistance and get the matching color bands.
- [Roman Numerals Converter](https://raw.org/tool/roman-numerals-converter/): Convert between Roman numerals and numbers, with the additive and subtractive notation rules explained alongside a symbol reference table.
- [Running Pace Calculator](https://raw.org/tool/running-pace/): Calculate running pace or finish time for 5K, 10K, half marathon, marathon, and custom distances in kilometers or miles.
- [SLA Uptime Calculator](https://raw.org/tool/sla-uptime-calculator/): Convert an SLA uptime percentage into daily, weekly, monthly, quarterly, and yearly downtime allowances.
- [Subresource Integrity (SRI) Hash Generator](https://raw.org/tool/sri-hash-generator/): Generate SHA-256, SHA-384, or SHA-512 SRI metadata from a URL, local file, or pasted content, entirely in your browser.
- [String Utility Toolkit](https://raw.org/tool/string-utility-toolkit/): Online string utility toolkit for Base64 and URL encode/decode, letter case conversion, deduplicating, trimming, and sorting lines.
- [Online IP Subnet Calculator](https://raw.org/tool/subnet-calculator/): Calculate IPv4 CIDR networks, subnet masks, wildcard masks, host ranges, subnet splits, and supernets from multiple input formats.
- [Sudoku Solver Online](https://raw.org/tool/sudoku-solver/): Solve any 9x9 Sudoku online, reveal one cell as a hint, and detect conflicting clues with a fast browser-based solver.
- [SVG Path Visualizer and Editor](https://raw.org/tool/svg-path-visualizer/): Visualize SVG path commands, drag endpoints and control handles, insert points without reshaping curves, and export the edited path.
- [Triangle Calculator](https://raw.org/tool/triangle-calculator/): Interactive triangle calculator with constraints, derivations, right-triangle theorems, and clickable incircle/circumcircle controls.
- [Unit Converter](https://raw.org/tool/unit-converter/): Type a query like "5 km to miles" or "98.6f to c" and get an exact, graph-routed conversion powered by Fraction.js.
- [Voltage Divider Calculator](https://raw.org/tool/voltage-divider-calculator/): Design loaded voltage dividers with IEC resistor values, tolerance limits, power loss, current draw, output impedance, and ranked component pairs.
- [Wire Size Calculator: AWG, mm2 and Ampacity](https://raw.org/tool/wire-size-calculator/): Convert AWG, mm2, in2, CMIL, and kcmil; estimate wire diameter, copper resistance, current, and the solid-copper skin-depth frequency.