Mathematics Lessons

Calculus & Analysis

Arc Length & Solid of Revolution — Estimate arc length, surface area, and volume with numerical calculus.
Derivative & Tangent Explorer — Drag a point along any function curve and watch the tangent line and slope update live - the geometric heart of calculus.
Euler Method Visualizer — Solve first-order ODEs with Euler steps and compare against exact reference curves.
Fourier Series Builder — Build square, triangle, and sawtooth waves from harmonics. Explore partial sums, component sine waves, and Gibbs overshoot.
Laplace Transform Lab — Study forward and inverse Laplace transforms for common functions used in ODEs and systems.
Limit Explorer — Approach a limit from both sides and classify discontinuities
Numerical Integration Lab — Compare rectangle, trapezoid, and Simpson methods for approximating definite integrals.
Parametric Curves — Plot x(t), y(t) parametric curves with animated tracing and tangent vectors
Polar Curves — Plot r(θ) polar curves with sweep animation and area calculation
Riemann Sum Explorer — Approximate integrals with left, right, midpoint, and trapezoid sums.
Slope Field & ODE Solver — Visualize dy/dx = f(x,y) slope fields and click to add solution curves with RK4.
Taylor Series Explorer — Compare a function with its Taylor polynomial around a center point.

Linear Algebra & Geometry

2D Eigenvector Explorer — Visualize eigendirections and scaling under a 2x2 linear transform.
Bezier Curve Explorer — Drag control points to explore Bezier curves and the de Casteljau algorithm
Conic Parameters Explorer — Explore ellipse, parabola, and hyperbola from standard-form parameters and orientation.
Conic Sections Explorer — Classify and plot conics from general quadratic coefficients.
Least-Squares Geometry Explorer — Drag points, compare linear/quadratic fits, and inspect residual bars and SSE impact.
Matrix Transformation Visualiser — See how 2x2 matrices transform the plane - eigenvectors, determinant, and area scaling
PCA 2D/3D Visualizer — Project 2D data into principal-component space and inspect explained variance and scores.
Pyramid Geometry — Compute square-pyramid slant height, area, volume, and face angle from side and height.
Secrets of Circle & Pi — See why π emerges from circumference, area, collisions, probability, and infinite series through seven interactive experiments.
Vector Calculator — Compute dot product, cross product, and angle between 2D/3D vectors

Algebra & Precalculus

Function Composition Calculator — Step-by-step function composition calculator for f(g(x)) and g(f(x)) with custom functions, equations, domain warnings, and graphs.
Inverse Functions Explorer — See f(x) and f^-1(x) mirrored across y=x, and test when restriction is needed.
Logarithm Explorer — Explore y = log_b(x) with a live base slider and compare against ln(x) and log10(x).
Logical Contradiction Lab — Generate uniquely solvable truth-and-liar puzzles, eliminate possible worlds, and request hints that expose the actual deduction.
Piecewise Modeling Lab — Build a two-segment piecewise linear model and inspect continuity at the breakpoint.
Polynomial Division Trainer — Practice polynomial long division with explicit quotient, remainder, and step traces.
Quadratic Equation Solver — Find roots of ax² + bx + c = 0 with discriminant working and complex root support.
Radical Equations Checker — Solve sqrt(ax+b)=cx+d while filtering extraneous roots introduced by squaring.
Rational Functions Explorer — Explore zeros, poles, and asymptotes of a one-zero one-pole rational function.
Sine/Cosine Wave Explorer — Explore y = A*sin(Bx + C) + D with interactive sliders for amplitude, frequency, phase shift, and vertical shift.
Triangle Solver — Solve triangles from sides/angles using the law of sines and law of cosines, including SSA ambiguity.
Unit Circle Explorer — Explore sin, cos, and tan on the unit circle. Adjust the angle to see the right triangle, coordinates, and Pythagorean identity update live.

Number Theory & Arithmetic

Modular Arithmetic Clock — Compute congruences and explore modular tables with clock-style visualization.
Musical Math Lab — Explore the deep connections between number theory, geometry, and music with interactive synthesizers, Euclidean rhythms, and tuning systems.
Prime Sieve & Ulam Spiral — Animated Sieve of Eratosthenes and Ulam spiral visualisation of prime distribution

Discrete Math & Sequences

Golden Ratio & Fibonacci Spiral — Visualize Fibonacci growth, spiral construction, and convergence toward φ.
Lottery Math — Build any lottery from its parameters - pool size, picks, bonus ball - and see the expected value breakdown, return composition, and jackpot probability over time. The math is never on your side.
Markov Chain Stationary Explorer — Explore transition matrices, k-step state probabilities, and long-run stationary distributions.
Scale of the Universe Explorer — Zoom from subatomic to cosmic scales and compare sizes using powers of ten.
Sequence & Series Basics — Compare arithmetic and geometric sequences with nth-term and partial-sum outputs.
Series Convergence Explorer — Visualise partial sums S_N and convergence of infinite series — harmonic, Basel, factorial, geometric, telescoping and more.
Sigma Summation Tool — Evaluate finite sigma notation sums and inspect the partial-sum trajectory.

Other Tools

Break-Even Point Calculator — Compute unit and revenue break-even thresholds from fixed cost, unit price, and variable cost.
Complex Number Calculator — Visualise complex arithmetic on the Argand plane with polar and rectangular forms
Goalkeeper Reaction Window — Compare a shot's flight time with reaction delay and acceleration-based goalkeeper reach.
Hyperbolic Functions Explorer — Compare sinh, cosh, and tanh with circular trigonometric functions and their geometry.
Newton Method Visualizer — Iterate tangents to find roots and inspect convergence behavior.
Pendulum Phase Portrait — Explore the nonlinear pendulum with phase portraits, separatrices, and exact period calculation