Visual Math Lab

Interactive, browser-based visualizations of numerical methods.

Visual Math Lab

Math to tinker with, and sometimes just to look at.

This website started out as a repository for computational math apps but has since grown to contain many different methods and a few beautiful proofs. The best way to use this site is to try breaking something. Have fun exploring!

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Gallery

Cats on Ladders

Parametric Curves

Knock over a ladder with a cat on it, purely in the name of geometry.

Particle Filter Tracking

Track a moving object from noisy range-only readings using a particle filter.

Spirographs

Parametric Curves

Roll one circle around another and trace the curve a pen draws.

Distribution Relationships

Explore how the standard probability distributions turn into one another.

1D Recursive Filters

Smooth a noisy signal with a moving average, an exponential moving average and a Kalman filter.

Positive Predictive Value

If you test positive, what are the chances you have the condition?

L1 vs. L2 Regression

Compare least-squares and least-absolute-deviations regression on data with outliers.

Polynomial Fits

Fit polynomials of increasing degree to noisy data and watch them overfit.

Adaptive Integration

Computational Math

Refine a numerical integral only where the estimate is still inaccurate.

Adaptive Methods for ODEs

Computational Math

Solve an ODE with a step size that adapts to keep the error near a tolerance.

Butcher Tableau Explorer

Computational Math

See how a Butcher tableau determines a Runge-Kutta method’s stages and order.

Explicit Methods for ODEs

Computational Math

Compare Euler, midpoint and RK4 on the same initial value problem.

Implicit Methods for ODEs

Computational Math

Compare implicit and explicit ODE solvers on a stiff problem.

Numerical Integration

Computational Math

Compare Riemann sums, the trapezoid rule and Simpson’s rule.

Polynomial Interpolation

Computational Math

Parametric Curves

Compare piecewise linear and cubic spline interpolation through a set of points.

Bisection Method

Computational Math

Find a root by repeatedly halving an interval where the function changes sign.

Fixed Point Iteration

Computational Math

Solve x = g(x) by applying g over and over, and see when that converges.

Newton’s Method

Computational Math

Find a root by following tangent lines down to the x-axis.

Secant Method

Computational Math

Find a root like Newton’s method, but without the derivative.

Sperner’s Lemma - Geometric Proof

Prove Sperner’s Lemma by counting oriented triangles.

Sperner’s Lemma - Combinatorial Proof

Prove Sperner’s Lemma by walking through doors.

Sperner’s Lemma - Statement

Color the vertices of a triangulated triangle and test Sperner’s Lemma.

Barycentric Coordinates

Explore barycentric coordinates on a triangle, the setting for Sperner’s Lemma.

Browse by topic

Math Art
Spirographs, and a cat on a ladder.

Sperner’s Lemma
Colored triangles, and two proofs.

Probability
Bayes’ theorem, distributions and filters.

Root Finding
Solving \(f(x) = 0\).

Interpolation & Integration
Splines and numerical integrals.

Differential Equations
Explicit, implicit and adaptive ODE solvers.

Model Fitting
Robust regression and overfitting.