Interactive tools

An interactive 1+1-dimensional Minkowski spacetime diagram: construct events, inertial worldlines, light rays, lines of simultaneity, observers, and constant-interval hyperbolae, and view them at once in two independently Lorentz-boostable reference frames — with relativistic Doppler colour shifts, energy / momentum / proper-time readouts, and a mode to “experience” a worldline's subjective time (co-moving frame plus a live backward-light-cone view). Includes worked scenes (twin paradox, pole and barn, light clock) and JSON import/export.

Enter a top row — the primes, prime gaps, a single spike, or various random models — and watch the triangular array of successive absolute differences build up, with parity or magnitude colouring, a live check of Gilbreath's conjecture on the left diagonal, and a zoomed-out canvas view for large arrays. A companion to the paper on Gilbreath's conjecture by Zachary Chase, Zach Hunter and Terence Tao.

A Scratch demo that solves a randomly chosen linear equation in one unknown using two operations.

A more developed Scratch version with 12 levels, emphasizing challenging, entertaining problems over routine drill.

A Scratch variant whose nth level is generated by playing n moves in reverse.

A Scratch solver for Lewis Carroll's syllogism puzzles.

An interactive textbook for first-order logic, written in JavaScript, HTML, and CSS. Source at github.com/teorth/QED.

Vector addition and subtraction, scalar multiplication, an elementary row operation (v − c·w), and the dot product.

Row-reduce a 4×5 augmented matrix by applying elementary row operations one step at a time, with an undo history and a running log.

Arithmetic on two matrices up to 5×5 — sums, products, powers, transpose, trace, determinant, and inverse.

Visualize how a 2×2 matrix transforms the plane — draw in the domain and watch the image appear in the range.

Explore the eigenlines and eigenvalues of a 2×2 matrix; drag a vector, or drag the columns of the matrix directly.

Orthogonalise a set of vectors step by step — subtract projections and normalise, with a live inner-product table.

An Argand-plane sandbox — drag a complex number and watch its Cartesian and polar forms, with buttons for basic operations.

Draw a curve in the domain and see its image under w = f(z) for a range of elementary functions.

Draw points, circles, and lines and watch a Möbius map w = (az+b)/(cz+d) send them to circles and lines.

Drag z and watch the several branches of the roots and the logarithm move — and swap across the branch cut.

See conformality: an analytic map acts locally like multiplication by f′(z), preserving angles.

Draw a contour and watch the running value of ∫ f(z) dz trace out as a vector sum.

Pick a center and see the Taylor and Laurent expansions of 1/((z−1)(z−2)) and their regions of convergence.

Draw different paths between two points; their antiderivative images all end at the same place.

Draw a contour around editable poles; the integral converges to 2πi times the enclosed residues.

Draw a contour and count how many times its image winds around 0 — the enclosed zeros minus poles.

The Perron-tree construction of a small-area set that still contains a unit segment in every direction — vary the iterations and overlap.

The infinite quadrant of the plane mapped conformally onto a bounded triangle, with infinity stretched onto the hypotenuse — draw curves in either region.

Interactive honeycombs (with Allen Knutson) modelling Littlewood–Richardson coefficients and Horn's problem — click hexagons to mutate, with the dual hive shown alongside.

Solve the exponent relations in named estimates — Hölder, Sobolev, Young, fractional integration, Strichartz, restriction/extension, interpolation, and scaling — with rational or symbolic inputs.

A multiple-choice quiz applet, later superseded by a wiki.