Matpic
mathematics, in pictures
The spine

Fields

Eleven areas of mathematics, each with its own way of arguing. An essay belongs to exactly one of them and to any number of themes.
The Pythagorean theorem by dissection. Two squares of the same size. Each holds four copies of one right triangle. The space left over is a single tilted square on the left and two upright squares on the right.

Geometry

Shapes, and the arguments that can be made by rearranging them.

39 essays A circle unrolled into a sine wave. On the left a radius turns through an angle; on the right the height of its tip is plotted against the angle, tracing a sine curve.

Analysis

Limits, curves, and what happens when the going does not stop.

39 essays A linear map redrawing the plane. The integer grid before and after a linear transformation; the shaded unit square becomes a parallelogram whose area is the determinant.

Algebra

Structure — what stays true when the numbers change.

39 essays Königsberg as a graph. The four landmasses as circles and the seven bridges as edges; every circle has an odd number of edges.

Discrete

Counting, graphs, and things that come in whole pieces.

39 essays A Möbius band. A strip joined end to end after a half twist, so it has one side and one edge.

Topology

What survives bending, and what does not.

39 essays A Galton board after 600 balls. 600 balls fall through 12 rows of pegs, each bouncing left or right at random, and pile up in a bell-shaped heap.

Probability

Randomness with a shape.

39 essays The sieve of Eratosthenes below 100. A grid of the whole numbers with the composites struck out by the prime that removes them.

Number

The whole numbers, and how much structure they turn out to have.

39 essays the logistic map at 3.2, iterated from 0.2. A map drawn as a curve with the diagonal across it, and the staircase that iterating it produces.

Dynamics

One rule, applied over and over, and what the sequence does in the end.

39 essays (p ∨ q) ∧ ¬r, drawn on the cube of 8 assignments. The assignments as corners of a cube, joined when they differ in one variable, with the satisfying corners filled.

Logic

What can be said in a system, what follows from it, and what it cannot settle about itself.

39 essays Two points, and everything one round of compass and straightedge adds. Two starting points with the line and circles they permit, and the four points where those objects cross.

Computation

A fixed set of operations, and the exact question of what it can and cannot build.

39 essays A majority cycle over 3 candidates, and how often 3 voters produce one. The majority tournament as a directed polygon with each arc's margin, beside one cell for every profile of the stated size, filled where no Condorcet winner exists.

Applied

A rule for choosing, stated exactly, and what it forces on whoever adopts it.

39 essays

A field says what an essay is about. Themes say what it rhymes with, ladders say how deep it goes, and the concept index says which essays name the same objects.