Maths

Posts on probability, geometry, combinatorics, and visualization

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With or Without Order

probability
puzzle

A student asked whether choosing with order or without order changes a probability. My first instinct was wrong.

Nov 27, 2025

Self-Fibonacci Numbers

number theory
research
open
fibonacci
exploration

For which n does n divide the nth Fibonacci number? A simple-sounding question with no clean answer.

Aug 11, 2025

Sperner’s Lemma - Geometric Proof

triangles
coloring
visualization
interactive
determinant

My new favorite proof of Sperner’s lemma: morph the vertices toward the cardinal colors and let the determinant do the work.

May 25, 2025

Sperner’s Lemma - Combinatorial Proof

combinatorics
triangles
coloring
visualization
interactive

The door-counting proof of Sperner’s lemma, as an interactive triangulation you can resize.

May 16, 2025

Sperner’s Lemma - Statement

combinatorics
triangles
coloring
visualization
interactive

What Sperner’s lemma says, with an interactive colored triangulation to play with.

May 14, 2025

Random points in a triangle

randomness
triangles

Randomness is hard to simulate. How to generate a uniformly random point inside a triangle, worked out so I could play with Sperner’s lemma.

May 12, 2025

Barycentric Coordinates

triangles
interactive
visualization

Every point in a triangle is a weighted average of its corners. An interactive look at what those weights mean.

May 11, 2025

Pythagoras using Hilbert 90

abstract algebra

Dummit and Foote classify Pythagorean triples using Hilbert’s Theorem 90, a surprisingly slick route to a classical fact.

Jun 8, 2024

Closed Convex Cones in LP

analysis
linear programming
convex analysis

A theorem I hit while formalizing linear programming in Lean, where the naive topological proof falls apart.

Jan 2, 2024

Combinatorial Nullstellensatz

combinatorics
problems
todo

A fun theorem I came across in a talk on tree colorings, and the polynomial trick behind it.

Nov 26, 2023

Logarithms and primes

todo
infinite series
number theory
riemann zeta

A NumberPhile video on the density of primes mod 4, and the passing remark in it that I found more interesting than the headline result.

Oct 26, 2023
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