Maths

Posts on probability, geometry, combinatorics, and visualization

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With or Without Order
probability
puzzle
Here’s a question about basic probability theory that a student once asked me in class: When computing probabilities, does “choosing with order” vs “choosing without order”…
Nov 27, 2025

Self-Fibonacci Numbers
number theory
research
open
fibonacci
exploration
Here’s a seemingly simple question that lacks a clean solution:
Aug 11, 2025

Bayes Theorem
probability
visualization
Here’s a classic probability problem that illustrates this challenge. A standard mammogram test has, say, 80% sensitivity and 90% specificity. This means if you have breast…
Jun 2, 2025

Sperner’s Lemma - Geometric Proof
triangles
coloring
visualization
interactive
determinant
This is my new favorite proof of Sperner’s lemma. In the following app the vertices are slowly morphed to the “cardinal” R, G, B vertices with time while preserving the…
May 25, 2025

Sperner’s Lemma - Combinatorial Proof
combinatorics
triangles
coloring
visualization
interactive
This picture is a combinatorial proof of Sperner’s Lemma.
May 16, 2025

Sperner’s Lemma - Statement
combinatorics
triangles
coloring
visualization
interactive
 
May 14, 2025

Random points in a triangle
randomness
triangles
Randomness is a surprisingly hard thing to simulate. Any program, by definition, has a predictable output. The best you can hope for is to predictably generate points that lo…
May 12, 2025

Barycentric Coordinates
triangles
interactive
visualization
Barycentric coordinates are a coordinate system for describing points inside a triangle.
May 11, 2025
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