Second Drafts

Self-Fibonacci Numbers

number theory

research

open

fibonacci

exploration

Here’s a seemingly simple question that lacks a clean solution:

Architects and Gardeners

philosophy

teaching

“I think there are two types of writers, the architects and the gardeners. The architects plan everything ahead of time, like an architect building a house. They know how…

Learning is Remembering

philosophy

teaching

buddhism

mindfulness

greeks

In Greek philosophy there is a theory of “anamnesis,” mostly due to Plato and Socrates, which roughly means “learning is remembering,” that wisdom is already inside you and…

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…

Sperner’s Lemma - Geometric Proof

triangles

coloring

questions

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…

Sperner’s Lemma - Combinatorial Proof

combinatorics

triangles

coloring

visualization

interactive

questions

This picture is a combinatorial proof of Sperner’s Lemma.

Sperner’s Lemma - Statement

combinatorics

triangles

coloring

questions

visualization

interactive

Monsky’s Theorem

combinatorics

triangles

questions

I discovered this theorem on this really cool blog, Math Mondays

Non-Profits

My apartment complex in DC is having some landlord issues. Our landlord is a shady, dishonest guy whose main skill is not getting sued. He will do the absolute least he can…

Random points in a triangle

randomness

triangles

barycentric coordinates

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…

Hopkins is a joke

It’s a crisp sunny day in the middle of way. We are deep into the final exam season. Everyone is stressed, sleep-deprived, over-caffeinated, over-worked. We have an exam for…

Barycentric Coordinates

affine geometry

triangles

interactive

visualization

Barycentric coordinates are a coordinate system for describing points inside a triangle.

Begin Again

I opened this page with a clear idea of what I wanted to write. I’ve now spent the last half hour updating quarto, setting up a new git repository, fixing a git merge issue…