Fox-Rabbit Chase Problem [Solution & Math Proof]
Pursuit problems are some of the most elegant challenges in classical mechanics. A fox chases a rabbit, both moving at constant speed. What path does the fox follow? I present…
Mathematics
Everywhere Continuous Non-differentiable Function
Weierstrass shocked the mathematical world in 1872 by constructing a function that's continuous everywhere but differentiable nowhere. Not at a few points. At no points whatsoever. I walk through the…
Dedekind’s Theory of Real Numbers
Most math students use real numbers without ever understanding how they're constructed. Dedekind solved this with his theory of cuts. He showed how to build the real numbers rigorously from…
Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem
The Dirichlet theorem connects the Gamma and Beta functions to evaluate complex multiple integrals. Liouville extended it further, making it even more powerful. I cover both theorems with complete proofs,…