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 the complete solution with mathematical proof, drawing from David Morin’s work. The calculus is surprisingly deep and the geometry is beautiful.
Mathematics
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 construction, explain why it was so revolutionary, and show why mathematical intuition about ‘smooth’ curves can be completely wrong.
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 the rationals, filling in all the gaps. I walk through the construction step by step, making this foundational concept accessible.
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, examples, and practical applications. If you’re studying real analysis or probability theory, you’ll use these results constantly.