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
In 1872, Weierstrass presented a function that’s continuous everywhere but differentiable nowhere. It shattered the assumption that smooth curves are normal. Here’s the full construction, the proof, the historical shock, and why the Baire category theorem shows most continuous functions behave this way.
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.