Fox-Rabbit Chase Problem [Solution & Math Proof]
Pursuit problems are some of the most elegant challenges in classical mechanics. Two objects moving, one chasing, the other evading. The math gets surprisingly deep. This problem comes from David…
Mathematics
Everywhere Continuous Non-differentiable Function
Weierstrass introduced a shocking idea in 1872. There exist functions that are continuous everywhere but differentiable nowhere. Not just at a few points. At no points whatsoever. This was a…
Dedekind’s Theory of Real Numbers
Most math students encounter real numbers without ever seeing how they're actually constructed. You use \( \pi \) and \( \sqrt{2} \) throughout calculus, but nobody explains what these objects…
Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem
The Gamma function is one of the most important special functions in mathematics. It extends the factorial to non-integer values. The Beta function is its close relative, and together they…