Gabriel’s Horn Paradox Infinite Surface Area vs. Finite Volume in Calculus
A rigorous calculus proof of Gabriel's Horn demonstrating how a geometric solid of revolution possesses finite volume but infinite surface…
Math Riddles
Rigorous arithmetic anomalies, algebraic puzzles, geometry enigmas, and combinatorics.
The St. Petersburg Paradox Infinite Expected Values and Bernoulli’s Expected Utility
A rigorous deconstruction of the St. Petersburg Paradox analyzing infinite mathematical expectation, logarithmic utility, and finite wealth truncation.
The Unexpected Hanging Paradox Gödelian Incompleteness and Retroactive Logic Traps
Dissecting the Unexpected Hanging Paradox through formal backward induction, self-referential epistemic logic, and Gödelian incompleteness.
The Birthday Paradox Combinatorial Probability, Hash Collisions, and Pigeonhole Logic
A formal mathematical proof of the Birthday Paradox exploring combinatorial probability, Taylor series approximations, and cryptographic hash collisions.