Explore a groundbreaking visual proof of Ptolemy's theorem and inequality in this 33-minute video lecture. Delve into the historical significance of this 2000-year-old mathematical concept, starting with an introduction to basic geometry and its applications. Examine the intricacies of Ptolemy's inequality and uncover common misconceptions. Witness innovative animated proofs that bring the theorem to life. Gain insights into the Almagest, trigonometric identities, and cyclic quadrilaterals. Discover higher-dimensional versions of the theorem and explore related mathematical concepts. Conclude with a unique "Degenerate Easter Egg" and acknowledgments.