The Day Pi Escaped Geometry

I explore how pi (π) escaped geometry, as mathematicians moved from approximating circles with polygons to expressing it through infinite products and infinite series. The story begins with Archimedes, then follows François Viète and John Wallis before reaching a young Isaac Newton, who used the generalized binomial theorem to rewrite the circle and calculate its area in a completely new way. This documentary follows the history of pi, Newton’s early calculus, infinite series, and the shift from classical geometry to modern mathematical analysis. _______ Time stamps: 00:00 The Day Pi Escaped Geometry 01:04 Archimedes and the Polygon Method 01:56 How Polygons Dominated Pi for 2,000 Years 02:45 Viète’s Infinite Product and Nested Square Roots 03:38 The Wallis Product: Pi Enters Infinity 04:36 The Plague Sends Newton Home 06:15 Newton Turns the Circle into a Calculus Problem 07:28 Pascal’s Triangle and the Generalized Binomial Theorem 08:55 Newton Rewrites the Circle as an Infinite Series 10:39 Comparing Pi Methods: Archimedes, Viète, Wallis, and Newton 11:55 Beyond Pi: Infinite Series and Logarithms 12:33 From Pi to Calculus: Why Newton’s Method Still Matters Music: Epidemic Sound Public domain images: Wikimedia Commons Additional licensed images: Envato Elements Math Animations: I use Python Manim to create the math visualizations in this video If you enjoy story-driven documentaries about mathematical breakthroughs, scientific ideas, and the people behind them, consider subscribing for future episodes. And feel free to leave a comment if there’s another scientific breakthrough, idea, or genius you’d like me to explore.