The Discovery That Transformed Pi

Summary by Krater

This video explores historical methods for calculating pi, from ancient polygon bisection by Archimedes to Newton's discovery of the binomial theorem and calculus-based infinite series.

From the video

Answers: How did Isaac Newton and ancient mathematicians calculate pi?

• calculating pi with polygons
• Archimedes polygon method
• Binomial Theorem
• Pascal's triangle
• Newton's generalized binomial theorem
• calculus and infinite series for pi

What it concludes

• Ancient mathematicians calculated pi by bisecting polygons inscribed in and circumscribed around a circle, a method used for 2,000 years.
• Ludolph van Ceulen spent 25 years computing pi to 35 decimal places using a polygon with 2^62 sides.
• Isaac Newton broke the standard binomial theorem by applying it to negative and fractional exponents, creating infinite series.
• By integrating the area under a circle's curve using Newton's binomial expansion, pi can be computed to high precision with much fewer terms than polygon bisection.