Exploring the Best Approximation of Euler's Number e

Explore a fascinating 20-minute mathematical investigation into Richard Sabey's remarkable approximation of Euler's number e, discovered in response to Eric Friedman's 2004 challenge to find optimal approximations of irrational numbers. Learn how Sabey achieved an approximation accurate to over 18 septillion digits using only the digits 1-9, and understand the mathematical techniques used to verify this accuracy without computing enormous numbers. Delve into key mathematical concepts including the limit definition of e, compound interest, and power series while following along with clear explanations of how to evaluate this groundbreaking pandigital approximation.