Geometric Definition of e

The idea comes from a video by Mathologer. Simon sketches a geometric definition of the Euler’s number (e) using integrals. He messed up a little with the integral notation, but corrected it later (after we stopped filming). Please see the photos below:

Advertisements

The irrationality of Pi and e

Simon has been watching a lot of Mathologer’s videos lately, mainly about Euler’s Number (e) and Pi. He is fascinated by the proofs Mathologer presented of why each number is irrational. “Mom, the proof that e is irrational actually doesn’t require any Calculus and the proof that Pi is irrational does! While you would expect it to be the other way around, right? Because e is about Calculus!”

Here are some of Simon’s notes, inspired by Mathologer. Some facts about e:

Notes about the proof that Pi is irrational:

Notes about the proof that e is irrational:

Simon watching the Mathologer channel: