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Formula for e

Simon’s project in online at https://www.geogebra.org/classic/j29phpus
the second part of Simon’s project: https://www.geogebra.org/classic/wym3kvxf

I’ve worked out a formula for e!


This came up when I was looking for an antiderivative, if n isn’t equal to 1:

if n is equal to 1, then it’s suddenly a natural log!

But I’ve realized that if I change it only a tiny bit, it becomes a really famous existing formula for e:

Still impressive that you have worked it out all on your own, Simon!

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Approximating pi and e with Randomness

This has been one of Simon’s most ambitious (successful) projects so far and a beautiful grand finale of 2019, also marking his channel reaching 1K subscribers. The project – approximating Euler’s number (e) in a very weird way – is based upon a Putnam exam puzzle that Simon managed to prove:

The main part of the project was inspired by 3Blue1Brown Grant Sanderson’s guest appearance on Numberphile called Darts in Higher Dimensions, showing how one’s probable score would end up being e to the power of pi/4. Simon automated the game and used the visualization to approximate e. Below is the main video Approximating pi and e with Randomness. You can run the project online at: https://editor.p5js.org/simontiger/present/fNl0aoDtW

Code: https://editor.p5js.org/simontiger/sketches/fNl0aoDtW

The history and the math behind the project:

Simon’s proof od the math behind the project:

Simon has visualized this problem and proof at: https://editor.p5js.org/simontiger/present/2uMPZ8THW

Code: https://editor.p5js.org/simontiger/sketches/2uMPZ8THW

Geometry Joys, Milestones, Murderous Maths, Notes on everyday life, Simon teaching, Simon's sketch book

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:

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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: