Mathematics

Maths recap 1: Group Theory, Combinatorics and Graham's Number

This week, I finally learned (roughly) what Lie Groups are (pronounced ‘LEE’). Imagine an n-sided polygon sitting on a flat surface. Rotate it $\frac{2\pi}{n}$ degrees. The polygon looks exactly the same. If you include the reflective symmetries, you create what’s known as a Dihedral group, written $D_{n}.$ Now consider the symmetries of a circle. We can rotate any $\theta \in [0,2\pi)$ and we still get an identical image. This makes the group an infinite group.

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5 Minutes
Mar 27, 2025
302 Words

Group Theory on 2x2s

Introduction

We define the group, $G,$ to be the set of all possible move sequences. This group is non-abelian under addition.

Example elements of this group are:

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7.5 Minutes
Mar 17, 2025
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Welcome Post

Welcome!

First “official” page with this new structure - I’ll see how it goes. I’ll soon begin populating pages with all sorts of topics: poetry, science, art, maths - whatever I feel like! :)

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Mar 27, 2025
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