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.

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:

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! :)

To be explained

To be explained

Breakdown