# Blog

## Schröder’s Equation

Introduction You probably know that, for natural number exponents anyways, exponentiation can be treated as repeated multiplication. $\displaystyle b^n:=\underbrace{bb\cdots b}_n$ More formally, we define exponentiation recursively by $b^0:=1$ and $b^{n+1}:=bb^n$ for $n\in\mathbb{N}$. You probably also know, however, that exponentiation isn’t solely defined for natural number exponents. Raising a number to the…

## Gauss and the Regular Heptadecagon

How many regular polygons are constructible? In other words, how many regular polygons can be drawn in a finite number of steps using just a compass and an unmarked straightedge? Since the time of Euclid, geometers knew how to construct the equilateral triangle, the square, and the regular pentagon. Construction of an equilateral triangle inscribed…

## Introduction

Welcome to the Aleph One Plex. I make math explainers here when I have the time (which, admittedly, I don’t have a lot of). As of writing this, I am an undergraduate student at UCLA studying pure math, and I might post videos on YouTube once I get myself familiar with Manim.