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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…


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.

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