Author Archives: Aidan Byer

Introduction You probably know that, for natural number exponents anyways, exponentiation can be treated as repeated multiplication. More formally, we define exponentiation recursively by and for . You probably also know, however, that exponentiation isn’t solely defined for natural number exponents. Raising a number to the power of , for example, gives us its multiplicativeContinue reading “Schröder’s Equation [The Aleph One Plex]”

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 inscribedContinue reading “Gauss and the Regular Heptadecagon [The Aleph One Plex]”