Pythagoras's Theorem as a Repeating Pattern

Abstract

IT may not be generally known that the Theorem of Pythagoras, Euclid I. 47, is closely connected with the Theory of Repeating Patterns in space of two dimensions. The simplest proof by dissection of that Theorem establishes at once that any two squares placed in contact as in the accompanying diagrams (Fig. 1) constitute a figure such that a number of them can be assembled so as completely to fill flat space.