The Square Root of 2 is Irrational

A visual approach

Fig. 0: We can construct √2 with compass and straight-edge, Euclid-style

Imagine a rectangle with aspect ratio of √2. Dissect it into a grid of tiny squares: u squares long by v squares wide (Figure 1).

Fig. 1: A rectangle with aspect ratio √2, divided into numerous itty bitty squares.