The golden ratio in special relativity

In this note we show that Euclid's construction of the golden rectangle can be used to derive both the dilation of time intervals and the Lorentz contraction of lengths as predicted by Einstein's theory of special relativity. In this simple exercise, the Lorentz factor arises as a direct consequence of the Pythagorean theorem, while the golden ratio, ϕ=1+5/2, is found to govern the transition from Newton's physics to relativistic mechanics.