Pi Beyond Circles

Pi is irrational — its digits never terminate and never repeat. It is also transcendental, which means no equation with whole-number coefficients can have pi as a solution. Lindemann proved this in 1882, finally settling the ancient puzzle of "squaring the circle."

But pi refuses to stay inside circles. It turns up in Heisenberg's uncertainty principle, in Coulomb's law, and in every wave equation for sound, light, or water. It even powers Fourier analysis, the math behind MP3 compression and Wi-Fi.