Pythagorean Days

Those of you who have been obsessing about today’s solar eclipse may have missed another equally amazing event just last Tuesday: the date, 8/15/17, made a Pythagorean triple.

A Pythagorean triple is a group of three positive integers that satisfy the equation $a^2+b^2=c^2$. According to the Pythagorean Theorem, by satisfying that equation, $a$ and $b$ can the legs and $c$ can be the hypotenuse in a right triangle. Since $$8^2+15^2 = 64+225 = 289 = 17^2,$$ $(8,15,17)$ is a Pythagorean triple.

There are lots of Pythagorean triples, but unfortunately, Pythagorean Days are actually quite rare. There are a few upcoming ones, like 12/16/20 and 10/24/26, but those two are not as exciting since they’re multiples of earlier Pythagorean Days (namely 3/04/05 and 5/12/13). The only other day based on a primitive Pythagorean triple (not a multiple of an earlier one) is on July 24, 2025. And after that, there are no more this century, since the remaining Pythagorean triples, like $(20,21,29)$, don’t correspond to calendar dates.

So, set your calendars for 8 years from now. It will be a once-in-a-lifetime event that doesn’t burn your retinas.