Pythagorean Days

Originally published August 21, 2017

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.