math.HO — History and Overview

$10/24/26$: Factoring a Pythagorean Date

Contributed by Scott Kominers

Written numerically, the date October 24, 2026 corresponds to a Pythagorean triple---the last one of the twenty-first century! The associated $10$--$24$--$26$ right triangle has area twice its perimeter; a classical factorization shows that exactly three integer-sided right triangles have this property and, more generally, counts those with any prescribed integer inradius. We also observe that $60$ is the smallest perimeter shared by two noncongruent integer-sided right triangles, one of which is the $10$--$24$--$26$ triangle.