Verse

Futility Closet · Jul 29, 2026

This poem was composed by English mathematician George Biddell Airy, the seventh Astronomer Royal. It’s written from the point of view of the irregular polygon in the middle of the figure. If two congruent right triangles are affixed to the bottom edges of this polygon, the resulting shape has the outline of two adjoining squares of side lengths a and b, the sides of the right triangles. If the same two triangles are instead affixed above the polygon, as shown, the result is a (tilted) square whose side is the length of the triangles’ hypotenuse. This proves the Pythagorean…