Set a beetle or a turtle on its back and it will right itself.

Remarkably, so will the Gömböc — a mathematical shape that can’t be knocked down. Set it down in any position and it will always “get to its feet”:

Each term in the Fibonacci sequence is derived by adding the two preceding terms:

0, 1, 1, 2, 3, 5, 8, 13, 21 …

Remarkably, you can use successive terms to convert miles to kilometers:

8 miles ≈ 13 kilometers
13 miles ≈ 21 kilometers

This works because the two units stand in the golden ratio (to within 0.5 percent).

(3 + 4)³ = 343

9 + 10 + 11 + 12 = 13 + 14 + 15

A “multi-magic” square: Each row and column sums to 260; square each term and they sum to 11,180.

“Numero deus impare gaudet [the god delights in odd numbers].” — Virgil

“Why is it that we entertain the belief that for every purpose odd numbers are the most effectual?” — Pliny

“This is the third time; I hope good luck lies in odd numbers. … They say there is divinity in odd numbers, either in nativity, chance, or death.” — Shakespeare, The Merry Wives of Windsor

Before his students arrived for a graduate course in logic, Raymond Smullyan wrote on the blackboard:

PLEASE DO NOT ERASE — BECAUSE IF YOU DO, THOSE WHO COME LATER WON’T KNOW THAT THEY SHOULDN’T ERASE.