A three, four, five triangle is the simplest example of a right triangle with whole number side lengths.

The longer version

Square the three sides and the arithmetic lines up: nine plus sixteen equals twenty-five, so the longest side squared matches the sum of the others. Any multiple works just as well, since scaling every side by the same factor scales every square by its square. Six, eight, ten and five, twelve, thirteen belong to the same family.

Such whole number triples were practical tools long before they were textbook exercises: a loop of cord knotted at these intervals lays out a right angle on open ground, which is how builders checked corners. A formula generates them from any two whole numbers, so there is no end to the list.

Where this entry sits

This section collects odd corners of mathematics, from stubborn prime numbers to counting systems older than modern schools. Expect famous constants, probability puzzles, shapes that break everyday intuition, and numbers far too large to picture. The full list sits on the Numbers and Math page, where every entry is listed in order.