The Spiral of Theodorus

Around 425 BC, the Greek mathematician Theodorus of Cyrene built an elegant spiral from right triangles, each with a short side of length 1. Each new triangle uses the previous hypotenuse as its base, so the hypotenuses come out to √2, √3, √4, √5, and onward.

The spiral turns abstract roots into measurable lengths you can draw on paper. Theodorus is credited with showing that the roots of the non-square numbers along it — √3, √5, √6, and up through √17 — are all irrational, extending the earlier discovery that √2 cannot be written as a fraction.