Spiral of Theodorus

The spiral of Theodorus, also called the square root spiral, the Pythagorean spiral, or Pythagoras's snail, is a spiral built from right triangles placed edge to edge, named for the mathematician Theodorus of Cyrene. Construction begins with an isosceles right triangle with legs of length one and a hypotenuse of the square root of two; each further triangle uses the previous triangle's hypotenuse as one leg and adds another leg of length one, so that the nth triangle in the sequence has side lengths equal to the square root of n, one, and the square root of n plus one. Theodorus's own writings are lost, but Plato records his work in the dialogue Theaetetus, and Theodorus is thought to have used the spiral to show that the square roots of the integers from three to seventeen, apart from the perfect squares among them, are irrational. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/