# Spiral of Pythagoras

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- A B Cron

In geometry, the spiral of Theodorus (also called

**square root spiral**, Einstein spiral or Pythagorean spiral)[1] is a spiral composed of contiguous right triangles. It was first constructed by Theodorus of Cyrene. Upon seeing this many student begin to understand square roots are not magic numbers created by math people to confuse the common person. Surds are another name for irrational roots. Up loaded 08/02/2015The special tool creates a triangle when clicked on the endpoints of a segment. I started with Segment AB.

**Construction**The spiral is started with an isosceles right triangle, with each leg having unit length. Another right triangle is formed, an automedian right triangle with one leg being the hypotenuse of the prior triangle (with length √2) and the other leg having length of 1; the length of the hypotenuse of this second triangle is √3. The process then repeats; the i th triangle in the sequence is a right triangle with side lengths √i and 1, and with hypotenuse √i + 1. For example, the 16th triangle has sides measuring 4 (=√16), 1 and hypotenuse of √17.