High Quality Content by WIKIPEDIA articles! In geometry, the spiral of Theodorus (also called square root spiral, Einstein spiral or Pythagorean spiral) is a spiral composed of contiguous right triangles. It was first constructed by Theodorus of Cyrene. The spiral is started with an isosceles right triangle, with each leg having a unit length of 1. Another right triangle is formed, with one leg being the hypotenuse of the prior triangle and the other with length of 1. The process then repeats. Although all of Theodorus' work has been lost, Plato put Theodorus into his dialogue Theaetetus, which tells the reader of his achievements. It is assumed that Theodorus had proved that all of the square roots of non-square integers from 3 to 17 are irrational by means of the Spiral of Theodorus. Plato quoted Theaetetus speaking to Socrates: It was about the nature of roots. Theodorus was describing them to us and showing that the third root and the fifth root, represented by the sides of squares, had no common measure. He took them up one by one until he reached the seventeenth, when he stopped.

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