# Theodore's Spiral

See this video and Wikipedia. Extract from Wikipedia below.

In geometry, the spiral of Theodorus (also called the square root spiral, Pythagorean spiral, or Pythagoras's snail) is a spiral composed of right triangles, placed edge-to-edge. It was named after Theodorus of Cyrene.

### 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 the square root of 2) and the other leg having length of 1; the length of the hypotenuse of this second triangle is the square root of 3. The process then repeats; the $n\text{th}$ triangle in the sequence is a right triangle with the side lengths $\sqrt[2]{n}$ and $1$ , and with hypotenuse $n+1$ .For example, the 16th triangle has sides measuring $4=\sqrt[2]{16}$ , $1$ and hypotenuse of $\sqrt[2]{17}$ .

This spiral is autoscaled depending on the number of iterations so it will always fit in the drawing area

With the inputs below the drawing process can be influenced.