Pythagorean Spiral

Pythagorean spiral

Start with a right-angled triangle with two equal sides (the one in orange).

Make another right-angled triangle, by adding a side of length 1 to the hypotenuse.

Repeat the process and you get this

Now the arms of the spiral overlap but if you keep going you get this

Each “lap” of the original spiral is called a winding and the gap between the windings finally reaches π

This is the mathematical theory. Essentially, the step length you add on each time goes into the distance between the spiral arms 3.142 times. An incredible result.