Spiral of Theodorus

The root of the screw or spiral Theodorus is a spiral, which is generated by right-angled triangles with sides 1, and.

Thus, the first triangle has sides of length 1, and. On the hypotenuse of this triangle is a right triangle with sides 1, and so establishes the contiguous other sides will form a spiral.

In contrast to the Archimedean or logarithmic spiral, the root worm consists of straight line segments. So it is not differentiable, but can be sure exactly through the countably many vertices describe.

1958 proved Erich Teuffel that no two of the hypotenuse will cover, no matter how far you draw the spiral. With growing number of turns the screw root asymptotically approaches an Archimedean spiral.