How long does the wheel of Theodorus go on?

Answer 1

The wheel continues on forever, it never ends.

This in Algebra, is called a fractal: a pattern that endlessly repeats.

[BTW: Every fractal has an equation to find that certain pattern to the Nth time]

Answer 2

The wheel of Theodorus can go on indefinitely, as it is a geometric construction that creates a series of right triangles with decreasing side lengths. Each new triangle is created by adding a hypotenuse to the previous right triangle. The pattern continues, generating a sequence of triangles without an end point.