Archimedes Circle-Triangle
1. Consider a circle of radius r.
2. Divided into N kind-of-triangles. You can choose N. (A kind-of triangle is a triangular shape bounded by two radii of the circle and a circular segment).
3. Unroll the circle (red slide)
4. Incline the triangles. If we pretend that the circular arcs are segments, we obtain a "large" green triangle. The larger is N, the closer is the shape we obtained to an "honest" right triangle.
What are the lengths of the legs of the right triangle (In the limit, when N goes to infinity)