The proof is intuitively wrong, but I just can't figure out where. (Circumference = 2pi*r) 1. Consider a rod of length L = 2. Draw a semicircle around it, which has radius R=1 and arclength C= pi 2. Now draw two small semi circles, one going from the midpoint of the rod to the top and to the bottom. Each of these smaller circles has R=1/2 and C=pi/2, making the total length of the arcs = pi 3. Then a 4-partitioned rod with 4 arcs would each have R=1/4 and C=pi/4, with a total arclength of pi. 4. Repeat this process with a limit to infinity; so with infinitely many semicircles you can approximate the sum of the arclengths to be the actual length of the rod. This makes it seem pi (sum of infinite C) = 2 (original length of rod) !!!