Abstract:

Because Pi Day fell on the Friday before break, many of you

may have missed out on the festivities. We’ll develop a bit of

integral geometry (a.k.a. geometric probability) that lets us compute

Pi by a random process – the Buffon Needle Problem – as well as the

lengths of curves in the plane and the sphere, eventually leading to

the now-classic theorem of Fenchel-Fary-Milnor about the total

curvature of space curves.