## Topical Seminar for Undergraduate Mathematicians

•  Matthew Hedden, MSU
•  Threading Fáry and Milnor with Buffon's Needle
•  11/04/2016
•  4:10 PM - 5:00 PM
•  C304 Wells Hall

There is a fundamental invariant of a curve in Euclidean 3-space called the total curvature which, roughly speaking, measures how 'twisted' the curve is. A beautiful result of Fáry and Milnor from the early 1950's relates this to a branch of mathematics called knot theory, and shows that if the curvature of a curve is small enough, then the curve is actually 'unknotted'; that is, it can be untied without cutting it. Their proofs were rather technical, and in this talk I'll relate their problem to an experimental method for computing the value of pi known as the Buffon Needle Problem. Using this interpretation I will give an elegant and self-contained proof of their result, due to Ari Turner. The talk should be accessible to anyone who has taken multivariable calculus.

## Contact

Department of Mathematics
Michigan State University