How Small Can a Needle's World Be?

Abstract: Imagine moving a unit-length needle through every possible direction in the plane. What is the smallest region of the plane in which this can be done? Intuitively, one might expect that a region of substantial area is necessary. The answer, however, is surprising! This seemingly paradoxical question, known as the Kakeya needle problem, leads to some remarkably deep mathematics that we shall discuss in this talk.

 

All are cordially invited to the seminar.