Albion College

Mathematics and Computer Science

Mathematics and Computer Science

COLLOQUIUM

When Does Inversion Preserve Convexity?

David E. Blair

Professor Emeritus

Department of Mathematics

Michigan State University

Professor Emeritus

Department of Mathematics

Michigan State University

Given a smooth closed convex curve in the plane, what is the setof points in the plane as centers of inversion for which the image of thegiven curve will again be a convex curve? This question has an attractive answer. After reviewing the geometry of curve theory and of inversion theory (reflection in circles), we will give a proof of the answer. If time permits, we will discuss the corresponding question for convex bodies in 3-space.