The 2022-23 Serge Lang Undergraduate Lecture was given on Friday, November 18, 2022 from 4-5PM in room 390 Hearst Memorial Mining Building on the Berkeley campus. Our lecturer this year was Professor Jeffrey Lagarias, University of Michigan.
MUSA and the Department of Mathematics, University of California, Berkeley, present
The 2022-23 Serge Lang Undergraduate Lecture
Professor Jeffrey Lagarias
University of Michigan
Topic: Polyhedra and Shadows
Abstract: This talk presents some mathematics, some history and some art. For history and art it surveys the artist Albrecht D ̈urer’s interest in mathematics as an aid to art, including two books he wrote late in life. This includes work on perspective and shadows– his engraving ‘Melencolia I’ made in 1514 has a polyhedron casting a shadow. It then discusses two modern mathematical developments involving polyhedra and shadows. The first concerns ‘equiprojective polyhedra’, which are polyhedra whose shadows cast from parallel light rays are polygons having the same number of vertices, in (almost) every direction. The second considers Moser’s Shadow Problem, posed in 1966: How large can the number of vertices of a polyhedron P be (as a function of n) if it has the property that a shadow cast by a point source located anywhere outside the polyhedron (onto a screen behind it) is a polygon having at most n sides?