Lecture – Henry Segerman

Oklahoma State University
Tuesday, April 18 – 4:30 pm
Room; Physics 130
Title: 3D Shadows: Casting light on the fourth dimension
Abstract: Our brains have evolved in a three-dimensional environment, and so
we are very good at visualising two- and three-dimensional objects. But what
about four-dimensional objects? The best we can really do is to look at
three-dimensional “shadows”. Just as a shadow of a three-dimensional object
squishes it into the two-dimensional plane, we can squish a four-dimensional
shape into three-dimensional space, where we can then make a sculpture of
it. If the four-dimensional object isn’t too complicated and we choose a
good way to squish it, then we can get a very good sense of what it is like.
We will explore the sphere in four-dimensional space, the four-dimensional
polytopes (which are the four-dimensional versions of the three-dimensional
polyhedra), and various 3D printed sculptures, puzzles, and virtual reality
experiences that have come from thinking about these things. I talk about
these topics and much more in my new book, Visualizing Mathematics with 3D
Printing.Note that he will be giving another talk at Geometry/Topology seminar on
April 17 at 3:15pm. Moreover, his book will be available at Duke Gothic
bookstore during his visit to Duke.Please spread the word. For more info on PLUM, visit
https://services.math.duke.edu/~hahn/PLUM.html


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