Clayton Shonkwiler: Geometry, Topology and Polymer Science

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Geometry and Topology Today is a "news show" on state-of-the-art mathematics research discussed for a general audience (including young people in high school). It is brought to you by Scott Baldridge and David Shea Vela-Vick in the mathematics department at Louisiana State University.
In this episode we meet Clayton Shonkwiler, a mathematician from Colorado State University, who talks to us about applications of geometry and topology to the study of random polygons and polymer science. The interview starts with a simple-sounding question "What percentage of triangles are acute?"
The problem presented in this video is related to his paper with Jason Cantarella and Tetsuo Deguchi, "Probability Theory of Random Polygons from the Quaternionic Viewpoint". The paper can be found at
arxiv.org/abs/1...
While the paper is not for a general audience (it's written for other mathematicians), high school students may still enjoy looking at it to see what advanced theorems and proofs look like.
More "Geometry & Topology Today" shows can be found at:
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[@IKnowTooTooBang]

Aren't there an uncountably infinite number of angle measures for acute and obtuse triangles?

[@scistate9297]

There certainly are - just as there are an uncountably infinite number of points on the round 2-sphere. The key idea is to understand why the two spaces are equivalent. This, in turn, allows one to answer questions about triangles in terms of properties of the 2-sphere.