Once More, With Turning | Roots of Unity - Scientific American

The Gauss-Bonnet theorem is a mathematical favorite by Evelyn Lamb, Freelance math and science writer based in Salt Lake City, Utah. 

Flat pieces combine to make a sphere in Edmund Harriss's Curvahedra toy.
Photo: Edmund Harriss

On our latest episode of our podcast My Favorite Theorem, my cohost Kevin Knudson and I talked with University of Arkansas mathematician and artist Edmund Harriss. I was lucky enough to be in the studio with him because we were both part of the Illustrating Mathematics semester program at the Institute for Computational and Experimental Research in Mathematics (ICERM) last fall.

You can listen to the episode here or at kpknudson.com, where there is also a transcript.

Harriss chose to talk about the Gauss-Bonnet theorem, which relates the topology of a two-dimensional surface to its geometry. The total curvature of a surface—how much it bends and in what directions—is related to a few large-scale properties (topology): whether it is orientable and how many holes it has.

With this episode, the Gauss-Bonnet theorem makes its second appearance on My Favorite Theorem...

In each episode of the podcast, we invite our guest to pair their theorem with something. While donuts are a classic pairing for anything topology-related, Harris went a little more sophisticated with a pear-walnut salad. Get all the details on the episode, ideally while eating a fancy salad.

You can find Harriss on Twitter and his blog. With Alex Bellos, he has put together two mathematics-themed coloring books. Learn more about Curvahedra here.
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Additional resources  

2 Continues its Reign as the Smallest Known Prime Number by Evelyn Lamb, Freelance math and science writer based in Salt Lake City, Utah. 

Source: Scientific American