2018-03-29

[public] 42.6K views, 1.96K likes, 42.0 dislikes audio only

PBS Infinite Series

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When you think about math, what do you think of? Numbers? Equations? Patterns maybe? How about… knots? As in, actual tangles and knots?

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Previous Episode:

How Big are All Infinities Combined? (Cantor’s Paradox)

/youtube/video/TbeA1rhV0D0

There is a special kind of mathematical tangle called a rational tangle, first defined by mathematician John Conway around 1970 which relates to biology and the study of DNA.

Written and Hosted by Tai-Danae Bradley

Produced by Rusty Ward

Graphics by Ray Lux

Assistant Editing and Sound Design by Mike Petrow and Linda Huang

Made by Kornhaber Brown (www.kornhaberbrown.com)

Resources:

Modeling protein-DNA complexes with tangles by Isabel Darcy

(the tangle examples in today’s episode can be found here)

https://www.sciencedirect.com/science/article/pii/S0898122107005718

Understanding Rational Tangles (Recreational Guide)

https://www.mathteacherscircle.org/assets/session-materials/JTantonRationalTangles.pdf

The Knot Book by Colin Adams

https://www.amazon.com/Knot-Book-Colin-Adams/dp/0821836781

Knot Theory and Its Applications by Kunio Murasugi

https://www.amazon.com/Theory-Applications-Modern-Birkh%C3%A4user-Classics/dp/081764718X

On the Classification of Rational Tangles by Louis Kauffman and Sofia Lambropoulou

https://arxiv.org/pdf/math/0311499.pdf

DNA Topology by Andrew Bates and Anthony Maxwell

https://www.amazon.com/Topology-Oxford-Biosciences-Andrew-Bates/dp/0198506554

Proof of Conway’s Rational Tangle Theorem

http://homepages.math.uic.edu/~kauffman/RTang.pdf

The Shape of DNA (video with Mariel Vasquez)

/youtube/video/AxxnziuL408

How DNA Unties its Own Knots (video on topoisomerase with Mariel Vasquez)

/youtube/video/UkmQNbvlK8s

Knots and Quantum Theory by Edward Witten

https://www.ias.edu/ideas/2011/witten-knots-quantum-theory

Tangles, Physics, and Category Theory

http://math.ucr.edu/home/baez/tangles.html

My Favorite Theorem Podcast

https://kpknudson.com/my-favorite-theorem/

Topics in Knots and Algebra (Online Course at Bridgewater State University)

https://www.youtube.com/watch?v=fpoGoAscqX4&list=PLL0ATV5XYF8BfT8CmmzKnfTlf3V9hQgj9

Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.

Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!

And thanks to Mauricio Pacheco and Andrew Poelstra who is supporting us at the Lemma level!