Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi When you think about math, what do you think of? Numbers? Equations? Patterns maybe? How about… knots? As in, actual tangles and knots? Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode: How Big are All Infinities Combined? (Cantor’s Paradox) https://www.youtube.com/watch?v=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) https://www.youtube.com/watch?v=AxxnziuL408 How DNA Unties its Own Knots (video on topoisomerase with Mariel Vasquez) https://www.youtube.com/watch?v=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 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!