Channel: PBS Infinite Series

Category: Education

Tags: infinite seriespbsconcatenationloopcontinuousassociativecatalan numbersinfinitymultiplicationhomotopyassociahedrapentagon

Description: Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: to.pbs.org/donateinfi What happens when you multiply shapes? This is part 2 of our episode on multiplying things that aren't numbers. You can check out part 1: The Multiplication Multiverse right here youtube.com/watch?v=H4I2C3Ts7_w Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com And discuss the episode further over on reddit at reddit.com/r/PBSInfiniteSeries Previous Episode The Multiplication Multiverse | Infinite Series youtube.com/watch?v=H4I2C3Ts7_w In our last episode, we talked about different properties of multiplication: associativity and commutativity are the most familiar, but they’re just two of many. We also saw it’s possible to multiply things that aren’t numbers, and in that case we may not have... associativity, for instance. But that’s not a bad thing. In fact, it’s a beautiful thing! References:: More on the associahedra: ams.org/samplings/feature-column/fcarc-associahedra claymath.org/library/academy/LectureNotes05/Lodaypaper.pdf arxiv.org/pdf/math/0212126.pdf More on multiplying non-numbers: math3ma.com/mathema/2017/11/24/multiplying-non-numbers An introduction to operads: math3ma.com/mathema/2017/10/23/what-is-an-operad-part-1 math3ma.com/mathema/2017/10/30/what-is-an-operad-part-2 Some applications in math and physics: arxiv.org/abs/1202.3245 citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.22.2871&rep=rep1&type=pdf bookstore.ams.org/conm-227 springer.com/us/book/9780817647346 Richard Stanley’s book on the Catalan Numbers: amazon.com/Catalan-Numbers-Richard-P-Stanley/dp/1107427746 Written and Hosted by Tai-Danae Bradley Produced by Rusty Ward Graphics by Ray Lux Assistant Editing and Sound Design by Meah Denee Barrington Made by Kornhaber Brown (kornhaberbrown.com) Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level! And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!