PBS Infinite Series | Associahedra: The Shapes of Multiplication | Infinite Series @pbsinfiniteseries | Uploaded 6 years ago | Updated 3 hours ago
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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
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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:
http://www.ams.org/samplings/feature-column/fcarc-associahedra
http://www.claymath.org/library/academy/LectureNotes05/Lodaypaper.pdf
arxiv.org/pdf/math/0212126.pdf
More on multiplying non-numbers:
http://www.math3ma.com/mathema/2017/11/24/multiplying-non-numbers
An introduction to operads:
http://www.math3ma.com/mathema/2017/10/23/what-is-an-operad-part-1
http://www.math3ma.com/mathema/2017/10/30/what-is-an-operad-part-2
Some applications in math and physics:
arxiv.org/abs/1202.3245
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.22.2871&rep=rep1&type=pdf
http://bookstore.ams.org/conm-227
http://www.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 (www.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!
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:
http://www.ams.org/samplings/feature-column/fcarc-associahedra
http://www.claymath.org/library/academy/LectureNotes05/Lodaypaper.pdf
arxiv.org/pdf/math/0212126.pdf
More on multiplying non-numbers:
http://www.math3ma.com/mathema/2017/11/24/multiplying-non-numbers
An introduction to operads:
http://www.math3ma.com/mathema/2017/10/23/what-is-an-operad-part-1
http://www.math3ma.com/mathema/2017/10/30/what-is-an-operad-part-2
Some applications in math and physics:
arxiv.org/abs/1202.3245
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.22.2871&rep=rep1&type=pdf
http://bookstore.ams.org/conm-227
http://www.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 (www.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!
