Associahedra: The Shapes of Multiplication | Infinite Series

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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    • The Multiplication Multiverse | Infin...  

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The Multiplication Multiverse | Infinite Series
   • The Multiplication Multiverse | Infin...  

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-...

http://www.claymath.org/library/acade...

https://arxiv.org/pdf/math/0212126.pdf

More on multiplying non-numbers:
http://www.math3ma.com/mathema/2017/1...

An introduction to operads:
http://www.math3ma.com/mathema/2017/1...

http://www.math3ma.com/mathema/2017/1...

Some applications in math and physics:
https://arxiv.org/abs/1202.3245

http://citeseerx.ist.psu.edu/viewdoc/...

http://bookstore.ams.org/conm-227

http://www.springer.com/us/book/97808...

Richard Stanley’s book on the Catalan Numbers:
https://www.amazon.com/Catalan-Number...


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)

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And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!