Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here:
https://to.pbs.org/donateinfiWhat 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
https://www.youtube.com/watch?v=H4I2C3Ts7_wTweet at us! @pbsinfinite
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The Multiplication Multiverse | Infinite Series
https://www.youtube.com/watch?v=H4I2C3Ts7_wIn 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 https://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-1http://www.math3ma.com/mathema/2017/10/30/what-is-an-operad-part-2 Some applications in math and physics:
https://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:
https://www.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!
About the Site 🌐
This site provides links to random videos hosted at YouTube, with the emphasis on random. 🎥
Origins of the Idea 🌱
The original idea for this site stemmed from the need to benchmark the popularity of a video against the general population of YouTube videos. 🧠
Challenges Faced 🤔
Obtaining a large sample of videos was crucial for accurate ranking, but YouTube lacks a direct method to gather random video IDs.
Even searching for random strings on YouTube doesn't yield truly random results, complicating the process further. 🔍
Creating Truly Random Links 🛠️
The YouTube API offers additional functions enabling the discovery of more random videos. Through inventive techniques and a touch of space-time manipulation, we've achieved a process yielding nearly 100% random links to YouTube videos.
About YouTube 📺
YouTube, an American video-sharing website based in San Bruno, California, offers a diverse range of user-generated and corporate media content. 🌟
Content and Users 🎵
Users can upload, view, rate, share, and comment on videos, with content spanning video clips, music videos, live streams, and more.
While most content is uploaded by individuals, media corporations like CBS and the BBC also contribute. Unregistered users can watch videos, while registered users enjoy additional privileges such as uploading unlimited videos and adding comments.
Monetization and Impact 🤑
YouTube and creators earn revenue through Google AdSense, with most videos free to view. Premium channels and subscription services like YouTube Music and YouTube Premium offer ad-free streaming.
As of February 2017, over 400 hours of content were uploaded to YouTube every minute, with the site ranking as the second-most popular globally. By May 2019, this figure exceeded 500 hours per minute. 📈
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