Who (else) cares about topology? Stolen necklaces and Borsuk-Ulam
The Borsuk-Ulam theorem from topology solving a counting puzzle. Truly unexpected, truly beautiful. Shirts/posters at DFTBA: http://3b1b.co/store The Great ...
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You know that feeling you get when two things that seem completely unrelated turn out to have a key connection. In math especially, there's a certain tingly sensation that I get whenever one of those connections starts to fall into place. That is what I have in store for you today. It takes a little time to set up, I have to introduce this fair division puzzle in discrete math, it's called the stolen necklace problem, and we also have to set up a certain topological fact about spheres that we'll use to solve it called the Borsuk-Ulam theorem. But trust me, seeing how these two seemingly disconnected pieces of math come together is well worth the setup. And more fun, I coordinated this video with Mathologer, who just put out a video solving a very similar fair divis...
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You know that feeling you get when two things that seem completely unrelated turn out to have a key connection. In math especially, there's a certain tingly sensation that I get whenever one of those connections starts to fall into place. That is what I have in store for you today. It takes a little time to set up, I have to introduce this fair division puzzle in discrete math, it's called the stolen necklace problem, and we also have to set up a certain topological fact about spheres that we'll use to solve it called the Borsuk-Ulam theorem. But trust me, seeing how these two seemingly disconnected pieces of math come together is well worth the setup. And more fun, I coordinated this video with Mathologer, who just put out a video solving a very similar fair divis...
