Who cares about topology? (Inscribed rectangle problem)
An unsolved conjecture, the inscribed square problem, and a clever topological solution to a weaker version of the question, the inscribed rectangle problem ...
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I've got several fun things for you this video. An unsolved problem, a very elegant solution to a weaker version of the problem, and a little bit about what topology is, and why people care. But before we jump into it, it's worth saying a few words on why I'm excited to share the solution. When I was a kid since I loved math and sought out various mathy things, I would occasionally find myself in some talk or a seminar where people wanted to get the youth excited about things that mathematicians care about. A very common go-to topic to excite our imaginations was "topology". We might be shown something like a Mobius strip, maybe building it out of construction paper by twisting a rectangle and gluing its ends. "Look!", we'd be told as we were asked t...
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I've got several fun things for you this video. An unsolved problem, a very elegant solution to a weaker version of the problem, and a little bit about what topology is, and why people care. But before we jump into it, it's worth saying a few words on why I'm excited to share the solution. When I was a kid since I loved math and sought out various mathy things, I would occasionally find myself in some talk or a seminar where people wanted to get the youth excited about things that mathematicians care about. A very common go-to topic to excite our imaginations was "topology". We might be shown something like a Mobius strip, maybe building it out of construction paper by twisting a rectangle and gluing its ends. "Look!", we'd be told as we were asked t...
