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dustingmixon.wordpress.com | ||
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gowers.wordpress.com
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| | | | | Although it was from only a couple of people, I had an enthusiastic response to a very tentative suggestion that it might be rewarding to see whether a polymath project could say anything useful about Frankl's union-closed conjecture. A potentially worrying aspect of the idea is that the problem is extremely elementary to state, does... | |
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polymathprojects.org
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| | | | | The Hadwiger-Nelson problem is that of determining the chromatic number of the plane ($latex \mathrm{CNP}$), defined as the minimum number of colours that can be assigned to the points of the plane so as to prevent any two points unit distance apart from being the same colour. It was first posed in 1950 and the... | |
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peterbloem.nl
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| | | | | [AI summary] The text provides an in-depth explanation of the Fundamental Theorem of Algebra, which states that every non-constant polynomial of degree $ n $ has exactly $ n $ roots in the complex number system, counting multiplicities. It walks through the proof by first establishing that every polynomial has at least one complex root (using the properties of continuous functions and the complex plane), then using polynomial division to factor the polynomial into linear factors, and finally addressing the nature of roots (real vs. complex) and their multiplicities. The text also touches on the conjugate root theorem, which explains why complex roots of polynomials with real coefficients come in conjugate pairs. | |
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blog.rongarret.info
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| | | A number of people have asked me to weigh in on this story in Quanta Magazine (based on this paper [ PDF version ] and also reported in t... | ||
