Bray Proves Penrose Conjecture in General Relativity (Math Chat)
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|Frank Morgan, MAA Online|
|In 1979 R. Schoen and S.-T. Yau proved that the total mass of a universe must be positive. Last year  G. Huisken and T. Ilmanen proved that the total mass is at least as large as the largest constituent mass: M >_ m1. Finally this year  H. Bray of MIT proved that M >_ sqrt(m12 + m22 + ...). These results are forms of the so-called Penrose Conjecture... Challenge: Abel writes down two distinct positive integers from 1 to 4. Beta sees one of them at random and tries to guess whether it is the larger of the two. What are Beta's chances? (What if Abel can choose from more numbers?)|
|Levels:||High School (9-12), College|
|Math Topics:||Probability, Relativity/Gravitational Theory|
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