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Mathematics Meetings Feature Proof of Dodecahedral Conjecture by Undergraduate Sean McLaughlin (Math Chat)

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Author:Frank Morgan, MAA Online
Description: The Dodecahedral Conjecture says a very symmetric conjectured arrangement, based on the regular 12-faced dodecahedron, it is the optimal arrangement locally to pack unit balls around one fixed ball. This conjecture has now been proved, by Hales's undergraduate student Sean McLaughlin. Also a solution to the challenge: Just last summer (see June 17 Math Chat) Thomas Hales of the University of Michigan proved that regular hexagons provide the least-perimeter (least-length) way to divide the plane into equal areas. What is the shortest network of curves you can find dividing the surface of the sphere into say four equal areas? five equal areas? other numbers of equal areas? For four equal areas, Joseph DeVincentis suggests a network based on the regular tetrahedron, with four congruent spherical triangles meeting in threes... New challenge: Was there any validity to the claim that the full moon of December 22, 1999 was the brightest that we shall see for millions of years?

Levels: High School (9-12), College
Languages: English
Resource Types: Problems/Puzzles, Articles
Math Topics: Higher-Dimensional Geometry, Elliptic & Spherical Geometry

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