Packing spheres around a sphere.Mathematicians have long known that it's possible to pack at most 12 identical spheres around and touching a 13th. In 1943, Hungarian mathematician L. Fejes Toth conjectured that the optimal arrangement of the surrounding spheres is a highly symmetric pattern based on the 12-faced geometric shape known as a dodecahedron dodecahedron: see polyhedron. . Sean T McLaughlin of the University of Michigan (body, education) University of Michigan - A large cosmopolitan university in the Midwest USA. Over 50000 students are enrolled at the University of Michigan's three campuses. The students come from 50 states and over 100 foreign countries. in Ann Arbor Ann Arbor, city (1990 pop. 109,592), seat of Washtenaw co., S Mich., on the Huron River; inc. 1851. It is a research and educational center, with a large number of government and industrial research and development firms, many in high-technology fields such as recently proved this conjecture CONJECTURE. Conjectures are ideas or notions founded on probabilities without any demonstration of their truth. Mascardus has defined conjecture: "rationable vestigium latentis veritatis, unde nascitur opinio sapientis;" or a slight degree of credence arising from evidence too weak or too and described his approach at last month's Joint Mathematics Meetings in Washington, D.C. Like an earlier proof of Kepler's sphere-packing conjecture by Michigan mathematician Thomas C. Hales (SN: 8/15/98, p. 103), McLaughlin's effort required extensive computer calculations involving more than 2,000 possible types of arrangements. |
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