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REV: Another Harmony of the Sphere
Posted:
Sep 6, 1992 6:33 PM
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Max, Nelson, Another harmony of the spheres, Nature 355 (9 January 1992)
115-116. Stewart, Ian, Mathematical recreations: The kissing number,
Scientiflc American (February 1992) 112-115.
In 1990, Wu-Yi Hsiang (University of California-Berkeley) announced a
proof that face centered cubic packing is the densest packing of spheres
in three dimensions, thereby settling a claim of Kepler's. Or is it
settled? Hsiang's original announcement was rejected by the Bulletin of
the AMS because the details of the proof had not yet been written down.
Hsiang's argument depends on the classification and analysis of a large
number of configurations, many of which he described originally only in
qualitative terms. Now there is a draft of all the details. But will
anyone "have the patience to repeat Hsiang's year-long verification that
all possibilities are covered?" Hsiang's cases are not easily amenable to
verification by computer, despite the fact that he used "only high-school
algebra, vector identities, a little calculus and a lot of spherical
geometry and spherical trigonometry," plus his TI-35+ calculator.
Finally, Hsiang has recently announced that he has solved the 'kissing"
problem in four dimensions, determining that the greatest number of
spheres that can surround and touch another is 24.
This review was reprinted with permission from Mathematics Magazine,
April 1992 issue.
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