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Illustration of the kissing number of a sphere
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Illustration of the "kissing number" of a sphere.

June 22, 2010
Illustration of the "kissing number" of a sphere. This kissing number is the number of equivalent spheres that can touch a given sphere without any intersections. Newton correctly believed that the kissing number in 3-dimensions was 12, but the first proofs were not produced until the 19th century. After packing 12 spheres around the central one (which can be done, for example, by arranging the spheres so that their points of tangency with the central sphere correspond to the vertices of an icosahedron), there is a significant amount of free space left (as pictured), although not enough to fit a 13th sphere. For more information, see the Kissing Number Web page.