Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, the kissing number is the maximum number of spheres of radius 1 that can simultaneously touch the unit sphere in n-dimensional Euclidean space. The kissing number problem seeks the kissing number as a function of n.In three dimensions the kissing number is 12, but the correct value was much more difficult to establish than in dimensions one and two. It is easy to arrange 12 spheres so that each touches a central sphere, but there is a lot of space left over, and it is not obvious that there is no way to pack in a 13th sphere. (In fact, there is so much extra space that any two of the 12 outer spheres can exchange places through a continuous movement without any of the outer spheres losing contact with the center one.) This was the subject of a famous disagreement between mathematicians Isaac Newton and David Gregory.

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