ABSTRACT
For k=4, we write a k to denote the maximum number with the property that one can place k points on the sphere S 2 so that the spherical distance between any two different points is at least a k . In case of thirteen points on S
reason is an equivalent formulation; namely, whether thirteen unit balls in can touch a given unit ball without overlapping. Isaac Newton and David Gregory discussed this problem in 1694, and Newton stated that the maximal number of touching balls should be twelve. He was right, but the first and still not complete solutions were provided only in 1874/75 by the physicists C.Bender [4], S.Günter [8] and R.Hoppe [9], The first “rigorous proof” was given by K.Schütte & B.L.van der Waerden [12], and this proof was further simplified by J.Leech [10] to an elegant argument.
