From Osher Doctorow
From a very recent Section of this thread, the numbers (1 + sqrt(n))/2
appear to be very important, especially for n prime, in both physics
and Probable Causation/Influence (PI).
These numbers now have yielded some arguably very interesting results
regarding "spherical two-distance sets" according to Oleg R. Musin, U.
Texas Brownsville USA, "Spherical two-distance sets," arXiv: 0801.3706
v1 [math.MG] 24 Jan 2008, 8 pages.
A "spherical 2-distance set" is a set S of unit vectors in Euclidean n-
dimensional space such that all inner products of different vectors of
S are either a or b for some two real numbers a, b.
It was already proven in 1977 by D. G. Larnow, C. A. Rogers and J. J.
Seidel that:
1) c^2/d^2 = (k - 1)/k, k integer, 2 < = k < = (1/2)(1 + sqrt(2n))
if c = a and d = b and c < = d and the cardinality of S in R^n > 2n +
3.
It was also proven that the largest cardinaly g(n) of S has an upper
bound:
2) g(s) < = n(n + 3)/2
Musin strengthens this to:
3) g(s) < = n(n + 1)/2 if a + b > = 0
Osher Doctorow
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