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Results tagged with spherical-geometry
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user 108884
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Maximal distance between $2d+1$ points on the $(d-1)$-sphere
I finally came to do the computations on Yoav Kallus' comment. After quite some tedious work one finds a cubic polynomial:
$$p_d(x)\,=\,d(d-2)^2 x^3 - d^2 x^2 - dx + 1$$
which has exactly one zero in …
- 13.6k
6
votes
Maximal distance between $2d+1$ points on the $(d-1)$-sphere
Turns out kodlu's idea works in all dimensions, regardless of the existence of any Hadamard matrices.
Consider all coordinate permutations of
$$(1,...,1,-d)\in\Bbb R^{d+1}\quad\text{and}\quad (-1,.. …
- 13.6k