Suppose we want to place $k$ ($k \geq 3$) points on the positive surface of a unit hyper-sphere in $\mathbb{R}^n$ ($n \geq 3$), where all coordinates of a point are positive, such that the minimum distance, $x$, between any pair of points is maximized. Is there a general formula to determine the value $x$?
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$\begingroup$ Why do you want all coordinates positives? This would be only 1/8 of a standard sphere in $\mathbb {R}^3$ say. $\endgroup$– Ivan MeirCommented Jun 26, 2020 at 7:11
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$\begingroup$ Equidistribution over the entire sphere is more standard and if you have a lower bound for the min distance over the whole surface it will also hold for the positive quadrant as well since deleting points only increases min distances between points. $\endgroup$– Ivan MeirCommented Jun 26, 2020 at 7:14
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$\begingroup$ For the sphere in $\mathbb {R}^3$ you may want to look at this post $\endgroup$– Ivan MeirCommented Jun 26, 2020 at 7:17
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1$\begingroup$ I have no hard reasons, but given that there are no such formulas for spheres, balls (solid spheres), cubes, ... etc, I highly doubt that there is one for the positive part of a sphere. $\endgroup$– M. WinterCommented Jun 26, 2020 at 13:12
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