Optimal Green energy points on the circles in d-space

Decomposing 3-space into Circles and Points

Lattice Points on Circles

We prove that the lattice points on the circles x2 + y2 = n are well distributed for most circles containing lattice points.

Close Lattice Points on Circles

We classify the sets of four lattice points that all lie on a short arc of a circle which has its center at the origin; specifically on arcs of length tR on a circle of radius R, for any given t > 0. In particular we prove that any arc of length ( 40 + 40 3 √ 10 )1/3 R on a circle of radius R, with R > √ 65, contains at most three lattice points, whereas we give an explicit infinite family of 4...

Delaunay Triangulations of Points on Circles

Delaunay triangulations of a point set in the Euclidean plane are ubiquitous in a number of computational sciences, including computational geometry. Delaunay triangulations are not well defined as soon as 4 or more points are concyclic but since it is not a generic situation, this difficulty is usually handled by using a (symbolic or explicit) perturbation. As an alternative, we propose to def...

the caspian sea s role in energy supply to china

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