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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.

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What is the maximum number of points on a plane such that some other point A is the nearest ... [closed]

Point $A$ on the plane is given. How many other points can be placed on this plane under the condition that $A$ is the nearest neighbor for any of these points? I can think of a regular pentagon with …
Alexander Piperski's user avatar