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Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these.

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Number of Nearest-Neighbors in high dimensions [closed]

Consider $n$ adversarially chosen points in $\mathbb{R}^{d}$ where $n \gg d$. Let $\mathbf{a}$ be one of the $n$ points. Is there an upper bound on the number of points among the remaining $n-1$ point …