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Lattices in the sense of discrete subgroups of Euclidean spaces, as used in number theory, discrete geometry, Lie groups, etc. (Not to be confused with lattice theory or lattices as used in physics! For lattices (ordered sets), use the tag: [lattice-theory])
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Why are two "random" vectors in $\mathbb R^n$ approximately orthogonal for large $n$?
Pick two random unit vectors. After picking the first vector, switch to a coordinate system in which this is the first basis vector. The probability distribution for the second vector is assumed to be …