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1. (geometry) The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (ax, ay) and b = (bx, by) is defined as: : d(\textbf{a}, \textbf{b}) = \sqrt{(\textbf{a}_x - \textbf{b}_x)^2 + (\textbf{a}_y - \textbf{b}_y)^2}