What's the minimum amount of extra "structure" do we need to add to the general concept of an affine space to get Euclidean space? That includes the concepts of angle and distance, in which we can describe things like polygons and circles, and in which we can derive all of the familiar theorems of Euclidean geometry.
2026-03-28 22:24:47.1774736687
Building Euclidean space
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In VI Arnold's classical mechanics page 5 he defines a Euclidean space as an affine space with a norm derived from the inner product on a real vector space. http://users.uoa.gr/~pjioannou/mech1/READING/Arnold_Clas_Mech_ch_1_2.pdf