Fixed points of isometry groups in Euclidean space
= Fixed points of isometry groups in Euclidean space
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In the context of Euclidean space, an isometry is a transformation that preserves distances. This means that if you have two points \\( A \\) and \\( B \\) in Euclidean space, an isometric transformation \\( T \\) will maintain the distance between these points, i.e., \\( d(T(A), T(B)) = d(A, B) \\), where \\( d \\) denotes the distance function.