Source: wikibot/fixed-points-of-isometry-groups-in-euclidean-space
= Fixed points of isometry groups in Euclidean space
{wiki=Fixed_points_of_isometry_groups_in_Euclidean_space}
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.