Euclidean group
Noun
Meaning
Euclidean group (plural Euclidean groups)
(mathematics) the set of rigid motions that are also affine transformations.
Examples
The positive solution for spaces of dimension at most two, and the negative solution for higher dimensions, comes from the fact that the Euclidean group is a solvable group for dimension at most two, and is not solvable for higher dimensions.
The set of all translations forms the translation group T, which is isomorphic to the space itself, and a normal subgroup of Euclidean group E(n ).
The structure of Euclidean spaces – distances, lines, vectors, angles ( up to sign), and so on – is invariant under the transformations of their associated Euclidean group.