group of plane rotations

См. также в других словарях:

• Plane symmetry — means a symmetry of a pattern in the Euclidean plane; that is, a transformation of the plane that carries any directioned lines to lines and preserves many different distances. If one has a pattern in the plane, the set of plane symmetries that… …   Wikipedia

• Group (mathematics) — This article covers basic notions. For advanced topics, see Group theory. The possible manipulations of this Rubik s Cube form a group. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines …   Wikipedia

• Wallpaper group — A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and… …   Wikipedia

• Rotation group — This article is about rotations in three dimensional Euclidean space. For rotations in four dimensional Euclidean space, see SO(4). For rotations in higher dimensions, see orthogonal group. In mechanics and geometry, the rotation group is the… …   Wikipedia

• Lorentz group — Group theory Group theory …   Wikipedia

• Orthogonal group — Group theory Group theory …   Wikipedia

• Euclidean plane isometry — In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length. There are four types: translations, rotations, reflections,… …   Wikipedia

• Euclidean group — In mathematics, the Euclidean group E ( n ), sometimes called ISO( n ) or similar, is the symmetry group of n dimensional Euclidean space. Its elements, the isometries associated with the Euclidean metric, are called Euclidean moves.These groups… …   Wikipedia

• Dihedral group — This snowflake has the dihedral symmetry of a regular hexagon. In mathematics, a dihedral group is the group of symmetries of a regular polygon, including both rotations and reflections.[1] Dihedr …   Wikipedia

• Symmetry group — Not to be confused with Symmetric group. This article is about the abstract algebraic structures. For other meanings, see Symmetry group (disambiguation). A tetrahedron can be placed in 12 distinct positions by rotation alone. These are… …   Wikipedia

• Coordinate rotations and reflections — Main article: Orthogonal group In geometry, 2D coordinate rotations and reflections are two kinds of Euclidean plane isometries which are related to one another. A rotation in the plane can be formed by composing a pair of reflections. First… …   Wikipedia