Point Reflection

In geometry, a point reflection or inversion in a point (or inversion through a point, or central inversion) is a type of isometry of Euclidean space. An object that is invariant under a point reflection is said to possess point symmetry; if it is invariant under point reflection through its center, it is said to possess central symmetry or to be centrally symmetric.

Point reflection can be classified as an affine transformation. Namely, it is an isometric involutive affine transformation, which has exactly one fixed point, which is the point of inversion. It is equivalent to a homothetic transformation with scale factor equal to -1. The point of inversion is also called homothetic center.

Read more about Point ReflectionTerminology, Examples, Formula, Point Reflection As A Special Case of Uniform Scaling or Homothety, Point Reflection Group, Point Reflections in Mathematics, Properties, Inversion With Respect To The Origin, See Also

Other articles related to "point reflection, reflection":

Symmetry - In Geometry - Point Reflection and Other Involutive Isometries
... Reflection symmetry can be generalized to other isometries of m-dimensional space which are involutions, such as (x1, … xm) ↦ (−x1, … −xk, xk+1 ... If k = m, then such transformation is known as point reflection, which on the plane (m = 2) is the same as the half-turn (180°) rotation see below ... Such "reflection" keeps orientation if and only if k is even ...
Point Reflection - See Also
... Clifford algebra Congruence (geometry) Euclidean group Orthogonal group Parity (physics) Reflection (mathematics) Riemannian symmetric space Spin group ...

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