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A reflection through an axis. In mathematics, a reflection (also spelled reflexion) [1] is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.
The set of all reflections in lines through the origin and rotations about the origin, together with the operation of composition of reflections and rotations, forms a group. The group has an identity: Rot(0). Every rotation Rot(φ) has an inverse Rot(−φ). Every reflection Ref(θ) is its own inverse. Composition has closure and is ...
Mirrors and Reflections: The Geometry of Finite Reflection Groups is an undergraduate-level textbook on the geometry of reflection groups.It was written by Alexandre V. Borovik and Anna Borovik and published in 2009 by Springer in their Universitext book series.
In mathematics, a reflection formula or reflection relation for a function f is a relationship between f(a − x) and f(x). It is a special case of a functional equation . It is common in mathematical literature to use the term "functional equation" for what are specifically reflection formulae.
The morphism is called the A-reflection arrow. (Although often, for the sake of brevity, we speak about A B {\displaystyle A_{B}} only as being the A -reflection of B ). This is equivalent to saying that the embedding functor E : A ↪ B {\displaystyle E\colon \mathbf {A} \hookrightarrow \mathbf {B} } is a right adjoint.
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2-dimensional space, there is a line/axis of symmetry, in 3-dimensional space, there is a plane of symmetry.
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