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- Reflection_(mathematics) abstract "In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection. For example the mirror image of the small Latin letter p for a reflection with respect to a vertical axis would look like q. Its image by reflection in a horizontal axis would look like b. A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state.The term "reflection" is sometimes used for a larger class of mappings from a Euclidean space to itself, namely the non-identity isometries that are involutions. Such isometries have a set of fixed points (the "mirror") that is an affine subspace, but is possibly smaller than a hyperplane. For instance a reflection through a point is an involutive isometry with just one fixed point; the image of the letter p under itwould look like a d. This operation is also known as a central inversion (Coxeter 1969, §7.2), and exhibits Euclidean space as a symmetric space. In a Euclidean vector space, the reflection in the point situated at the origin is the same as vector negation. Other examples include reflections in a line in three-dimensional space. Typically, however, unqualified use of the term "reflection" means reflection in a hyperplane. A figure which does not change upon undergoing a reflection is said to have reflectional symmetry.".
- Reflection_(mathematics) thumbnail Simx2=traslOK.png?width=300.
- Reflection_(mathematics) wikiPageExternalLink Understanding2DReflection.
- Reflection_(mathematics) wikiPageExternalLink Understanding3DReflection.
- Reflection_(mathematics) wikiPageExternalLink Reflection.shtml.
- Reflection_(mathematics) wikiPageID "295829".
- Reflection_(mathematics) wikiPageRevisionID "596862909".
- Reflection_(mathematics) authorlink "Vladimir L. Popov".
- Reflection_(mathematics) first "V.L.".
- Reflection_(mathematics) hasPhotoCollection Reflection_(mathematics).
- Reflection_(mathematics) id "R/r080510".
- Reflection_(mathematics) last "Popov".
- Reflection_(mathematics) title "Reflection".
- Reflection_(mathematics) urlname "Reflection".
- Reflection_(mathematics) subject Category:Euclidean_symmetries.
- Reflection_(mathematics) subject Category:Functions_and_mappings.
- Reflection_(mathematics) subject Category:Linear_operators.
- Reflection_(mathematics) subject Category:Transformation_(function).
- Reflection_(mathematics) type Abstraction100002137.
- Reflection_(mathematics) type Attribute100024264.
- Reflection_(mathematics) type EuclideanSymmetries.
- Reflection_(mathematics) type Function113783816.
- Reflection_(mathematics) type FunctionsAndMappings.
- Reflection_(mathematics) type LinearOperator113786595.
- Reflection_(mathematics) type LinearOperators.
- Reflection_(mathematics) type MathematicalRelation113783581.
- Reflection_(mathematics) type Operator113786413.
- Reflection_(mathematics) type Property104916342.
- Reflection_(mathematics) type Relation100031921.
- Reflection_(mathematics) type SpatialProperty105062748.
- Reflection_(mathematics) type Symmetry105064827.
- Reflection_(mathematics) comment "In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection. For example the mirror image of the small Latin letter p for a reflection with respect to a vertical axis would look like q.".
- Reflection_(mathematics) label "Reflection (mathematics)".
- Reflection_(mathematics) label "Reflexão (matemática)".
- Reflection_(mathematics) label "Riflessione (geometria)".
- Reflection_(mathematics) label "Réflexion (mathématiques)".
- Reflection_(mathematics) label "Spiegeling (meetkunde)".
- Reflection_(mathematics) label "Spiegelung (Geometrie)".
- Reflection_(mathematics) label "Отражение (геометрия)".
- Reflection_(mathematics) label "انعكاس (رياضيات)".
- Reflection_(mathematics) label "反射 (数学)".
- Reflection_(mathematics) label "鏡映".
- Reflection_(mathematics) sameAs Spiegelung_(Geometrie).
- Reflection_(mathematics) sameAs Réflexion_(mathématiques).
- Reflection_(mathematics) sameAs Riflessione_(geometria).
- Reflection_(mathematics) sameAs 鏡映.
- Reflection_(mathematics) sameAs 반사_(수학).
- Reflection_(mathematics) sameAs Spiegeling_(meetkunde).
- Reflection_(mathematics) sameAs Reflexão_(matemática).
- Reflection_(mathematics) sameAs m.01r70h.
- Reflection_(mathematics) sameAs Q426221.
- Reflection_(mathematics) sameAs Q426221.
- Reflection_(mathematics) sameAs Reflection_(mathematics).
- Reflection_(mathematics) wasDerivedFrom Reflection_(mathematics)?oldid=596862909.
- Reflection_(mathematics) depiction Simx2=traslOK.png.
- Reflection_(mathematics) isPrimaryTopicOf Reflection_(mathematics).