- Reflection symmetry
Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is
symmetrywith respect to reflection.
In 2D there is an axis of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric (see
mirror image). Also see pattern.
The axis of symmetry of a two-
dimensional figure is a line such that, if a perpendicularis constructed, any two points lying on the perpendicular at equal distances from the axis of symmetry are identical. Another way to think about it is that if the shape were to be folded in half over the axis, the two halves would be identical: the two halves are each other's mirror image. Thus a square has four axes of symmetry, because there are four different ways to fold it and have the edges all match. A circle has infinitely many axes of symmetry, for the same reason.
If the letter T is reflected along a vertical axis, it appears the same. Note that this is sometimes called horizontal symmetry, and sometimes vertical symmetry. One can better use an unambiguous formulation, e.g. "T has a vertical symmetry axis."
triangles with this symmetry are isosceles. The quadrilaterals with this symmetry are the kites and the isosceles trapezoids.
For each line or plane of reflection, the
symmetry groupis isomorphic with "Cs" (see point groups in three dimensions), one of the three types of order two ( involutions), hence algebraically "C2". The fundamental domainis a half-plane or half-space. Bilateria(bilateral animals, including humans) are more or less symmetric with respect to the sagittal plane.
In certain contexts there is rotational symmetry anyway. Then mirror-image symmetry is equivalent with inversion symmetry; in such contexts in modern physics the term P-symmetry is used for both (P stands for parity).
For more general types of reflection there are corresponding more general types of reflection symmetry. Examples:
*with respect to a non-isometric
affine involution(an oblique reflectionin a line, plane, etc).
*with respect to circle inversion.
*cite book |title=Symmetry |last=Weyl |first=Hermann |authorlink=Hermann Weyl |coauthors= |date=1982 |origdate=1952 |publisher=Princeton University Press |location=Princeton |isbn=0-691-02374-3 |pages= |url= |ref=Weyl 1982
* [http://republika.pl/fraktal/mapping.html Mapping with symmetry - source in Delphi]
* [http://www.mathsisfun.com/geometry/symmetry-reflection.html Reflection Symmetry Examples] from
Math Is Fun
Wikimedia Foundation. 2010.
Look at other dictionaries:
space-reflection symmetry — noun (physics) parity is conserved in a universe in which the laws of physics are the same in a right handed system of coordinates as in a left handed system • Syn: ↑parity, ↑conservation of parity, ↑mirror symmetry • Topics: ↑physics, ↑natural… … Useful english dictionary
Symmetry — For other uses, see Symmetry (disambiguation) … Wikipedia
symmetry — /sim i tree/, n., pl. symmetries. 1. the correspondence in size, form, and arrangement of parts on opposite sides of a plane, line, or point; regularity of form or arrangement in terms of like, reciprocal, or corresponding parts. 2. the proper or … Universalium
Symmetry in biology — For other uses, see Symmetry (disambiguation) and Bilateral (disambiguation). Bilateral symmetry redirects here. For bilateral symmetry in mathematics, see reflection symmetry. The elaborate patterns on the wings of butterflies are one example of … Wikipedia
Symmetry (biology) — Bilateral symmetry redirects here. For bilateral symmetry in mathematics, see reflection symmetry. Symmetry in biology is the balanced distribution of duplicate body parts or shapes. The body plans of most multicellular organisms exhibit some… … Wikipedia
Symmetry in physics — refers to features of a physical system that exhibit the property of symmetry that is, under certain transformations, aspects of these systems are unchanged , according to a particular observation. A symmetry of a physical system is a physical or … Wikipedia
Symmetry combinations — This article discusses various symmetry combinations.In 2D, mirror image symmetry in combination with n fold rotational symmetry, with the center of rotational symmetry on the line of symmetry, implies mirror image symmetry with respect to lines… … 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
Symmetry in mathematics — For other uses, see Symmetry (disambiguation) and Bilateral (disambiguation). Symmetry occurs not only in geometry, but also in other branches of mathematics. It is actually the same as invariance: the property that something does not change… … Wikipedia
Symmetry operation — In the context of molecular symmetry, a symmetry operation may be defined as a permutation of atoms such that the molecule or crystal is transformed into a state indistinguishable from the starting state. Two basic facts follow from this… … Wikipedia