All Topics  
Reflection symmetry

 
Reflection Symmetry

 
   Email Print
   Bookmark   Link
 

 

Reflection symmetry
 
 
  Topics Reflection symmetry Topic Home

The triangle
Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or wikt:vertex and three sides or edges which are line segments....
s with this symmetry are isosceles. The quadrilateral
Quadrilateral

In geometry, a quadrilateral is a polygon with four 'sides' or edges and four vertices or corners. Sometimes, the term quadrangle is used, for analogy with triangle, and sometimes tetragon for consistency with pentagon , hexagon and so on....
s with this symmetry are the kite
Kite (geometry)

In geometry a kite, or deltoid, is a quadrilateral with two disjoint sets pairs of congruent adjacent sides, in contrast to a parallelogram, where the congruent sides are opposite....
s and the isosceles trapezoid
Isosceles trapezoid

An isosceles trapezoid is a quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid. Two opposite sides are Parallel , the two other sides are of equal length....
s.

For each line or plane of reflection, the symmetry group
Symmetry group

The symmetry group of an object is the group of all isometries under which it is invariant with Function composition as the operation. It is a subgroup of the isometry group of the space concerned....
 is isomorphic with Cs (see point groups in three dimensions
Point groups in three dimensions

In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere....
), one of the three types of order two (involution
Involution

In mathematics, an involution, or an involutary function, is a function that is its own inverse function, so that...
s), hence algebraically C2. The fundamental domain
Fundamental domain

In geometry, the fundamental domain of a symmetry group of an object or pattern is a part of the pattern, as small as possible, which, based on the symmetry, determines the whole object or pattern....
 is a half-plane or half-space.

Bilateria
Bilateria

The Bilateria are all animals having a symmetry #Bilateral symmetry, i.e. they have a front and a back end, as well as an upside and downside....
 (bilateral animals, including humans) are more or less symmetric with respect to the sagittal plane
Anatomical terms of location

Standard anatomical terms of location are employed in sciences dealing with the anatomy of animals to avoid ambiguities which might otherwise arise....
.

In certain contexts there is rotational symmetry anyway.






Discussion
Ask a question about 'Reflection symmetry'
Start a new discussion about 'Reflection symmetry'
Answer questions from other users
Full Discussion Forum



Encyclopedia


The triangle
Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or wikt:vertex and three sides or edges which are line segments....
s with this symmetry are isosceles. The quadrilateral
Quadrilateral

In geometry, a quadrilateral is a polygon with four 'sides' or edges and four vertices or corners. Sometimes, the term quadrangle is used, for analogy with triangle, and sometimes tetragon for consistency with pentagon , hexagon and so on....
s with this symmetry are the kite
Kite (geometry)

In geometry a kite, or deltoid, is a quadrilateral with two disjoint sets pairs of congruent adjacent sides, in contrast to a parallelogram, where the congruent sides are opposite....
s and the isosceles trapezoid
Isosceles trapezoid

An isosceles trapezoid is a quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid. Two opposite sides are Parallel , the two other sides are of equal length....
s.

For each line or plane of reflection, the symmetry group
Symmetry group

The symmetry group of an object is the group of all isometries under which it is invariant with Function composition as the operation. It is a subgroup of the isometry group of the space concerned....
 is isomorphic with Cs (see point groups in three dimensions
Point groups in three dimensions

In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere....
), one of the three types of order two (involution
Involution

In mathematics, an involution, or an involutary function, is a function that is its own inverse function, so that...
s), hence algebraically C2. The fundamental domain
Fundamental domain

In geometry, the fundamental domain of a symmetry group of an object or pattern is a part of the pattern, as small as possible, which, based on the symmetry, determines the whole object or pattern....
 is a half-plane or half-space.

Bilateria
Bilateria

The Bilateria are all animals having a symmetry #Bilateral symmetry, i.e. they have a front and a back end, as well as an upside and downside....
 (bilateral animals, including humans) are more or less symmetric with respect to the sagittal plane
Anatomical terms of location

Standard anatomical terms of location are employed in sciences dealing with the anatomy of animals to avoid ambiguities which might otherwise arise....
.

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
Parity (physics)

In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all spatial coordinates:...
).

For more general types of reflection
Reflection (mathematics)

In mathematics, a reflection is a function that transforms an object into its mirror image. For example, a reflection of the small English letter p in respect to a vertical line would look like q....
 there are corresponding more general types of reflection symmetry. Examples:
  • with respect to a non-isometric affine involution
    Affine involution

    In Euclidean geometry, of special interest are involutions which are linear transformation or affine transformations over the Euclidean space Rn....
     (an oblique reflection
    Oblique reflection

    In Euclidean geometry, oblique reflections generalize ordinary reflection by not requiring that reflection be done using perpendiculars. If two points are oblique reflections of each other, they will still stay so under affine transformations....
     in a line, plane, etc).
  • with respect to circle inversion.


See also

  • Rotational symmetry
    Rotational symmetry

    File:The armoured triskelion on the flag of the Isle of Man.svgGenerally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation....
  • Translational symmetry
    Translational symmetry

    In geometry, a translation "slides" an object by a a: Ta = p + a.In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation....


External links

  • from Math Is Fun
    Math Is Fun

    Math Is Fun is an educational website maintained by Rod Pierce devoted to the concept that mathematics is, indeed, fun.There are several aspects to the website:...