Reflection symmetry
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Reflection symmetry, reflectional symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry.
In 2D there is a line 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 or line of symmetry of a two-dimensional figure is a line such that, for each perpendicular constructed, if the perpendicular intersects the figure at a distance 'd' from the axis along the perpendicular, then there exists another intersection of the shape and the perpendicular, at the same distance 'd' from the axis, in the opposite direction along the perpendicular. 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."(this may also be called a line of symmetry)
The 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 group is isomorphic with Cs (see point groups in three dimensions), one of the three types of order two (involutions), hence algebraically C2. The fundamental domain is a half-plane or half-space.
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 reflection in a line, plane, etc.).
- with respect to circle inversion.
Mirrored symmetry is also found in the design of ancient structures, including Stonehenge.[1]
See also
References
- ^ Johnson, Anthony, Solving Stonehenge: The New Key to an Ancient Enigma. (Thames & Hudson, 2008) ISBN 978-0-500-05155-9
- Weyl, Hermann (1982) [1952]. Symmetry. Princeton: Princeton University Press. ISBN 0-691-02374-3.
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External links
