In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or more particularly if it cannot be mapped to its mirror image by rotations and translations alone. Such objects come in two forms, called enantiomorphs. The word chirality is derived from the Greek χειρ (cheir), the hand, the most familiar chiral object; the word enantiomorph stems from the Greek εναντιος (enantios) 'opposite' and μορφη (morphe) 'form'. A non-chiral figure is called Including:
In three dimensions, every figure which possesses a plane of symmetry or a center of symmetry is achiral. (A plane of symmetry of a figure F is a plane P, such that F is invariant under the mapping , when P is chosen to be the x-y-plane of the coordinate system. A center of symmetry of a figure See also:
A clockwise motion is one that proceeds 'like the clock's hands': from the top to the right, then down and then to the left, and back to the top. In a mathematical sense, a circle defined parametrically by the equations x = r sin t and y = r cos t, where r is the radius of the circle, is traced clockwise as t increases in value. The opposite sense of rota ...
In two dimensions, every figure which possesses an axis of symmetry is achiral, and it can be shown that every bounded achiral figure must have an axis of symmetry. (An axis of symmetry of a figure F is a line L, such that F is invariant under the mapping , when L is chosen to be the x-axis of the coordinate system.) Consider the following pattern:
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