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A rotation through 180 degrees (pi radians).

A linear transformation A:R^n->R^n is hyperbolic if none of its eigenvalues has modulus 1. This means that R^n can be written as a direct sum of two A-invariant subspaces E^s ...

The symmetry operation corresponding to a rotation followed by an inversion operation, also called a rotoinversion. This operation is denoted n^_ for an improper rotation by ...

An image of an object obtained by reflecting it in a mirror so that the signs of one of its coordinates are reversed.

Two objects form a mirror pair if one can be translated and rotated in such a way that the two objects together possess mirror symmetry, i.e., one is the mirror image of the ...

The Poincaré group is another name for the inhomogeneous Lorentz group (Weinberg 1972, p. 28) and corresponds to the group of inhomogeneous Lorentz transformations, also ...

An object is reflexible if it is superposable with its image in a plane mirror. Also called amphichiral.

The rotation operator can be derived from examining an infinitesimal rotation (d/(dt))_(space)=(d/(dt))_(body)+omegax, where d/dt is the time derivative, omega is the angular ...

Sinai billiards is the reflection of a ray of light by an arrangement of perfectly reflecting circles in the plane (Trott 2004, pp. 28-30). The path is extremely sensitive to ...

To translate an object means to perform a translation. A translate of a mathematical object means a shifted (i.e., translated) version of the object. Hence, one can speak of ...