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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 ...

The substitution of x=w-p/(3w) (1) into the standard form cubic equation x^3+px=q. (2) The result reduces the cubic to the equation w^3-(p^3)/(27w^3)-q=0, (3) which is easily ...

An affine transformation is any transformation that preserves collinearity (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of ...

In geometry, the term "enlargement" is a synonym for expansion. In nonstandard analysis, let X be a set of urelements, and let V(X) be the superstructure with individuals in ...

If T is a linear transformation of R^n, then the null space Null(T), also called the kernel Ker(T), is the set of all vectors X such that T(X)=0, i.e., Null(T)={X:T(X)=0}. ...

An automorphic function f(z) of a complex variable z is one which is analytic (except for poles) in a domain D and which is invariant under a countably infinite group of ...

The parameters alpha, beta, gamma, and delta which, like the three Euler angles, provide a way to uniquely characterize the orientation of a solid body. These parameters ...