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A unimodular matrix is a real square matrix A with determinant det(A)=+/-1 (Born and Wolf 1980, p. 55; Goldstein 1980, p. 149). More generally, a matrix A with elements in ...

In a given circle, find an isosceles triangle whose legs pass through two given points inside the circle. This can be restated as: from two points in the plane of a circle, ...

In the Minkowski space of special relativity, a four-vector is a four-element vector x^mu=(x^0,x^1,x^2,x^3) that transforms under a Lorentz transformation like the position ...

The envelope of the plane lx+my+nz=c, (1) where c is the speed of propagation of a wave in the direction (l,m,n) (i.e., l, m, and n are the direction cosines) is known as the ...

A Lorentz transformation is a four-dimensional transformation x^('mu)=Lambda^mu_nux^nu, (1) satisfied by all four-vectors x^nu, where Lambda^mu_nu is a so-called Lorentz ...

Several prizes are awarded periodically for outstanding mathematical achievement. There is no Nobel Prize in mathematics, and the most prestigious mathematical award is known ...

Minkowski's question mark function is the function y=?(x) defined by Minkowski for the purpose of mapping the quadratic surds in the open interval (0,1) into the rational ...

The spherical harmonics can be generalized to vector spherical harmonics by looking for a scalar function psi and a constant vector c such that M = del x(cpsi) (1) = psi(del ...

The Zernike polynomials are a set of orthogonal polynomials that arise in the expansion of a wavefront function for optical systems with circular pupils. The odd and even ...

The Fields Medals are commonly regarded as mathematics' closest analog to the Nobel Prize (which does not exist in mathematics), and are awarded every four years by the ...