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The general displacement of a rigid body (or coordinate frame) with one point fixed is a rotation about some axis. Furthermore, a rotation may be described in any basis using ...

A function phi(t) satisfies the Hölder condition on two points t_1 and t_2 on an arc L when |phi(t_2)-phi(t_1)|<=A|t_2-t_1|^mu, with A and mu positive real constants. In some ...

The finite zeros of the derivative r^'(z) of a nonconstant rational function r(z) that are not multiple zeros of r(z) are the positions of equilibrium in the field of force ...

Based on a problem in particle physics, Dyson (1962abc) conjectured that the constant term in the Laurent series product_(1<=i!=j<=n)(1-(x_i)/(x_j))^(a_i) is the multinomial ...

Let u and v be any functions of a set of variables (q_1,...,q_n,p_1,...,p_n). Then the expression ...

An equilibrium minimal surface for a crystal or drop which has the least anisotropic surface free energy for a given volume. It is the anisotropic analog of a sphere. In the ...

Archimedes' spiral is an Archimedean spiral with polar equation r=atheta. (1) This spiral was studied by Conon, and later by Archimedes in On Spirals about 225 BC. Archimedes ...

The circle map is a one-dimensional map which maps a circle onto itself theta_(n+1)=theta_n+Omega-K/(2pi)sin(2pitheta_n), (1) where theta_(n+1) is computed mod 1 and K is a ...

The term Euclidean refers to everything that can historically or logically be referred to Euclid's monumental treatise The Thirteen Books of the Elements, written around the ...

The quantum electrodynamical law which applies to spin-1/2 particles and is the relativistic generalization of the Schrödinger equation. In 3+1 dimensions (three space ...