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A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2), (3) and an ...

Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be ...

The operation of exchanging all points of a mathematical object with their mirror images (i.e., reflections in a mirror). Objects that do not change handedness under ...

Scherk's two minimal surfaces were discovered by Scherk in 1834. They were the first new surfaces discovered since Meusnier in 1776. Beautiful images of wood sculptures of ...

There are two types of singular values, one in the context of elliptic integrals, and the other in linear algebra. For a square matrix A, the square roots of the eigenvalues ...

Underdamped simple harmonic motion is a special case of damped simple harmonic motion x^..+betax^.+omega_0^2x=0 (1) in which beta^2-4omega_0^2<0. (2) Since we have ...

The nth root (or "nth radical") of a quantity z is a value r such that z=r^n, and therefore is the inverse function to the taking of a power. The nth root is denoted ...

A n×n matrix A is an orthogonal matrix if AA^(T)=I, (1) where A^(T) is the transpose of A and I is the identity matrix. In particular, an orthogonal matrix is always ...

Exchanges branches of the hyperbola x^'y^'=xy. x^' = mu^(-1)x (1) y^' = -muy. (2)

Let m and m+h be two consecutive critical indices of f and let F be (m+h)-normal. If the polynomials p^~_k^((n)) are defined by p^~_0^((n))(u) = 1 (1) p^~_(k+1)^((n))(u) = ...