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A Euclidean motion of R^n is an affine transformation whose linear part is an orthogonal transformation.

An array of "trees" of unit height located at integer-coordinate points in a point lattice. When viewed from a corner along the line y=x in normal perspective, a quadrant of ...

A system of congruences a_i mod n_i with 1<=i<=k is called a complete residue system (or covering system) if every integer y satisfies y=a_i (mod n) for at least one value of ...

A 1-form w is said to be exact in a region R if there is a function f that is defined and of class C^1 (i.e., is once continuously differentiable in R) and such that df=w.

A method which can be used to solve any quadratic congruence equation. This technique relies on the fact that solving x^2=b (mod p) is equivalent to finding a value y such ...

The fractal illustrated above.

A continuous real function L(x,y) defined on the tangent bundle T(M) of an n-dimensional smooth manifold M is said to be a Finsler metric if 1. L(x,y) is differentiable at ...

The flat norm on a current is defined by F(S)=int{Area T+Vol(R):S-T=partialR}, where partialR is the boundary of R.

The distance p (sometimes also denoted k) from the focus to the conic section directrix of a conic section. The following table gives the focal parameter for the different ...

The permanent of an n×n integer matrix with all entries either 0 or 1 is 0 iff the matrix contains an r×s submatrix of 0s with r+s=n+1. This result follows from the ...