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If the trilinear polars of the polygon vertices of a triangle are distinct from the respectively opposite sides, they meet the sides in three collinear points.

The number of ways to arrange n distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is P_n=(n-1)!. The number is (n-1)! instead ...

A linear operator A:D(A)->H from its domain D(A) into a Hilbert space H is closable if it has a closed extension B:D(B)->H where D(A) subset D(B). Closable operators are ...

Codimension is a term used in a number of algebraic and geometric contexts to indicate the difference between the dimension of certain objects and the dimension of a smaller ...

A partially ordered set (or ordered set or poset for short) (L,<=) is called a complete lattice if every subset M of L has a least upper bound (supremum, supM) and a greatest ...

Let P be the principal (initial investment), r be the annual compounded rate, i^((n)) the "nominal rate," n be the number of times interest is compounded per year (i.e., the ...

Let X and Y be sets, and let R subset= X×Y be a relation on X×Y. Then R is a concurrent relation if and only if for any finite subset F of X, there exists a single element p ...

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

The science of adversarial information protection.