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If (sinalpha)/(sinbeta)=m/n, then (tan[1/2(alpha-beta)])/(tan[1/2(alpha+beta)])=(m-n)/(m+n).

Suppose f(x) is a function of x that is twice differentiable at a stationary point x_0. 1. If f^('')(x_0)>0, then f has a local minimum at x_0. 2. If f^('')(x_0)<0, then f ...

The sum of the values of an integral of the "first" or "second" sort int_(x_0,y_0)^(x_1,y_1)(Pdx)/Q+...+int_(x_0,y_0)^(x_N,y_N)(Pdx)/Q=F(z) and ...

A convex body in Euclidean space that is centrally symmetric with center at the origin is determined among all such bodies by its brightness function (the volume of each ...

Let M be the midpoint of the arc AMB. Pick C at random and pick D such that MD_|_AC (where _|_ denotes perpendicular). Then AD=DC+BC.

If g(theta) is a trigonometric polynomial of degree m satisfying the condition |g(theta)|<=1 where theta is arbitrary and real, then g^'(theta)<=m.

There exists a total computable predicate P such that for any algorithm computing P(x) with running time T(x), there exists another algorithm computing P(x) with computation ...

Every continuous map f:S^n->R^n must identify a pair of antipodal points.

If the total group of the canonical series is divided into two parts, the difference between the number of points in each part and the double of the dimension of the complete ...

Let t be a nonnegative integer and let x_1, ..., x_t be nonzero elements of Z_p which are not necessarily distinct. Then the number of elements of Z_p that can be written as ...