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If a univariate real function f(x) has a single critical point and that point is a local maximum, then f(x) has its global maximum there (Wagon 1991, p. 87). The test breaks ...

The conjecture that, for any triangle, 8omega^3<ABC (1) where A, B, and C are the vertex angles of the triangle and omega is the Brocard angle. The Abi-Khuzam inequality ...

A maximal irredundant set is an irredundant set that cannot be expanded to another irredundant set by addition of any vertex in the graph. Note that a maximal irredundant set ...

Let |z| be a vector norm of a vector z such that ||A||=max_(|z|=1)||Az||. Then ||A|| is a matrix norm which is said to be the natural norm induced (or subordinate) to the ...

Enclose a sphere in a cylinder and cut out a spherical segment by slicing twice perpendicularly to the cylinder's axis. Then the lateral surface area of the spherical segment ...

Let F_0 and F_1 denote two directly similar figures in the plane, where P_1 in F_1 corresponds to P_0 in F_0 under the given similarity. Let r in (0,1), and define ...

If f is a schlicht function and D(z_0,r) is the open disk of radius r centered at z_0, then f(D(0,1)) superset= D(0,1/4), where superset= denotes a (not necessarily proper) ...

Let five circles with concyclic centers be drawn such that each intersects its neighbors in two points, with one of these intersections lying itself on the circle of centers. ...

Let any finite or infinite set of points having no finite limit point be prescribed and associate with each of its points a principal part, i.e., a rational function of the ...

Let 0<p_1<p_2<... be integers and suppose that there exists a lambda>1 such that p_(j+1)/p_j>lambda for j=1, 2, .... Suppose that for some sequence of complex numbers {a_j} ...