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Let A be a commutative complex Banach algebra. A nonzero homomorphism from A onto the field of complex numbers is called a character. Every character is automatically ...

A bounded entire function in the complex plane C is constant. The fundamental theorem of algebra follows as a simple corollary.

Draw lines P_AQ_A, P_BQ_B, and P_CQ_C through the symmedian point K and parallel to the sides of the triangle DeltaABC. The points where the parallel lines intersect the ...

The Sendov conjecture, proposed by Blagovest Sendov circa 1958, that for a polynomial f(z)=(z-r_1)(z-r_2)...(z-r_n) with n>=2 and each root r_k located inside the closed unit ...

Let C=C^+ union C^- (where C^+ intersection C^-=emptyset) be the disjoint union of two finite components C^+ and C^-. Let alpha and beta be two involutions on C, each of ...

Two points which are collinear with respect to a similitude center but are not homologous points. Four interesting theorems from Johnson (1929) follow. 1. Two pairs of ...

An Aztec diamond of order n is the region obtained from four staircase shapes of height n by gluing them together along the straight edges. It can therefore be defined as the ...

Bisection is the division of a given curve, figure, or interval into two equal parts (halves). A simple bisection procedure for iteratively converging on a solution which is ...

As defined by Kyrmse, a canonical polygon is a closed polygon whose vertices lie on a point lattice and whose edges consist of vertical and horizontal steps of unit length or ...

If the four points making up a quadrilateral are joined pairwise by six distinct lines, a figure known as a complete quadrangle results. A complete quadrangle is therefore a ...