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

A function f such that |f(x)-f(y)|<=C|x-y| for all x and y, where C is a constant independent of x and y, is called a Lipschitz function. For example, any function with a ...

For an arbitrary not identically constant polynomial, the zeros of its derivatives lie in the smallest convex polygon containing the zeros of the original polynomial.

A line of constant longitude on a spheroid (or sphere). More generally, a meridian of a surface of revolution is the intersection of the surface with a plane containing the ...

The constant ratio by which all distances are increased (or decreased) in a similarity. A similarity with ratio of magnification equal to 1 is called an isometry.

In any triangle, the locus of a point whose pedal triangle has a constant Brocard angle and is described in a given direction is a circle of the Schoute coaxal system.

A three-dimensional surface with constant vector field on its boundary which traps at least one trajectory which enters it.

Pick three points P=(x_1,y_1), Q=(x_2,y_2), and R=(x_3,y_3) distributed independently and uniformly in a unit disk K (i.e., in the interior of the unit circle). Then the ...

An unsolved problem in mathematics attributed to Lehmer (1933) that concerns the minimum Mahler measure M_1(P) for a univariate polynomial P(x) that is not a product of ...

Let theta(t) be the Riemann-Siegel function. The unique value g_n such that theta(g_n)=pin (1) where n=0, 1, ... is then known as a Gram point (Edwards 2001, pp. 125-126). An ...