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Let s_1, s_2, ... be an infinite series of real numbers lying between 0 and 1. Then corresponding to any arbitrarily large K, there exists a positive integer n and two ...

Each centered convex body of sufficiently high dimension has an "almost spherical" k-dimensional central section.

The three diagonal points of a complete quadrilateral are never collinear.

A great circle is a section of a sphere that contains a diameter of the sphere (Kern and Bland 1948, p. 87). Sections of the sphere that do not contain a diameter are called ...

Let R(z) be a rational function R(z)=(P(z))/(Q(z)), (1) where z in C^*, C^* is the Riemann sphere C union {infty}, and P and Q are polynomials without common divisors. The ...

S_n=sum_(i)eta_imu(E_i), where mu(E_i) is the measure of the set E_i of points on the x-axis for which f(x) approx eta_i.

The intersection of two lines L_1 and L_2 in two dimensions with, L_1 containing the points (x_1,y_1) and (x_2,y_2), and L_2 containing the points (x_3,y_3) and (x_4,y_4), is ...

A geometric construction done with a movable compass alone. All constructions possible with a compass and straightedge are possible with a movable compass alone, as was ...

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

An orbifold is the object obtained by identifying any two points of a map which are equivalent under some symmetry of the map's group.