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If one part of the total intersection group of a curve of order n with a curve of order n_1+n_2 constitutes the total intersection with a curve of order n_1, then the other ...

A theorem about (or providing an equivalent definition of) compact sets, originally due to Georg Cantor. Given a decreasing sequence of bounded nonempty closed sets C_1 ...

König's line coloring theorem states that the edge chromatic number of any bipartite graph equals its maximum vertex degree. In other words, every bipartite graph is a class ...

The Euler-Gergonne-Soddy circle, a term coined here for the first time, is the circumcircle of the Euler-Gergonne-Soddy triangle. Since the Euler-Gergonne-Soddy triangle is a ...

Consider two cylinders as illustrated above (Hubbell 1965) where the cylinders have radii r_1 and r_2 with r_1<=r_2, the larger cylinder is oriented along the z-axis, and ...

Pick two points at random in a circular sector of radius 1 and central angle theta, and consider the length s of the line joining them. The following table summarizes ...

The curve formed by the intersection of a cylinder and a sphere is known as Viviani's curve. The problem of finding the lateral surface area of a cylinder of radius r ...

Consider the plane figure obtained by drawing each diagonal in a regular polygon with n vertices. If each point of intersection is associated with a node and diagonals are ...

There are four completely different definitions of the so-called Apollonius circles: 1. The set of all points whose distances from two fixed points are in a constant ratio ...

1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...