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Four circles c_1, c_2, c_3, and c_4 are tangent to a fifth circle or a straight line iff T_(12)T_(34)+/-T_(13)T_(42)+/-T_(14)T_(23)=0. (1) where T_(ij) is the length of a ...

A catenary of revolution. The catenoid and plane are the only surfaces of revolution which are also minimal surfaces. The catenoid can be given by the parametric equations x ...

The Cayley-Purser algorithm is a public-key cryptography algorithm that relies on the fact that matrix multiplication is not commutative. It was devised by Sarah Flannery ...

A class of complete orientable minimal surfaces of R^3 derived from Enneper's minimal surface. They are named for the mathematicians who found the first two examples in 1982. ...

A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of ...

The figure determined by four lines, no three of which are concurrent, and their six points of intersection (Johnson 1929, pp. 61-62). Note that this figure is different from ...

There are a number of attractive polyhedron compounds of two cubes. The first (left figures) is obtained by allowing two cubes to share opposite polyhedron vertices then ...

The classic treatise in geometry written by Euclid and used as a textbook for more than 1000 years in western Europe. An Arabic version The Elements appears at the end of the ...

The path traced out by a point P on the edge of a circle of radius b rolling on the outside of a circle of radius a. An epicycloid is therefore an epitrochoid with h=b. ...

An equilateral zonohedron is a zonohedron in which the line segments of the star on which it is based are of equal length (Coxeter 1973, p. 29). Plate II (following p. 32 of ...