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A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere, ...

The spherical curve taken by a ship which travels from the south pole to the north pole of a sphere while keeping a fixed (but not right) angle with respect to the meridians. ...

A square pyramid is a pyramid with a square base. It is a pentahedron. The lateral edge length e and slant height s of a right square pyramid of side length a and height h ...

Consider the solid enclosed by the three hyperboloids specified by the inequalities x^2+y^2-z^2 <= 1 (1) y^2+z^2-x^2 <= 1 (2) z^2+x^2-y^2 <= 1. (3) This work dubs this solid ...

Just as the ratio of the arc length of a semicircle to its radius is always pi, the ratio P of the arc length of the parabolic segment formed by the latus rectum of any ...

The Alexander polynomial is a knot invariant discovered in 1923 by J. W. Alexander (Alexander 1928). The Alexander polynomial remained the only known knot polynomial until ...

In most modern literature, a Boolean model is a probabilistic model of continuum percolation theory characterized by the existence of a stationary point process X and a ...

Bowling, known as "ten pins" throughout most of the world, is a game played by rolling a heavy ball down a long narrow track and attempting to knock down ten pins arranged in ...

The word configuration is sometimes used to describe a finite collection of points p=(p_1,...,p_n), p_i in R^d, where R^d is a Euclidean space. The term "configuration" also ...

The cycloid is the locus of a point on the rim of a circle of radius a rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find ...