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A lune is a plane figure bounded by two circular arcs of unequal radii, i.e., a crescent. (By contrast, a plane figure bounded by two circular arcs of equal radius is known ...

An algorithm for finding the nearest local minimum of a function which presupposes that the gradient of the function can be computed. The method of steepest descent, also ...

The point on a line segment dividing it into two segments of equal length. The midpoint of a line segment is easy to locate by first constructing a lens using circular arcs, ...

The geodesic on an oblate spheroid can be computed analytically, although the resulting expression is much more unwieldy than for a simple sphere. A spheroid with equatorial ...

O_h is the point group of symmetries of the octahedron having order 48 that includes inversion. It is also the symmetry group of the cube, cuboctahedron, and truncated ...

If two points A and A^' are inverse (sometimes called conjugate) with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to ...

A pyramidal frustum is a frustum made by chopping the top off a pyramid. It is a special case of a prismatoid. For a right pyramidal frustum, let s be the slant height, h the ...

The radical lines of three circles are concurrent in a point known as the radical center (also called the power center). This theorem was originally demonstrated by Monge ...

The Smale horseshoe map consists of a sequence of operations on the unit square. First, stretch in the y direction by more than a factor of two, then compress in the x ...

The small cubicuboctahedron is the uniform polyhedron with Maeder index 13 (Maeder 1997), Wenninger index 69 (Wenninger 1989), Coxeter index 38 (Coxeter et al. 1954), and ...