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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 ...

A mathematical structure A is said to be closed under an operation + if, whenever a and b are both elements of A, then so is a+b. A mathematical object taken together with ...

A dihedron is a regular tiling or map on a sphere composed of two regular p-gons, each occupying a hemisphere and with edge lengths of 2pi/p on a unit sphere. Its Schläfli ...

The plumbing of a p-sphere and a q-sphere is defined as the disjoint union of S^p×D^q and D^p×S^q with their common D^p×D^q, identified via the identity homeomorphism. This ...

The surface corresponding to the region of obscuration when a solid is illuminated from a point light source (located at the radiant point). A disk is the shadow of a sphere ...

A closed geometric figure on the surface of a sphere which is formed by the arcs of great circles. The spherical polygon is a generalization of the spherical triangle. If ...

To each epsilon>0, there corresponds a delta such that ||f-g||<epsilon whenever ||f||=||g||=1 and ||(f+g)/2||>1-delta. This is a geometric property of the unit sphere of ...

The south pole is the point on a sphere with minimum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

The parametric equations for a catenary are x = t (1) y = cosht, (2) giving the involute as x_i = t-tanht (3) y_i = secht. (4) The involute is therefore half of a tractrix.

The linear fractional transformation z|->(i-z)/(i+z) that maps the upper half-plane {z:I[z]>0} conformally onto the unit disk {z:|z|<1}.