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The orthographic projection is a projection from infinity that preserves neither area nor angle. It is given by x = cosphisin(lambda-lambda_0) (1) y = ...

The van der Grinten projection is a map projection given by the transformation x = (1) y = sgn(phi)(pi|PQ-Asqrt((A^2+1)(P^2+A^2)-Q^2)|)/(P^2+A^2), (2) where A = ...

Let a be the angle between v and x, b the angle between v and y, and c the angle between v and z. Then the direction cosines are equivalent to the (x,y,z) coordinates of a ...

Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of ...

An authalic latitude which is directly proportional to the spacing of parallels of latitude from the equator on an ellipsoidal Mercator projection. It is defined by ...

An auxiliary latitude also called the reduced latitude and denoted eta or theta. It gives the latitude on a sphere of radius a for which the parallel has the same radius as ...

A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines. This can be ...

An auxiliary latitude which gives a sphere having correct distances along the meridians. It is denoted mu (or omega) and is given by mu=(piM)/(2M_p). (1) M_p is evaluated for ...

The necessary condition for the polychoron to be regular (with Schläfli symbol {p,q,r}) and finite is cos(pi/q)<sin(pi/p)sin(pi/r). Sufficiency can be established by ...

Given a spheroid with equatorial radius a and polar radius c, the ellipticity is defined by e={sqrt((a^2-c^2)/(a^2)) c<a (oblate spheroid); sqrt((c^2-a^2)/(c^2)) c>a (prolate ...