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Stereographic projection is conformal, meaning that it preserves the angles at which curves cross each other (see figures). On the other hand, stereographic projection does not preserve area; in general, the area of a region of the sphere does not equal the area of its projection onto the plane. The area element is given in (X, Y) coordinates by
Stereographic projection of the world north of 30°S. 15° graticule. The stereographic projection with Tissot's indicatrix of deformation.. The stereographic projection, also known as the planisphere projection or the azimuthal conformal projection, is a conformal map projection whose use dates back to antiquity.
A Wulff net is used to read a pole figure. The stereographic projection of a trace is an arc. The Wulff net is arcs corresponding to planes that share a common axis in the (x,y) plane. If the pole and the trace of a plane are represented on the same diagram, then we turn the Wulff net so the trace corresponds to an arc of the net;
The title can be translated as "celestial plane" or "star chart". In this work Ptolemy explored the mathematics of mapping figures inscribed in the celestial sphere onto a plane by what is now known as stereographic projection. This method of projection preserves the properties of circles.
A stereographic projection of the world north of 30°S. The stereographic projection is a ... net shown here is the stereographic projection ... interest in anything ...
A stereographic projection of a Clifford torus performing a simple rotation Topologically a rectangle is the fundamental polygon of a torus, with opposite edges sewn together. In geometric topology, the Clifford torus is the simplest and most symmetric flat embedding of the Cartesian product of two circles S 1 a and S 1
A single 30-tetrahedron Boerdijk–Coxeter helix ring within the 600-cell, seen in stereographic projection. [ad] A 30-tetrahedron ring can be seen along the perimeter of this 30-gonal orthogonal projection of the 600-cell. [an] The 30-cell ring as a {30/11} polygram of 30 edges wound into a helix that twists around its axis 11 times.
Stereographic projection of a 3-sphere (again removing the north pole) maps to three-space in the same manner. (Notice that, since stereographic projection is conformal, round spheres are sent to round spheres or to planes.) A somewhat different way to think of the one-point compactification is via the exponential map. Returning to our picture ...