Search results
Results from the WOW.Com Content Network
Stereographic projection of the unit sphere from the north pole onto the plane z = 0, shown here in cross section. The unit sphere S 2 in three-dimensional space R 3 is the set of points (x, y, z) such that x 2 + y 2 + z 2 = 1.
The stereographic projection maps the -sphere onto -space with a single adjoined point at infinity; under the metric thereby defined, {} is a model for the -sphere. In the more general setting of topology , any topological space that is homeomorphic to the unit n {\displaystyle n} -sphere is called an n ...
Stereographic projection of complex numbers and onto the points and of the Riemann sphere - connect () with A or B by a line and determine the intersection with the sphere. In mathematics , the Riemann sphere , named after Bernhard Riemann , [ 1 ] is a model of the extended complex plane (also called the closed complex plane ): the complex ...
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 ...
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. Like the orthographic projection and gnomonic projection, the stereographic projection is an azimuthal projection, and when on a sphere, also a perspective projection.
Stereographic projection as an inversion of a sphere. A stereographic projection usually projects a sphere from a point (north pole) of the sphere onto the tangent plane at the opposite point (south pole). This mapping can be performed by an inversion of the sphere onto its tangent plane.
Each torus is the stereographic projection of the inverse image of a circle of latitude of the 2-sphere. (Topologically, a torus is the product of two circles ...
Stereographic projection of a pole. The upper sphere is projected on a plane using the stereographic projection. Consider the (x,y) plane of the reference basis; its trace on the sphere is the equator of the sphere. We draw a line joining the South pole with the pole of interest P.