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In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r. Special cases are right triangles (p q 2).
Conformal symmetries of a sphere are generated by the inversion in all of its hyperspheres. On the other hand, Riemannian isometries of a sphere are generated by inversions in geodesic hyperspheres (see the Cartan–Dieudonné theorem.) The Euclidean sphere can be mapped to the conformal sphere in a canonical manner, but not vice versa.
Indiana University Indianapolis (IU Indianapolis or IU Indy) is an urban public research university located in Indianapolis, Indiana, and is a core campus of the Indiana University system. It was founded on July 1, 2024 after its predecessor institution, Indiana University–Purdue University Indianapolis (IUPUI), split into IU Indianapolis and ...
Indiana University has two core campuses, five regional campuses, and two regional centers under the administration of IU Indianapolis. Indiana University Bloomington (IU Bloomington) is the flagship campus of Indiana University. [ 3 ]
T. W. Jacobsen, a professor of classical archaeology and classical studies at Indiana University, began excavations at Franchthi Cave in 1967.The dig was only intended to temporarily occupy Jacobsen and his fellow researcher, M.H. Jameson, for one short season, while they waited for land use issues to be resolved at a nearby site.
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 ...
The Gauss map can be defined for hypersurfaces in R n as a map from a hypersurface to the unit sphere S n − 1 ⊆ R n. For a general oriented k-submanifold of R n the Gauss map can also be defined, and its target space is the oriented Grassmannian ~,, i.e. the set of all oriented k-planes in R n. In this case a point on the submanifold is ...
The University of Indianapolis (UIndy) is a private United Methodist Church-affiliated university in Indianapolis, Indiana. It offers Associate, Bachelor's, Master's, and Doctoral degrees. [ 5 ] It was founded in 1902 as Indiana Central University and was popularly known as Indiana Central College from 1921 until 1975.