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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.
The Indiana University Bloomington campus of 1,933 acres (7.82 km 2) includes abundant green space and historic buildings dating to the university's reconstruction in the late nineteenth century. The campus rests on a bed of Indiana Limestone , specifically Salem Limestone and Harrodsburg Limestone , with outcroppings of St. Louis Limestone .
The Bloomington campus is home to numerous premier Indiana University schools, including the College of Arts and Sciences, the Jacobs School of Music, an extension of the Indiana University School of Medicine, the School of Informatics, Computing, and Engineering, which includes the former School of Library and Information Science (now ...
Kirkwood Observatory is an astronomical observatory owned and operated by Indiana University. It is located in Bloomington, Indiana, United States. It is named for Daniel Kirkwood (1814–1895) an astronomer and professor of mathematics at Indiana University who discovered the divisions of the asteroid belt known as the Kirkwood Gaps.
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 ...
The sum of the angles of a spherical triangle is not equal to 180°. A sphere is a curved surface, but locally the laws of the flat (planar) Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees. A sphere with a spherical triangle on it.
A topological sphere need not be smooth; if it is smooth, it need not be diffeomorphic to the Euclidean sphere (an exotic sphere). The sphere is the inverse image of a one-point set under the continuous function ‖ x ‖ , so it is closed; S n is also bounded, so it is compact by the Heine–Borel theorem .
Independent regional campuses, such as Indiana University Kokomo, are included. Indiana has several universities that meet the definition of a flagship institution, with the most commonly cited being Indiana University Bloomington and Purdue University. The Indiana state code designates the Indiana University System as the university of the ...