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The location of the state of Indiana in the United States of America An enlargeable map of the state of Indiana An enlargeable map of the 92 counties of the state of Indiana. Indigenous peoples. Evidence of human activity date as early 8000 BC. Hopewell culture developed agriculture and begins Indiana's first permanent settlements. 200 BC-400 AD
Evansville, the third largest city in Indiana, is located in the southwestern corner of the state. It is located in a tri-state area that includes Illinois, Indiana, and Kentucky. The southern cities of Clarksville, Jeffersonville, and New Albany are part of the Louisville metropolitan area and are in the area called Kentuckiana.
"Second-class" cities had a population of at least 34,000 and up to 600,000 at time of designation, and have a nine-member city council and an elected clerk. Indianapolis is the only "first-class" city in Indiana under state law, making it subject to a consolidated city-county government known as Unigov. A town is differentiated from a city in ...
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.
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For example, one sphere that is described in Cartesian coordinates with the equation x 2 + y 2 + z 2 = c 2 can be described in spherical coordinates by the simple equation r = c. (In this system—shown here in the mathematics convention—the sphere is adapted as a unit sphere, where the radius is set to unity and then can generally be ignored ...
Indiana (/ ˌ ɪ n d i ˈ æ n ə / ⓘ IN-dee-AN-ə) [15] is a state in the Midwestern region of the United States.It borders Lake Michigan to the northwest, Michigan to the north and northeast, Ohio to the east, the Ohio River and Kentucky to the south and southeast, and the Wabash River and Illinois to the west.
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).