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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.
Gary is located along the southern shore of Lake Michigan about 25 miles (40 km) southeast of downtown Chicago. The city is the western gateway to the Indiana Dunes National Park, and is within the Chicago metropolitan area. [6] [7] Gary was named after lawyer Elbert Henry Gary, who was the founding chairman of the United States Steel Corporation.
Munster is a suburban town in North Township, Lake County, Indiana, United States.It is in the Chicago metropolitan area, approximately 30 miles (48 km) southeast of the Chicago Loop, and shares municipal boundaries with Hammond to the north, Highland to the east, Dyer and Schererville to the south, and Lansing and Lynwood directly west over the Illinois border.
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 ...
East Chicago is a city in Lake County, Indiana, United States. The population was 26,370 at the 2020 census . Centered around heavy industry, the city is home to the Indiana Harbor and Ship Canal , an artificial freshwater harbor characterized by industrial and manufacturing activity.
Dyer is roughly 30 miles from downtown Chicago and 12 miles from Chicago's south side. Dyer is built on mostly flat land with an exception being the steep sand ridge south of US Highway 30. This is the Glenwood Shoreline. According to the 2010 census, Dyer has a total area of 6.1 square miles (15.80 km 2), all land. [9]
With a population of 829,817, Indianapolis is the largest city in Indiana and the 12th-largest in the United States, according to the 2010 census. Three other cities in Indiana have a population greater than 100,000: Fort Wayne (253,617), Evansville (117,429) and South Bend (101,168). [124]
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.