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Gott, Goldberg and Vanderbei’s double-sided disk map was designed to minimize all six types of map distortions. Not properly "a" map projection because it is on two surfaces instead of one, it consists of two hemispheric equidistant azimuthal projections back-to-back. [5] [6] [7] 1879 Peirce quincuncial: Other Conformal Charles Sanders Peirce
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.
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.
The Illinois–Indiana–Kentucky tri-state area within their states. Dark shaded counties were included only by WTVW prior to the rollout of digital television.. The Illinois–Indiana–Kentucky tri-state area is a tri-state area where the U.S. states of Illinois, Indiana, and Kentucky intersect, and a region of the Upland South.
Northern Illinois is dominated by the Chicago metropolitan area, including the city of Chicago, its suburbs, and the adjoining exurban area into which the metropolis is expanding. The " collar counties " are the five counties that surround the centrally located Cook County in the Chicago metropolitan area: DuPage County, Kane County, Lake ...
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).
Middlebury is a town in Middlebury Township, Elkhart County, Indiana, United States. It is located approximately 35 miles east of South Bend, 130 miles east of Chicago, Illinois, and 165 miles north of Indianapolis. Middlebury is nestled in Northern Indiana's Amish country. As of the 2010 census, the town population was 3,420.
The city of Rockford, Illinois's third-largest city and center of the state's fourth largest metropolitan area, sits along Interstates 39 and 90 some 75 mi (121 km) northwest of Chicago. The Quad Cities region, located along the Mississippi River in northern Illinois, had a population of 381,342 in 2011.