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Since the surface of a sphere is different from a(n Eucleadian) plane, are there shapes similar/analogous to Eucledian plane shapes? Are there analogues of a square, a circle, a star polygon, etc? If yes, how do they look, what are they called, and what are the properties? Are they considered 2 dimensional?

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    There are spherical triangles, [spherical polygons](http://mathworld.wolfram.com/SphericalPolygon.html)...2011-05-02
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    spherical geometry and trigonometry have been used for a long time by astronomers and sailors2011-05-02

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