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## Main Question or Discussion Point

Are circles considered straight lines in Non-Euclidean Geometry?

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Are circles considered straight lines in Non-Euclidean Geometry?

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HallsofIvy

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In elliptic geometry, "straight lines" (as yenchin said, geodesics) may be closed paths but, technically, there still exist "circles" that are quite different from those. In hyperbolic geometry, all "lines" are unbounded and so are definitely NOT "circles".

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tiny-tim

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Hi ƒ(x)!

In Lobachevsky space, all straight lines go off to infinity, so none of them are circles.

(Though there is a "map" of Lobachevsky space, in which all the straight lines are

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