Elliptical geometry is a term used to refer to geometries in which there are no parallel lines and the third axiom of order, which states that, of three points of a straight line, there is one and only one that lies between the other two, cannot be satisfied. One possible representation of elliptical geometry is on a sphere. This is because the closest analogue to lines on a sphere is a great circle, and any two great circles on a sphere must intersect.
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