Difference between revisions of "Elliptical geometry"
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| − | '''Elliptical geometry''' is a term used to refer to [[geometry | geometries]] in which there are no parallel lines. 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. | + | '''Elliptical geometry''' is a term used to refer to [[geometry | 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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* [[Hyperbolic geometry]] | * [[Hyperbolic geometry]] | ||
| + | * [http://www.ams.org/journals/bull/1902-08-10/S0002-9904-1902-00923-3/S0002-9904-1902-00923-3.pdf Mathematical Problems Lecture] | ||
{{stub}} | {{stub}} | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
Latest revision as of 12:22, 20 November 2012
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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