Difference between revisions of "Elliptic space"
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| − | Elliptic space is an example of a geometry in which Euclid's [[parallel postulate]] does not hold. Instead, as in [[spherical geometry]], there are no [[parallel | + | Elliptic space is an example of a geometry in which Euclid's [[parallel postulate]] does not hold. Instead, as in [[spherical geometry]], there are no [[parallel line]]s since any two [[line]]s [[intersect]]. However, unlike in [[spherical geometry]], two [[line]]s are usually assumed to [[intersect]] at a single [[point]] (rather than two). [[Elliptic geometry]] has a variety of properties that differ from those of classical [[Euclidean plane]] geometry. For example, the [[sum]] of the [[interior angle]]s of any [[triangle]] is always greater than 180°. |
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Latest revision as of 20:52, 27 February 2025
Elliptic space is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Elliptic geometry has a variety of properties that differ from those of classical Euclidean plane geometry. For example, the sum of the interior angles of any triangle is always greater than 180°.
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