Hyperbolic Geometry - Revision history

Caseorganic at 13:04, 25 August 2026

2026-08-25T13:04:05Z

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 ===Definition===
-"In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai-Lobachevskian geometry) is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced. The parallel postulate in Euclidean geometry is equivalent to the statement that, in two dimensional space, for any given line l and point P not on l, there is exactly one line through P that does not intersect l; i.e., that is parallel to l. In hyperbolic geometry there are at least two distinct lines through P which do not intersect l, so the parallel postulate is false. Models have been constructed within Euclidean geometry that obey the axioms of hyperbolic geometry, thus proving that the parallel postulate is independent of the other postulates of Euclid" [http://en.wikipedia.org/wiki/Hyperbolic_geometry].
+"In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced. The parallel postulate in Euclidean geometry is equivalent to the statement that, in two dimensional space, for any given line ''l'' and point ''P'' not on ''l'', there is exactly one line through ''P'' that does not intersect ''l''; i.e., that is parallel to ''l''. In hyperbolic geometry there are at least two distinct lines through ''P'' which do not intersect ''l'', so the parallel postulate is false. Models have been constructed within Euclidean geometry that obey the axioms of hyperbolic geometry, thus proving that the parallel postulate is independent of the other postulates of Euclid."<ref>[https://en.wikipedia.org/wiki/Hyperbolic_geometry Hyperbolic geometry]; see also [https://mathworld.wolfram.com/HyperbolicGeometry.html Wolfram MathWorld].</ref>
-<private>Place image here of social situation caused by hyperbolic social relations and desciebe, if have time. Esle, remove this entry in its entirety</private>
+The geometry was developed independently by Nikolai Lobachevsky and János Bolyai in the 1820s and 1830s, with Carl Friedrich Gauss having reached similar conclusions privately and declined to publish them.

Caseorganic at 00:01, 5 June 2011

2011-06-05T00:01:18Z

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	<private>Place image here of social situation caused by hyperbolic social relations and desciebe, if have time. Esle, remove this entry in its entirety</private>		<private>Place image here of social situation caused by hyperbolic social relations and desciebe, if have time. Esle, remove this entry in its entirety</private>

	~~[[Category:Book Pages]]~~
	~~[[Category:Unfinished]]~~

Caseorganic at 16:54, 16 May 2011

2011-05-16T16:54:00Z

← Older revision		Revision as of 16:54, 16 May 2011
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	===Definition===		===Definition===
	"In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai-Lobachevskian geometry) is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced. The parallel postulate in Euclidean geometry is equivalent to the statement that, in two dimensional space, for any given line l and point P not on l, there is exactly one line through P that does not intersect l; i.e., that is parallel to l. In hyperbolic geometry there are at least two distinct lines through P which do not intersect l, so the parallel postulate is false. Models have been constructed within Euclidean geometry that obey the axioms of hyperbolic geometry, thus proving that the parallel postulate is independent of the other postulates of Euclid" [http://en.wikipedia.org/wiki/Hyperbolic_geometry].		"In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai-Lobachevskian geometry) is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced. The parallel postulate in Euclidean geometry is equivalent to the statement that, in two dimensional space, for any given line l and point P not on l, there is exactly one line through P that does not intersect l; i.e., that is parallel to l. In hyperbolic geometry there are at least two distinct lines through P which do not intersect l, so the parallel postulate is false. Models have been constructed within Euclidean geometry that obey the axioms of hyperbolic geometry, thus proving that the parallel postulate is independent of the other postulates of Euclid" [http://en.wikipedia.org/wiki/Hyperbolic_geometry].

			<private>Place image here of social situation caused by hyperbolic social relations and desciebe, if have time. Esle, remove this entry in its entirety</private>

	[[Category:Book Pages]]		[[Category:Book Pages]]
	[[Category:Unfinished]]		[[Category:Unfinished]]

Caseorganic: Created page with '===Definition=== "In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai-Lobachevskian geometry) is a non-Euclidean geometry, meaning that the parallel…'

2011-01-31T21:41:11Z

Created page with '===Definition=== "In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai-Lobachevskian geometry) is a non-Euclidean geometry, meaning that the parallel…'

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===Definition===
"In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai-Lobachevskian geometry) is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced. The parallel postulate in Euclidean geometry is equivalent to the statement that, in two dimensional space, for any given line l and point P not on l, there is exactly one line through P that does not intersect l; i.e., that is parallel to l. In hyperbolic geometry there are at least two distinct lines through P which do not intersect l, so the parallel postulate is false. Models have been constructed within Euclidean geometry that obey the axioms of hyperbolic geometry, thus proving that the parallel postulate is independent of the other postulates of Euclid" [http://en.wikipedia.org/wiki/Hyperbolic_geometry].

[[Category:Book Pages]]
[[Category:Unfinished]]