Difference between revisions of "Hyperbolic geometry"
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| − | Hyperbolic geometry (geometry of Lobachevsky) is the non-Euclidean geometry in which the parallel postulate is replaced. In David Hilbert's 1900 lecture before the International Congress of Mathematicians, he states that "We may therefore say that [hyperbolic geometry] is a geometry standing next to euclidean geometry." | + | Hyperbolic geometry (geometry of Lobachevsky) is the non-Euclidean geometry in which the parallel postulate is replaced. Instead of one parallel line through any point, there are infinitely many of them. In David Hilbert's 1900 lecture before the International Congress of Mathematicians, he states that "We may therefore say that [hyperbolic geometry] is a geometry standing next to euclidean geometry." |
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| + | ==Properties== | ||
| + | * Angles in a polygon add up to less than they're supposed to | ||
| + | * No finite 2-manifold can represent it accurately | ||
| + | * Lines that are parallel to another line need not be parallel | ||
| + | |||
| + | == See Also == | ||
| + | |||
| + | *[[Elliptical 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}} | ||
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| + | [[Category:Geometry]] | ||
Latest revision as of 19:57, 3 November 2024
Hyperbolic geometry (geometry of Lobachevsky) is the non-Euclidean geometry in which the parallel postulate is replaced. Instead of one parallel line through any point, there are infinitely many of them. In David Hilbert's 1900 lecture before the International Congress of Mathematicians, he states that "We may therefore say that [hyperbolic geometry] is a geometry standing next to euclidean geometry."
Properties
- Angles in a polygon add up to less than they're supposed to
- No finite 2-manifold can represent it accurately
- Lines that are parallel to another line need not be parallel
See Also
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