File:Hyperbolic parallelity.svg
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English: The picture illustrates David Hilbert's formulation for "hyperbolic parallelity" (in Felix Klein's model of a hyperbolic plane). For a hyperbolic line b and a point A not on b there are exactly two rays a1 and a2 with initial point A with the properties: (1) Both do not meet b. (2) Every ray beginning in A and lying WITHIN the angle between a1 and a2 (cyan) meets b. (3) Every ray beginning in A and lying OUTSIDE the angle between a1 and a2 misses b. Deutsch: Das Bild illustriert Hilberts hyperbolisches Parallelenaxiom im Kleinschen Kreisscheibenmodell der (reellen) hyperbolischen Geometrie. Für eine hyperbolische Gerade b und einen Punkt A, der nicht auf b liegt gibt es genau zwei Halbstrahlen a1 und a2, die in A beginnen und die folgenden Eigenschaften haben: (1) Beide schneiden b nicht. (2) Jeder Strahl mit Anf.pkt. A, der INNERHALB des durch (a1,a2) bestimmten Winkelfeldes liegt, schneidet b. (3) Jeder Strahl mit Anf.pkt. A, der AUSSERHALB des durch (a1,a2) bestimmten Winkelfeldes liegt, schneidet b NICHT. Die Trägergeraden der "Grenzstrahlen" a1, a2 werden manchmal als DIE "Holoparallelen " zu b durch A bezeichnet. |
| Date | |
| Source | Own work |
| Author | KlioKlein |
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I, the copyright holder of this work, hereby publish it under the following license:
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:32, 4 August 2013 | | 160 × 160 (2 KB) | KlioKlein (talk | contribs) | Marked the inner points of the circle, as real points of the Model, hided the hyperbolic parallels behind the circle line. |
| 07:01, 25 July 2013 |  | 160 × 160 (2 KB) | KlioKlein (talk | contribs) | User created page with UploadWizard |
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