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Ultraparallel Theorem
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Geliefert zwischen Do., 05.02.2026 und Fr., 06.02.2026
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High Quality Content by WIKIPEDIA articles! In hyperbolic geometry, the ultraparallel theorem states that every pair of ultraparallel lines in the hyperbolic plane has a unique common perpendicular hyperbolic line. In the Klein model of the hyperbolic plane, two ultraparallel lines correspond to two non-intersecting chords. The poles of these two lines are the respective intersections of the tangent lines to the unit circle at the endpoints of the chords. Lines perpendicular to line A are modeled by chords whose extension passes through the pole of A. Hence we draw the unique line between the poles of the two given lines, and intersect it with the unit disk; the chord of intersection will be the desired common perpendicular of the ultraparallel lines. If one of the chords happens to be a diameter, we do not have a pole, but in this case any chord perpendicular to the diameter is perpendicular as well in the hyperbolic plane, and so we draw a line through the pole of the other line intersecting the diameter at right angles to get the common perpendicular.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131167904
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- Größe H4mm x B220mm x T150mm
- EAN 9786131167904
- Format Fachbuch
- Titel Ultraparallel Theorem
- Gewicht 128g
- Herausgeber Betascript Publishing
- Anzahl Seiten 84
- Genre Mathematik
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