Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-25T23:01:50.760Z Has data issue: false hasContentIssue false

Constructions In Hyperbolic Geometry

Published online by Cambridge University Press:  20 November 2018

Frans Handest*
Affiliation:
University of Toronto
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Introduction. In hyperbolic geometry we have three compasses, namely an ordinary compass for drawing ordinary circles with a given centre and a given radius, a hypercompass for drawing hypercycles with a given axis and a given radius, and a horocompass for drawing horocycles with a given diameter and passing through a given point.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Andrianov, S. N., A synthetic demonstration of a theorem in Lobachevskian geometry (Russian), Učenye Zapiski Kazan, Univ. 101, kn 3 (1941), 2223.Google Scholar
2. Coxeter, H. S. M., Review of Andrianov's paper, Math. Rev., 10 (1949), 319.Google Scholar
3. Höttemann, F., Ein Beitrag zu den Steinerschen Konstruktionen, Jber. dtsch. Math. Ver., 43 (1934), 184185.Google Scholar
4. Juel, C., Vorlesungen öber projektive Geometrie (Berlin, 1934).Google Scholar
5. Liebmann, H., Nichteuklidische Geometrie, Sammlung Schubert XLIX (Leipzig, 1912).Google Scholar
6. Nestorovič, N. M., Sur Vequivalence par rapport à la construction du complexe MB et du complexe E, C.R. Acad. Sci. URSS (N.S.), 22 (1939), 224227.Google Scholar
7. Nestorovič, N. M., Sur la puissance constructive d'un complexe E sur le plan de Lobatchevski, C.R. Acad. Sci. URSS (N.S.), 43 (1944), 186188.Google Scholar
8. Nestorovič, N. M., Geometrical constructions with horocycle-compass and ruler in the Lobatčevskiĭ plane (Russian), Doklady Akad. Nauk. SSSR (N.S.), 66 (1949), 10471050.Google Scholar
9. Nestorovič, N. M., On the equivalence of a hypercircle to an ordinary circle in constructions in the Lobačevskiĭ plane (Russian), Doklady Akad. Nauk. SSSR (N.S.), 69 (1949), 731735.Google Scholar
10. Obláth, R., Bemerkungen zur Theorie der geometrischen Konstruktionen, Monatsh. Math. Phys. 26 (1915), 295298.Google Scholar
11. Schur, F., Grundlagen der Geometrie (Leipzig, 1909).Google Scholar
12. Smogorževskiĭ, A. S., Geometric constructions in the Lobačevskĭĭ plane (Serbo-croatian), Gosudarstv. Izdat. Tehn.-Teor. Lit., (Moscow and Leningrad, 1951).Google Scholar
13. Zöhlke, P., Konstruktionen in begrenzter Ebene, Mathematische Bibliothek XI (Leipzig, 1913).Google Scholar