Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-14T19:09:08.530Z Has data issue: false hasContentIssue false

83.46 Equifacial tetrahedra and a famous location problem

Published online by Cambridge University Press:  01 August 2016

Y. S. Kupitz
Affiliation:
Mathematical Institute, The Hebrew University of Jerusalem, Jerusalem, Israel
H. Martini
Affiliation:
Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, GERMANY

Abstract

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Notes
Copyright
Copyright © The Mathematical Association 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Chorlton, F. A geometrical result established using statics, Math. Gaz. 66 (1982) pp. 4647.CrossRefGoogle Scholar
2. Pick, G. Mathematical appendix to: Weber, A. Über den Standort der Industrien, Tübingen (1909) English translation by Friedrich, C. J. Theory of the location of industries, Univ. of Chicago Press (1929).Google Scholar
3. Pólya, G. Induction and analogy in mathematics, Princeton Univ. Press, Princeton (1954).Google Scholar
4. Glaister, P. Tetrahedra—Fermat points and centroids, Math. Gaz. 77 (1993) pp. 360361.Google Scholar
5. Lindelöf, L. Sur les maxima et minima d’une fonction des rayons vecteurs menés d’un point mobile à plusieurs centres fixes, Acta Soc. Sc. Fenn. 8 (1867) pp. 191203.Google Scholar
6. Sturm, R. Über den Punkt kleinster Entfernungssumme von gegebenen Punkten, J. reine angew. Math. 97 (1884) pp. 4961.Google Scholar
7. Altshiller-Court, N. Modern pure solid geometry, Chelsea, New York (1964).Google Scholar
8. Bottema, O. The centroids of a simplex (Dutch), Euclides (Groningen) 47 (1971/1972) pp. 206210.Google Scholar
9. Couderc, P. Ballicioni, A. Premier livre du tétraè dre, Gauthier-Villars, Paris (1953).Google Scholar
10. Dévide, V. Über eine Klasse von Tetraedern, Rad. Jugosl. Akad. Znan. Umjet. 408 (1984) pp. 4550.Google Scholar
11. Kupitz, Y. S. Martini, H. The Fermat-Torricelli point and isosceles tetrahedra, Journal of Geometry 49 (1994) pp. 150162.Google Scholar
12. Thébault, V. Parmi les belles figures de la géométrie dans l’espaces (Géométrie du tétraè dre), Librairie Vuibert, Paris (1955).Google Scholar
13. Post, K. A. Geodesic lines on a closed convex polyhedron. Studio Sci. Math. Hungar. 5 (1970) pp. 411416.Google Scholar
14. Strantzen, J. Lu, Y. Regular simple geodesic loops on a tetrahedron, Geom. Dedicata 42 (1992) pp. 139153.CrossRefGoogle Scholar
15. Kupitz, Y. S. Martini, H. Geometric aspects of the generalized Fermat-Torricelli problem, In: Intuitive geometry (Budapest, 1995), Eds. Bárány, I. and Böröczky, K. Bolyai Soc. Math. Studies 6 (1997) pp. 55127.Google Scholar
16. Frankl, P. Maehara, H. Simplices with given 2-faces areas, European Journal of Combinatorics 11 (1990) pp. 241247.Google Scholar
17. Martini, H. Regular simplices in spaces of constant curvature, Amer. Math. Monthly 100 (1993) pp. 169171.Google Scholar
18. Jarden, D. The Tetrahedron (A collection of papers), published by the author, Jerusalem, (1964).Google Scholar