Ceva’s and Menelaus’ theorems for higher-dimensional simplexes
- 67 Downloads
We prove that Ceva’s and Menelaus’ theorems for higher-dimensional Euclidean simplexes provided by Buba-Brozawa also hold in spherical and hyperbolic spaces.
KeywordsCeva’s theorem Menelaus’ theorem simplex hyperbolic geometry spherical geometry
Mathematics Subject ClassificationPrimary 51M09 Secondary 51N20
The author wishes to express his gratitude to the anonymous referee for improving the manuscript, in particular, for pointing out the relationship between the function \(\ell \) and .
- 5.Papadopoulos, A., Su, W.: On hyperbolic analogues of some classical theorems in spherical geometry. In: Hyperbolic Geometry and Geometric Group Theory, vol. 73 of Adv. Stud. Pure Math., pp. 225–253. Math. Soc. Japan, Tokyo (2017)Google Scholar
- 6.Ratcliffe, J.G.: Foundations of Hyperbolic Manifolds, volume 149 of Graduate Texts in Mathematics, 2nd edn. Springer, New York (2006)Google Scholar