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Journal of Geometry

, 110:13 | Cite as

Ceva’s and Menelaus’ theorems for higher-dimensional simplexes

  • Akira UshijimaEmail author
Article
  • 67 Downloads

Abstract

We prove that Ceva’s and Menelaus’ theorems for higher-dimensional Euclidean simplexes provided by Buba-Brozawa also hold in spherical and hyperbolic spaces.

Keywords

Ceva’s theorem Menelaus’ theorem simplex hyperbolic geometry spherical geometry 

Mathematics Subject Classification

Primary 51M09 Secondary 51N20 

Notes

Acknowledgements

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 [3].

References

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics and Physics Institute of Science and EngineeringKanazawa UniversityIshikawaJapan

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