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The median triangle theorem as an entrance to certain issues in higher-dimensional geometry

Abstract

The median triangle theorem states that the three medians of a triangle can serve as the sides of another triangle. This theorem together with other related results from plane geometry are presented, and intriguing questions are set about analogues in higher dimensions. Answers to these questions are also presented, and by this way a reader can smoothly enter to certain issues of tetrahedral and then higher-dimensional geometry.

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Acknowledgements

We would like to thank the anonymous referees for their valuable comments, which helped improve the presentation of the article.

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Correspondence to Panagiotis T. Krasopoulos.

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Hajja, M., Krasopoulos, P.T. & Martini, H. The median triangle theorem as an entrance to certain issues in higher-dimensional geometry. Math Semesterber (2021). https://doi.org/10.1007/s00591-021-00308-5

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Keywords

  • Median triangle theorem
  • Apollonius’ theorem
  • Pompeiu’s theorem
  • Centroid
  • Tetrahedron
  • Simplex