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Recovering a Circumscriptible Tetrahedron from Its Face Areas

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Abstract

It is shown that a circumscriptible tetrahedron is completely determined by its face areas. This contrasts heavily with the fact that a general tetrahedron is not completely determined by its face areas, even if its volume and its circumradius are also given.

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References

  1. Altshiller-Court, N.: Modern Pure Solid Geometry, second edn. Chelsea Publishing Company, New York (1964)

    MATH  Google Scholar 

  2. Barbeau, E.J., Klamkin, M.S., Moser, W.O.J.: Five Hundred Mathematical Challenges. MAA, Washington, D. C. (1995)

    MATH  Google Scholar 

  3. Berger, M.: Geometry I. Springer, New York (1987)

    Book  Google Scholar 

  4. Gerber, L.: The orthocentric simplex as an extreme simplex. Pac. J. Math. 56, 97–111 (1975)

    Article  MathSciNet  Google Scholar 

  5. Hajja, M.: Coincidence of centers of edge-incentric, or balloon, simplices. Res. Math. 49, 237–263 (2006)

    Article  MathSciNet  Google Scholar 

  6. Hajja, M., Hayajneh, M., Martini, H.: More characterizations of certain special families of simplices. Res. Math. 69, 23–47 (2016)

    Article  MathSciNet  Google Scholar 

  7. Herzog, F.: Completely tetrahedral sextuples. Am. Math. Mon. 66, 460–464 (1959)

    Article  MathSciNet  Google Scholar 

  8. Izumi, S.: Sufficiency of simplex inequalities. Proc. Am. Math. Soc. 144, 1299–1307 (2016)

    Article  MathSciNet  Google Scholar 

  9. Mazur, M.: Problem 10717. Am. Math. Mon. 106, 167 (1999)

    Article  MathSciNet  Google Scholar 

  10. Mazur, M.: Solution. ibid 107, 466–467 (2000)

  11. Sommerville, D.M.Y.: An Introduction to the Geometry of \(N\) Dimensions. Dover, New York (1958)

    MATH  Google Scholar 

  12. Veljan, D.: The distance matrix of a simplex. Croat. Chem. Acta 68, 39–52 (1995)

    MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Basic Sciences and Mathematics, Philadelphia University, P. O. Box 1, Amman, 13932, Jordan

    Mowaffaq Hajja

  2. Department of Informatics, K.E.A.O. Unified Social Security Fund, 12 Patision St., 10677, Athens, Greece

    Panagiotis T. Krasopoulos

Authors
  1. Mowaffaq Hajja
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  2. Panagiotis T. Krasopoulos
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Correspondence to Mowaffaq Hajja.

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Hajja, M., Krasopoulos, P.T. Recovering a Circumscriptible Tetrahedron from Its Face Areas. Mediterr. J. Math. 16, 156 (2019). https://doi.org/10.1007/s00009-019-1435-6

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  • DOI: https://doi.org/10.1007/s00009-019-1435-6

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