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Recovering a Circumscriptible Tetrahedron from Its Face Areas

  • Mowaffaq HajjaEmail author
  • Panagiotis T. Krasopoulos
Article
  • 43 Downloads

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.

Keywords

Circumscriptible tetrahedron face areas 

Mathematics Subject Classification

Primary 51M04 Secondary 52B10 

Notes

References

  1. 1.
    Altshiller-Court, N.: Modern Pure Solid Geometry, second edn. Chelsea Publishing Company, New York (1964)zbMATHGoogle Scholar
  2. 2.
    Barbeau, E.J., Klamkin, M.S., Moser, W.O.J.: Five Hundred Mathematical Challenges. MAA, Washington, D. C. (1995)zbMATHGoogle Scholar
  3. 3.
    Berger, M.: Geometry I. Springer, New York (1987)CrossRefGoogle Scholar
  4. 4.
    Gerber, L.: The orthocentric simplex as an extreme simplex. Pac. J. Math. 56, 97–111 (1975)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hajja, M.: Coincidence of centers of edge-incentric, or balloon, simplices. Res. Math. 49, 237–263 (2006)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hajja, M., Hayajneh, M., Martini, H.: More characterizations of certain special families of simplices. Res. Math. 69, 23–47 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Herzog, F.: Completely tetrahedral sextuples. Am. Math. Mon. 66, 460–464 (1959)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Izumi, S.: Sufficiency of simplex inequalities. Proc. Am. Math. Soc. 144, 1299–1307 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Mazur, M.: Problem 10717. Am. Math. Mon. 106, 167 (1999) MathSciNetCrossRefGoogle Scholar
  10. 10.
    Mazur, M.: Solution. ibid 107, 466–467 (2000)Google Scholar
  11. 11.
    Sommerville, D.M.Y.: An Introduction to the Geometry of \(N\) Dimensions. Dover, New York (1958)zbMATHGoogle Scholar
  12. 12.
    Veljan, D.: The distance matrix of a simplex. Croat. Chem. Acta 68, 39–52 (1995)MathSciNetGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Basic Sciences and MathematicsPhiladelphia UniversityAmmanJordan
  2. 2.Department of InformaticsK.E.A.O. Unified Social Security FundAthensGreece

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