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.
Similar content being viewed by others
References
Altshiller-Court, N.: Modern Pure Solid Geometry, second edn. Chelsea Publishing Company, New York (1964)
Barbeau, E.J., Klamkin, M.S., Moser, W.O.J.: Five Hundred Mathematical Challenges. MAA, Washington, D. C. (1995)
Berger, M.: Geometry I. Springer, New York (1987)
Gerber, L.: The orthocentric simplex as an extreme simplex. Pac. J. Math. 56, 97–111 (1975)
Hajja, M.: Coincidence of centers of edge-incentric, or balloon, simplices. Res. Math. 49, 237–263 (2006)
Hajja, M., Hayajneh, M., Martini, H.: More characterizations of certain special families of simplices. Res. Math. 69, 23–47 (2016)
Herzog, F.: Completely tetrahedral sextuples. Am. Math. Mon. 66, 460–464 (1959)
Izumi, S.: Sufficiency of simplex inequalities. Proc. Am. Math. Soc. 144, 1299–1307 (2016)
Mazur, M.: Problem 10717. Am. Math. Mon. 106, 167 (1999)
Mazur, M.: Solution. ibid 107, 466–467 (2000)
Sommerville, D.M.Y.: An Introduction to the Geometry of \(N\) Dimensions. Dover, New York (1958)
Veljan, D.: The distance matrix of a simplex. Croat. Chem. Acta 68, 39–52 (1995)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00009-019-1435-6