DOI QR코드

DOI QR Code

VOLUME FORMULAS OF A EUCLIDEAN TETRAHEDRON

  • Park, Joon Suk (Department of Physics, Yonsei University) ;
  • Cho, Yunhi (Department of Mathematics, University of Seoul)
  • Received : 2012.10.16
  • Accepted : 2012.12.31
  • Published : 2013.03.25

Abstract

We survey and study several volume formulas of a Euclidean tetrahedron.

Keywords

Euclidean tetrahedron;volume formula

References

  1. Cho, Jinsok, The Volume of a Tetrahedron, College Math. J, 32:4 (2001), 294-296. https://doi.org/10.2307/2687568
  2. Cho, Yunhi, Volume of a tetrahedron in terms of dihedral angles and circumradius, Appl. Math. Lett. 13:4 (2000), 45-47.
  3. Coxeter, H. S. M., Discrete groups generated by reflections, Ann. of Math. 35:3 (1934), 588-621. https://doi.org/10.2307/1968753
  4. Dove, K. L. and Sumner, J. S., Tetrahedra with Integer Edges and Integer Volume, Math. Mag. 65 (1992), 104-111. https://doi.org/10.2307/2690489
  5. Mihai, Vasile and Zhou, Li, A Tetrahedron with All Faces Congruent:10934, Amer. Math. Monthly 110:9 (2003), 846-847. https://doi.org/10.2307/3647815
  6. Smith, C., An Elementary Treatise on Solid Geometry, 11th ed., Macmillan and Co., New York (1907).
  7. Smith, H. L., Note on the Volume of a Tetrahedron, Math. News Lett. 6:4 (1932), 23-24.
  8. Srinivasan, V. K., Computation techniques for the volume of a tetrahedron, International J. of Mathematical Education in Science and Technology 41:7 (2010), 979-990. https://doi.org/10.1080/0020739X.2010.493237
  9. Townes, S. B., Classroom Notes: The Volume of a Tetrahedron as a Determinant, Amer. Math. Monthly 63:8 (1956), 574-575.
  10. Berger, Marcel, Geometry I, Universitext, Springer-Verlag, Berlin (1987).
  11. Cho, E. C., The Volume of a Tetrahedron, Appl. Math. Lett. 8:2 (1995), 71-73.