Hedronometric Proportions for Rectangular Tetrahedra

Abstract

The main aim of this paper is to obtain hedronometric proportions, which are three dimensional versions of trigonometric proportions for right triangle, as well as for dihedral and vertex angles of rectangular tetrahedron in terms of hypotenuse and perpendicular face area

Keywords

• Tetrahedron, hedronometry, proportion, dihedral angle, vertex angle

References

1. Cho E., Pythagoren Theorems on Rectangular Tetrahedron, Appl. Math. Lett., 4:6, 37-38, (1991).
2. Cho E., Dihedral Angles of n−simplices, Appl. Math. Lett., 5(4), 55-57, (1992).
3. Grunbaum B., Convex Polytopes, John Wiley and Sons Ltd., New York, (1967).
4. Henderson D.W., Taimina D., Experiencing Geometry in Euclidean, Spherical and Hyperbolic Spacees, Pearson, (2000).
5. Leng G.S. and Zhang Y., Vertex Angles for Simplices, Appl. Math. Lett. 12(1), 1-5, (1999).
6. Quadret J.P., Lasserre J.B., and Hiriart-Urruty J.B., Pythagoras’ Theorem for Areas, Amer. Math. Monthly, 108(6), 549-552, (2001).
7. Veljan D. The 2500 Years Old Pythagorean Theorem, Mathematics Magazine, 73(4), 259-272, (2000).
8. Veljan D., The Sine Theorem and Inequalities for Volume Simplices, Linear Algeb.and Its Applications,70-91, (1995).

9. Yakut A.T., Savas M., Kader S., On The Schlafli Differential Formula Based on Edge Lengths of Tetrahedron in H3 and S3, Geometriae Dedicata, 1, 99-115, (2009).
10. Wirth K., Dreiding A.S., Relations between Edge Lengths, Dihedral Angles and Solid Angles in Tetrahedra, J. Math. Chem., 52, 1624-1638, (2014).