n−dimensional Trigonometric Proportions for Rectangular Simplices
n−dimensional Trigonometric Proportions for Rectangular Simplices
The main aim of this paper is to obtain n−dimensional versions of trigonometric proportions for right triangle in terms of hypotenuse and perpendicular volume faces of a rectangular simplices.
___
- Cho E., The generalized cross product and volumes of a simplex, Appl. Math. Lett., 4(6), 51-53, (1991).
- Cho E., Dihedral angles of n−simplices, Appl. Math. Lett., 5(4), 55-57, (1992).
- Grunbaum B., Convex polytopes, John Wiley and Sons Ltd., New York, (1967).
- Karliga B., Hedronometric Proportions on Rectangular Tetrahedra, Preprint, (2015).
- Leng G.S. and Zhang Y., Vertex angles for simplices, Appl. Math. Lett. 12(1), 1-5, (1999).
- Quadret J.P., Lasserre J.B., and Hiriart-Urruty J.B., Pythagoras’ theorem for areas, Amer. Math. Monthly, 108(6), 549-552, (2001).
- Veljan D., The sine theorem and inequalities for volumes simplices and determinants, Linear Algebra and Its Applications, 219, 79-91, (1995).
- Veljan D. The 2500 years old pythagorean theorem, Mathematics Magazine, 73(4), 259-272, (2000).