Journal for Geometry and Graphics 08 (2004), No. 2, 163--169
Copyright Heldermann Verlag 2004
A Note on Bang's Theorem on Equifacial Tetrahedra
Mowaffaq Hajja
Dept. of Mathematics, Yarmouk University, Irbid, Jordan
mhajja@yu.edu.jo
Fathi Saidi
Dept. of Basic Sciences, University of Sharjah, P. O. Box 27272, Sharjah, United Arab Emirates
fsaidi@sharjah.ac.ae
We give an analytic proof based on Pythagoras' theorem of a theorem of Bang stating that if the faces of a tetrahedron have equal areas then they are congruent. We also place Bang's theorem in the more general context that deals with the existence and uniqueness of a tetrahedron PABC having a given base ABC and having lateral faces of given areas. Our approach shows also how to construct counter-examples to Bang's statement in higher dimensions.
Keywords: Isosceles tetrahedron, equifacial tetrahedron, Bang's Theorem, regular simplex, barycentric coordinates, trilinear coordinates.
MSC: 51M20; 52B11
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