
Journal for Geometry and Graphics 08 (2004), No. 2, 163169 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 counterexamples to Bang's statement in higher dimensions. Keywords: Isosceles tetrahedron, equifacial tetrahedron, Bang's Theorem, regular simplex, barycentric coordinates, trilinear coordinates. MSC: 51M20; 52B11 [ Fulltextpdf (102 KB)] for subscribers only. 