There are least two Bang's theorems, one concerning tetrahedra (Bang 1897), and the
other with widths of convex domains (Bang 1951).
The theorem of Bang (1897) states that the lines drawn to the polyhedron vertices of a face of a tetrahedron from the
point of contact of the face with the insphere
form three angles at the point of contact which are the
same three angles in each face.
The theorem of Bang (1951) states that if a convex domain is covered by a collection of strips,
then the sum of the widths of the strips is at least , where is the width of the narrowest strip which covers .
Altshiller-Court, N. §245 in Modern Pure Solid Geometry. New York: Chelsea, p. 74, 1979.Bang,
A. S. Tidskrift for Math., p. 48, 1897.Bang, T. "A
Solution of the 'Plank Problem.' " Proc. Amer. Math. Soc.2, 990-993,
1951.Brown, B. H. "Undergraduate Mathematics Clubs: Theorem
of Bang. Isosceles Tetrahedra." Amer. Math. Monthly33, 224-226,
1926.Gehrke. Tidskrift for Math., p. 84, 1897.Honsberger,
R. Mathematical
Gems II. Washington, DC: Math. Assoc. Amer., p. 93, 1976.Wells,
D. The
Penguin Dictionary of Curious and Interesting Geometry. London: Penguin,
p. 13, 1991.White, H. S. "Two Tetrahedron Theorems."
Nouvelles Ann. de Math14, 220-222, 1907-1908.White, H. S.
Bull. Amer. Math. Soc.14, 220, 1907-1908.
is covered by a collection of strips,
then the sum of the widths of the strips is at least 
, where 
is the width of the narrowest strip which covers 
.
