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# Bang's Theorem

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 .

Tetrahedron

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## References

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. Monthly 33, 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 Math 14, 220-222, 1907-1908.White, H. S. Bull. Amer. Math. Soc. 14, 220, 1907-1908.

Bang's Theorem

## Cite this as:

Weisstein, Eric W. "Bang's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BangsTheorem.html