- Art Gallery -

In geometry, Bang's theorem on tetrahedra states that, if a sphere is inscribed within a tetrahedron, and segments are drawn from the points of tangency to each vertex on the same face of the tetrahedron, then all four points of tangency have the same triple of angles. In particular, it follows that the 12 triangles into which the segments subdivide the faces of the tetrahedron form congruent pairs across each edge of the tetrahedron.[1] It is named after A. S. Bang, who posed it as a problem in 1897.[2]

Bang s theoremtetrahedra


Brown, B. H. (April 1926), "Theorem of Bang. Isosceles tetrahedra", Undergraduate Mathematics Clubs: Club Topics, The American Mathematical Monthly, 33 (4): 224–226, JSTOR 2299548.
"Opgaver til Løsning", Nyt tidsskrift for matematik (in Danish), 8 (A): 48, 1897, JSTOR 24528123, problem 266.

Undergraduate Texts in Mathematics

Graduate Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia



Hellenica World - Scientific Library

Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License