On 2/12/10, Richard Guy <rkg@cpsc.ucalgary.ca> wrote:
Can anyone help me find information about A S Bang, e.g.,
A.~S.~Bang, {\it Tidskrift for Math.}, 1897, p. 48.
AS OPPOSED TO
Th\o ger Sophus Vilhelm Bang, 1917-1996 A Solution of the 'Plank Problem.' {\it Proc.\ Amer.\ Math.\ Soc.} {\bf2}(1951) 990-993.
?? Thanks in anticipation. R.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I did a quick google on this, but found only what RKG doubtless knew already ---- Eric W. Weisstein "CRC concise encyclopedia of mathematics" p160 ; also http://mathworld.wolfram.com/BangsTheorem.html "A Theorem on Isogonal Tetrahedra" B. H. Brown (1924) www.jstor.org/stable/2298822 (I don't have access to this) According to BangsTheorem.html --- "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." This is obviously false --- consider the limiting case of a semi-infinite triangular prism with equilateral cross-section: the angles at the finite base are all 2pi/3, whereas at the infinite sides they are pi/2, 3pi/4, 3pi/4. So what does Bang (1897) actually prove, I wonder? I suspect there is some extra constraint on the tetrahedron, such as self-reciprocity. WFL