[math-fun] Mathematical and Scientific Joke Competition
http://www.simonsingh.com/Joke_Competition.html " ... I received dozens of entries for the world's funniest mathematical or scientific joke. I published my favourite fifteen and asked for your votes. Below you will find the winning joke sent in by Robert Williams and the fourteen runners-up. ... " --- co-chair http://ocjug.org/
Try http://mathoverflow.net/questions/1083/do-good-math-jokes-exist-closed On Thu, Feb 4, 2010 at 5:52 PM, Ray Tayek <rtayek@ca.rr.com> wrote:
http://www.simonsingh.com/Joke_Competition.html " ... I received dozens of entries for the world's funniest mathematical or scientific joke. I published my favourite fifteen and asked for your votes. Below you will find the winning joke sent in by Robert Williams and the fourteen runners-up. ... "
--- co-chair http://ocjug.org/
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-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com
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.
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.
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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
On Sat, Feb 13, 2010 at 8:47 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
"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.
I don't replicate the result you get here. I find that the point of contact of the insphere with the semi-infinite sides is s/(2*sqrt(3)) above the base of the prism, thus forming more 30-60-90 triangles and repeating the 2pi/3 angles as Bang's theorem would give, not 45-45-90 triangles as you indicate. So at least one of us has the wrong answer here. --Joshua Zucker
I also find some more Bang's theorems: If all the faces of a tetrahedron have the same perimeter, then the faces are all congruent triangles. If the faces of a tetrahedron have equal areas then they are congruent. Or, I suspect perhaps of more interest to Prof. Guy: http://tinyurl.com/BangThmAmazon Paraphrasing: In the sequence a^n - 1 or a^n + 1, for fixed a>1 and variable n, every term has a prime factor that does not divide any previous term, except if a = 2 and n = 6 for the -1 case, and a = 2 and n = 3 for the +1 case. (Zsigmondy generalized this result to a^n - b^n and a^n + b^n, with the same exceptions). But in any case I don't find any further biographical information... --Joshua Zucker
Withdrawn, accompanied by my (by now customary) red face! WFL On 2/13/10, Joshua Zucker <joshua.zucker@gmail.com> wrote:
On Sat, Feb 13, 2010 at 8:47 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
"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.
I don't replicate the result you get here.
I find that the point of contact of the insphere with the semi-infinite sides is s/(2*sqrt(3)) above the base of the prism, thus forming more 30-60-90 triangles and repeating the 2pi/3 angles as Bang's theorem would give, not 45-45-90 triangles as you indicate. So at least one of us has the wrong answer here.
--Joshua Zucker
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participants (5)
-
Fred lunnon -
Joshua Zucker -
Mike Stay -
Ray Tayek -
Richard Guy