Re: Tetrahedron
- From: Chip Eastham <hardmath@xxxxxxxxx>
- Date: Sun, 26 Apr 2009 04:41:16 -0700 (PDT)
On Apr 26, 1:48 am, AI <vcpan...@xxxxxxxxx> wrote:
a) Find a tetrahedron whose edges are consecutive positive integers
and whose volume is a positive integer.
b) Prove that there is only one such tetrahedron.
[do not distinguish between a tetrahedron and its mirror image]
Again it's not a homework :)
I don't know the answer, but there is a
formula attributed to Piero della Francesca
for the volume of a tetrahedron in terms of
its edge lengths.
So if you are thinking these edges have the
lengths n,n+1,n+2,n+3,n+4,n+5, then it can
in principle be checked for what values of
n the resulting volume is an integer. One
needs to be careful about the ordering of
the edges:
http://www.mathpages.com/HOME/kmath424.htm
regards, chip
.
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