| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
Does there exist a tetrahedron such that all its edge lengths, all its face areas, and its volume are integers? If so, give a numerical example. [problem proposed by the Carleton Ottawa Problem Solvers, in Crux Mathematicorum, 10(1984)88, problem 930]
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 274.1 | New to the file. | FGVAXU::SPELLMAN | Write on the right wright rite! | Tue Mar 24 1987 16:30 | 21 |
Clearly this problem is one of the burning issues in this notes
file, judging by the tremendous volume of responses it has gotten,
since it was first posed back in May 1985. :-)
To recap, the problem is
> Does there exist a tetrahedron such that all its edge lengths, all its
> face areas, and its volume are integers? If so, give a numerical
> example.
>
> [problem proposed by the Carleton Ottawa Problem Solvers, in
> Crux Mathematicorum, 10(1984)88, problem 930]
I think that the answer is: no. Consider one face of the tetrahedron.
It is an equilateral triangle. If it has side N, it will have area
sqrt(3)*N^2/4, which can't be an integer.
I don't know the volume of a tetrahedron, but I expect it also will
involve a square root and be non-integral.
Chris
| |||||
| 274.2 | CLT::GILBERT | eager like a child | Tue Mar 24 1987 17:44 | 2 | |
I'm sure the problem isn't referring to a regular tetrahedron --
that is, all the sides need not be of equal length.
| |||||