29 Nov
2006
29 Nov
'06
7:20 p.m.
On 11/29/06, Michael Kleber <michael.kleber@gmail.com> wrote:
Oof, of course; very nice. What's more, starting with a 3-4-5 and rotating about the midpoints of the length 3 and 5 sides gets you one extra rational (integer, even!) value; you end up with {3, 4, 5, 13, 5*sqrt(145), sqrt(7081)}.
Sorry, MK --- this one is a dud, with no planar perms at all!
Er, well, yes. One does need to clear *all* one's denominators. How do you like {3*18, 4*18, 5*18, 13, 5*sqrt(145), sqrt(7081)} ? Triply planar, I hope.
--Michael*18 Kleber
Looks OK to me. My program only checks for two configurations not three, however. Here is one with no right triangles: [ 272, 2*sqrt(6401), 130, 290, 50, 2*sqrt(6890)] Jim Buddenhagen