9 Feb
2011
9 Feb
'11
3:17 p.m.
Dear Funsters, Can anyone help with the following problems? (1) Do there exist tetrahedra with each face a Primative Pythagorean Triangle? I have discovered one with 3 of the four faces PPTs having edges 42601, 41449, 9840, 11849, 40920 and 6601. Unfortunately the face with edges 9840, 11849 and 6601 has a common factor of 41. I think I've eliminated all cases with edges less that 10^8. (2) Do there exist tetrahedra with each face a Pythagorean Triangle such that the ratio of shortest to longest edge is more than 410688/743665 = .55224866? This occurs for a tetrahedron with edges of 743665, 609960, 425425, 591313, 450984 and 410688. I think I've eliminated all cases with edges less that 2x10^7. Best, Dick Hess