23 Jun
2019
23 Jun
'19
5:16 p.m.
I think some girth combinations are impossible. For example, the girths 1, eps, eps where eps is some very small epsilon. If a girth is very small, then both of the semiaxes in its plane must be very small, so the remaining semiaxis will be close to 1/4, in which case both of the remaining girths will be close to 1. Dan Asimov writes:
Come to think of it, how can we prove that the mapping (0,oo)^3 —> (0,oo)^3 of positive octants via
(a,b,c) |—> (girth_ab, girth_bc, girth_ca)
is one-to-one? Or is it?
—Dan