23 Jun
2019
23 Jun
'19
5:16 p.m.
If we lengthen axis a, we must shorten axis b and c to preserve the ab and ac girths. Consequently the bc girth decreases, a contradiction. The inverse holds for shortening axis a. A root-solving algorithm should converge to arbitrary precision given enough time and a good enough initial guess. —Brad
On Jun 23, 2019, at 5:24 PM, Dan Asimov <dasimov@earthlink.net> wrote:
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
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