so, last I mentioned it I hadn't really gotten to the materials science part of the proportion story, but it's short: 'tatami-' describes proportion by material embodying it; 'golden-,' too, but in reverse-- the proportion embodying an abstract quality described by the material. There must be others
I first thought of crystal lattice constants (zb, CdS-paned, 1:1.624.., close to gold!), and the 7 systems caught my eye though I still don't know what to do with them. speaking of which, yesterday I spent some time extending Euclid's algorithm to unequal pane dimensions, but didn't get farther than 2:1, and even that I think I might have mixed up. funny that the thing I came up with kind of reminded me of the Stein's binary version with the factors of two taken out and saved for later. I just kept in mind parity of the number of subtractions before switching measures, and used the last parity leading to zero remainder to either divide by 2 or not. I'm not sure if this is really right to have done but it seemed to work and the sounds surprised me!