Yes, I am a big fan of the “golden integers” and “golden rationals”. They are very useful when trying to work out any kind of metrical geometry questions w/r/t

Yes, I am a big fan of the “golden integers” and “golden rationals”. They are very useful when trying to work out any kind of metrical geometry questions w/r/t the symmetry system of the pentagon, icosahedron, 120-cell, etc. I think a lot more students should spend significant time with Zometool construction toys while in school, and should work out a lot of the arithmetic of golden integers for themselves. (If you are a math teacher, I recommend getting some of these.) If you use Wildberger’s “rational trigonometry”, then it is possible to answer essentially every metrical geometry question about configurations of Zometool using golden rational arithmetic without ever resorting to approximations. The squared length between every pair of Zome-constructible points is a golden integer and the squared sine of every Zome-constructible angle is a golden rational number. I’m just pointing out that “It's possible to use Binet's formula, too [using golden integers]” is not actually any different in practice than the matrix computation.