How do I calculate Phi for a certain number?

I know how to calculate the A and B components of Phi if I have one of the numbers to start with, but what if I have the total and want the two component numbers? I have a total length of 6", how do I find the two numbers with the Phi ratio that add up to that? Thanks!

Do you mean the golden ratio? Given a+b = 6, you want to find a and b such that a/b = phi = 1.618…?

I’m going to assume this isn’t homework given your signup date, but this is rather straightforward algebra:

a/b = phi = (a+b)/a
a+b/a = phi
6/a = phi

solve for a, then use a+b =6 to find b.

No, definitely not homework, just a project I’m working on and couldn’t figure it out. My straightforward algebra is about 20 years rusty at this point. This is exactly what I needed. Thanks, mnemosyne!

Note that the ratio of 6 to the larger of your two smaller numbers will also be phi. That’s what phi is, really.