Definition of the golden rectangle?

Question

Is this true:

The golden rectangle is defined as:

1. $X=A+B$;
2. $Y=A$;
3. $Y:X=B:Y$.

For bonus points: what other shapes with defined orientation but undefined size can be defined in an $XY$ grid by using exactly 2 values and exactly 3 non trivial expressions?

Answer 1

The golden rectangle is more commonly defined as the rectangle with sides $A$ and $B$ where

$$A:B=(A+B):A$$

Note that $B$ is the shorter side and $A$ is the longer.

Your expression (3) puts $X=B$: I think you meant $Y:X$ is as $B:Y$.

As for the bonus points: what do you mean by "2 terms"? You have more than 2 terms, with $A$, $B$, $A+B$, $X$, and $Y$.