Comment by Xmd5a

It can be useful in a "primitive" environment: with the metric or even the imperial system, you need to multiply the length of your measurement unit by a certain factor in order to build the next unit (10x1cm = 1dm for instance).

But if your units follow a golden ratio progression, you just need to "concatenate" 2 consecutive units (2 measuring sticks) in order to find the third. And so on.