If you've never heard of the "Golden Ratio" and how it applies to user interface design, you may want to search it up at google.
Here's one link where the author refers to it as the "Golden section ratio (phi)". It doesn't get into the UI part, but has a nice history with references to Euclid, pyramids, and Fibonacci numbers.
There’s just one person behind this website; if this article was helpful (or interesting), I’d appreciate it if you’d share it. Thanks, Al.