The Golden Ratio

Factual Questions
21

[QUOTE=Spectre of Pithecanthropus]
Another curious fact about φ is that it’s the number whose square is one more than itself. How that relates to all its other attributes I have little, if any, idea.
[/QUOTE]

You can define φ as the positive root of x[sup]2[/sup] - x - 1, and many texts do.

22

Also, iff you add a square to the side of a Golden Rectangle, you get another Golden Rectangle.