Take a square of unit side `1' as above. A red line centred at the mid-point of bd scribes a semi-circle from points a to e.

You will recognize this as the standard method of constructing a Golden Rectangle.

From this both the positive and negative values of Phi can be determined.

Negative

There is a tendency to think of Phi as a mathematical algorithm, the result of which gives a value of 1.618033989 to nine decimal places, but in essence it is really a geometric construction, and is best considered as such.

A lot has been written concerning Phi and its appearance or non-appearance in Pharaonic architecture. The general consensus being that Phi is so ubiquitous, that it is accidental when it appears in antiquity; yet it is a simple matter to demonstrate that the pyramid builders could easily have understood the principal of Phi.

For a more in depth treatment of this matter, please go to the page What is Phi?