What does "pi" and "phi" have to do with the dimensions of a pyramid?

Question

More specifically, the Great Pyramid of Cheops, or Khufu, or whatever, is supposed to have a relationship with those measurements somehow, though why it's relevant eludes me. And what the heck is the measurement of "phi"? Pi I've heard of, but phi?

Answer 1

The Pi Pyramid is based on a formula that says:

  the height is to the perimeter as a radius is to its circumference.

The Phi Pyramid is based on a formula that says:

   the square of the height equals exactly the area of the face side.  Phi in this case is the golden ratio.

Khufu is pretty close to these -- suggesting the egyptions knew about pi, or phi, or both.  

Answer 2

Ancient Egyptian mathematics were pretty smart cookies and knew about both π and φ (phi).

It's thought they built both into pyramid design. The perimeter of the pyramid divided by its height is very close to 2π, and the slope of each face is close to 4/π.

http://www.math.washington.edu/~greenber...

Phi is called the "golden ratio," which is when the ratio between the sum of two quantities and the larger quantity is the same as the ratio between the larger quantity and the smaller one. Mathematically it's:

(a+b)/a = a/b

It's often used in construction, art, and many other disciplines.

http://en.wikipedia.org/wiki/Golden_rati...