Phi is known as the golden ratio.
Believed to be aesthetically pleasing.
Also irrational, approximately 1.61803...
Phi is an algebraic number as it satisfies with
Phi=1.61803...
The height of a woman over the height of her belly button.
Phi is the ratio of successive Fibonacci numbers.
(or any series like it)
Most quickly proved irrational number, again by contradiction
(simple proof 1975).
Interesting number to invert in a calculator. The decimal part
never changes.
(A cool number to put in you calculator and while pressing 1/x)
Lots more do that as well, found by changing the 1 to n in the equation
for phi:)
Supposedly used in the design of buildings and art.
The Parthenon
Leonardo
Da Vinci
Had shown how all
different body parts
were related by the
Golden Ratio.
with 
The Parthenon