How can the golden ratio be expressed as a geometric mean?

Expert Answers
baxthum8 eNotes educator| Certified Educator

Given a length of segment divided into 2 parts, a and b.

The golden ration is the ratio of:

`(a+b)/a = a/b =phi`

``phi is the ratio of the segment when divided in this special way.

The equation has as its unique positive solution the algebraic irrational number:

`phi = (1+sqrt(5))/2 = 1.61803397887...`