If for , three successive terms of a Geometric Progression with common ratio represent sides of a triangle, then find the maximum value of
Take some triangle with side lengths for some and . Without loss of generality, let and find the allowable values of for a triangle to exist:
(i) true for all but for the golden ratio
(ii) true for all
(iii) true for all
Therefore, to satisfy this condition. It can be shown that:
Therefore the max value of this function on the allowable interval is 2.
QED