Quandaries
and Queries 

hi, my name is cristina and im a middle school student. im having trouble with golden ratios. i know what it is but im doing a project and nowhere on the internat have i found an answer to my question..... please help.... here is the question: For the above segment, let x represent the longer segment.
to find the golden ratio, write a proportion such that the longer of
the two segments is the geometric mean between the shorter segment
and the entire segment.Use the quadratic Formula to solve the proportion
for X. Find the value in both radical and decimal form. 

Cristina, what you have is a poor way of describing the Golden ratio. "The longer of the two segments is the geometric mean between the shorter segment and the entire segment" says that
which can be converted to
and the golden ration is the larger root of this quadratic (use the quadratic formula). A proper way to describe the golden ratio from your diagram is that x and 1x and 1 satisfy that the proportions of (1x)/x and x/1 are the same, which leads to x^{2} = 1x as above, etc. Penny 

