Golden Ratio and Golden Rectangle

Date: 2/14/96 at 23:7:51
From: Anonymous
Subject: Golden Ratio

I am an eighth grader in Lebanon, NH. I have had no luck in 
learning about the golden ratio or golden rectangle. Could you 
please help?

Thank You
Tom Dickerson

Date: 2/15/96 at 13:23:17
From: Doctor Byron
Subject: Re: Golden Ratio

The golden ratio is a special number approximately equal to:
1.6180339887498948482...

It is an irrational number with an unending series of digits in it, 
however, so it is often better to use its exact value given by:

 1 + (sqrt) 5
 ------------
      2

The way we find the value of the golden ratio is kind of complex.  
First, we define the golden ratio as the ratio between x and y if

  x             y
 ---    =     -----
  y            x+y


Let's say x is 1. Then we have 1/y = y/(y+1). If we solve this equation 
to find y, we'll find that it is the value given above, about 1.618.

A golden rectangle is a rectangle in which the ratio of the length 
to the width is the golden ratio.  In other words, if one side of 
a golden rectangle is 2 ft. long, the other side will be approximately 
equal to 2 * (1.62) = 3.24.

-Doctor Byron,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/