Golden Ratio and Golden RectangleDate: 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/ |
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