Difference between revisions of "Phi"
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Phi (<math>\phi</math>) is defined as the limit of the ratio of successive terms of the [[Fibonacci sequence]]. It can be shown that this limit is a solution to the [[quadratic equation]] <math>x^2-x-1=0</math>. Since the terms of the fibonacci is positive, we take the positive solution of the quadratic and define <math>\phi=\frac{1+\sqrt{5}}{2}</math>. | Phi (<math>\phi</math>) is defined as the limit of the ratio of successive terms of the [[Fibonacci sequence]]. It can be shown that this limit is a solution to the [[quadratic equation]] <math>x^2-x-1=0</math>. Since the terms of the fibonacci is positive, we take the positive solution of the quadratic and define <math>\phi=\frac{1+\sqrt{5}}{2}</math>. | ||
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| + | Phi is also known as the Golden Ratio. It was commonly believed by the Greeks to be the most aesthetically pleasing ratio between side lengths in a rectangle. | ||
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| + | The first few digits of Phi in decimal representation are: 1.61803398874989... | ||
Revision as of 07:32, 21 June 2006
Phi (
) is defined as the limit of the ratio of successive terms of the Fibonacci sequence. It can be shown that this limit is a solution to the quadratic equation 
. Since the terms of the fibonacci is positive, we take the positive solution of the quadratic and define 
.
Phi is also known as the Golden Ratio. It was commonly believed by the Greeks to be the most aesthetically pleasing ratio between side lengths in a rectangle.
The first few digits of Phi in decimal representation are: 1.61803398874989...
