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 08:32, 21 June 2006

Phi ($\phi$) 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 $x^2-x-1=0$. Since the terms of the fibonacci is positive, we take the positive solution of the quadratic and define $\phi=\frac{1+\sqrt{5}}{2}$.

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...