Difference between revisions of "Phi"

Revision as of 21:32, 21 June 2006

Phi ( $\phi$ ) is a letter in the Greek alphabet. It is often used to represent the constant $\frac{1+\sqrt{5}}{2}$ . $\phi$ appears in a variety of different mathematical contexts: it is the limit of the ratio of successive terms of the Fibonacci sequence, as well as the positive solution of the quadratic equation $x^2-x-1=0$ .

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...

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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 a letter in the Greek alphabet.  It is often used to represent the constant <math>\frac{1+\sqrt{5}}{2}</math>.  <math>\phi</math> appears in a variety of different mathematical contexts: it is the limit of the ratio of successive terms of the [[Fibonacci sequence]], as well as the positive solution of the [[quadratic equation]] <math>x^2-x-1=0</math>.
 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...

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Difference between revisions of "Phi"

Revision as of 21:32, 21 June 2006