Difference between revisions of "Phi"

Revision as of 15:50, 22 September 2007

Phi ( $\phi$ ) is a letter in the Greek alphabet. It is often used to represent the constant $\frac{1+\sqrt{5}}{2}$ . (The Greek letter tau ( $\tau$ ) was also used in pre-Renaissance times.) $\phi$ 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 Golden Rectangle is a rectangle with side lengths of 1 and $\phi$ ; it has a number of interesting properties.

The first fifteen digits of $\phi$ in decimal representation are: 1.61803398874989...

$\phi$ is also commonly used to represent Euler's totient function.

$\phi$ appears in many uses, including Physics, Biology and many others.

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-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>. (The Greek letter <math>\tau</math> was also used in pre-Renaissance times.) <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 (<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>. (The Greek letter tau (<math>\tau</math>) was also used in pre-Renaissance times.) <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 [[Golden Rectangle]] is a rectangle with side lengths of 1 and <math>\phi</math>; it has a number of interesting properties.
+<cmath>\phi</cmath> 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 [[Golden Rectangle]] is a rectangle with side lengths of 1 and <math>\phi</math>; it has a number of interesting properties.
-The first few digits of Phi in decimal representation are: 1.61803398874989...
+The first fifteen digits of <cmath>\phi</cmath> in decimal representation are: 1.61803398874989...
-Phi is also commonly used to represent [[Euler's totient function]].
+<cmath>\phi</cmath> is also commonly used to represent [[Euler's totient function]].
-Phi appears in many uses, including [[Physics]], [[Biology]] and many others.
+<cmath>\phi</cmath> appears in many uses, including [[Physics]], [[Biology]] and many others.
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Difference between revisions of "Phi"

Revision as of 15:50, 22 September 2007

See also