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Phi (uppercase Φ, lowercase φ or ϕ), pronounced [fī] in modern Greek and as [faɪ] in English, is the 21st letter of the Greek alphabet. In modern Greek, it represents [f], a voiceless labiodental fricative. In Ancient Greek it represented [pʰ], an aspirated voiceless bilabial plosive (from which English ultimately inherits the spelling "ph" in words derived from Greek). In the system of Greek numerals it has a value of 500 (φʹ) or 500,000 (͵φ).

The lower-case letter $varphi\; ,$ (or often its variant, $phi\; ,$) is used as a symbol for:

- The golden ratio 1.618... in mathematics, art, and architecture.
- Euler's totient function φ(n) in number theory; also called Euler's phi function.
- The probability density function of the normal distribution in mathematics and statistics.
- An angle, typically the second angle mentioned, after θ (theta). Especially:
- The argument of a complex number.
- The phase of a wave in signal processing.
- In spherical coordinates, mathematicians usually refer to phi as the polar angle (from the z-axis). The convention in physics is to use phi as the azimuthal angle (from the x-axis).
- One of the dihedral angles in the backbones of proteins.
- Internal or effective angle of friction
- Electric potential in physics.
- The work function in electronics.
- A shorthand representation for an aromatic functional group in organic chemistry
- The fugacity coefficient in thermodynamics
- The ratio of free energy destabilizations of protein mutants in phi value analysis
- In cartography and navigation, latitude.
- A sentence in first-order logic.
- Porosity in geology.

The upper-case letter Φ is used as a symbol for:

- The golden ratio conjugate 0.618... in mathematics.
- The magnetic flux and electric flux in physics, with subscripts distinguishing the two.
- The cumulative distribution function of the normal distribution in mathematics and statistics.
- Philosophy.
- Strength (or resistance) reduction factor in structural engineering, used to account for statistical variabilities in materials and construction methods.
- The number of phases in a power system in electrical engineering, for example 1Φ for single phase, 3Φ for three phase.
- The symbol of the voiceless bilabial fricative in the international phonetic alphabet.

The diameter symbol in engineering, ⌀, is often incorrectly referred to as "phi". This symbol is used to indicate the diameter of a circular section, for example ⌀14 means the diameter of the circle is 14 units.

- upper case:
- U+03A6 GREEK CAPITAL LETTER PHI (Φ): Greek capital letter phi
- lower case:
- GREEK SMALL LETTER PHI (φ): letter phi, used in Greek texts.
- U+03D5 GREEK PHI SYMBOL (ϕ): phi symbol, for mathematical and technical contexts.

In HTML/XHTML, the upper and lower case phi character entity references are `Φ` (Φ) and `φ` (φ) respectively.

In LaTeX, the math symbols are `Phi` ($Phi,!$), `phi` ($phi\; ,!$), and `varphi` ($varphi,!$).

In some browsers (e.g. Internet Explorer 6), the shapes of the U+03C6 GREEK SMALL LETTER PHI (which should be viewed as a curl) and U+03D5 GREEK PHI SYMBOL (which should be viewed as a circle crossed by a slash) are exchanged. Compare these samples to check your browser:

- Phi letter: right $varphi,!$; possible wrong φ

- Phi symbol: right $phi,!$; possible wrong ϕ

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Last updated on Wednesday October 08, 2008 at 04:39:21 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Wednesday October 08, 2008 at 04:39:21 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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