Phi (letter)

Look up Φ or φ in Wiktionary, the free dictionary.

Greek alphabet
Αα	Alpha	Νν	Nu
Ββ	Beta	Ξξ	Xi
Γγ	Gamma	Οο	Omicron
Δδ	Delta	Ππ	Pi
Εε	Epsilon	Ρρ	Rho
Ζζ	Zeta	Σσς	Sigma
Ηη	Eta	Ττ	Tau
Θθ	Theta	Υυ	Upsilon
Ιι	Iota	Φφ	Phi
Κκ	Kappa	Χχ	Chi
Λλ	Lambda	Ψψ	Psi
Μμ	Mu	Ωω	Omega
Obsolete letters
	Digamma		Qoppa
	San		Sampi
Other characters
	Stigma		Sho
	Heta
Greek diacritics

Phi (uppercase Φ, lowercase φ or ϕ), pronounced [fi] in modern Greek and [faɪ], [fʌɪ] or [fiː] in English^[1], 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 Cyrillic letter Ef (Ф, ф) arose from phi. In economics, this greek symbol is usually an addative term.

The lower-case letter (or often its variant, ) is used as a symbol for:

• The golden ratio in mathematics, art, and architecture.
• Euler's totient function φ(n) in number theory; also called Euler's phi function.
• In algebra, group or ring homomorphisms
• 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 and hydrology.
• Strength (or resistance) reduction factor in structural engineering, used to account for statistical variabilities in materials and construction methods.
• The symbol for a voiceless bilabial fricative in linguistics.

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.
• 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.

Computing

In Unicode, there are multiple forms of the phi letter:

• Uppercase:
  • U+03A6 GREEK CAPITAL LETTER PHI (Φ): used in Greek texts
• Lowercase:
  • U+03C6 GREEK SMALL LETTER PHI (φ): used in Greek texts
  • U+03D5 GREEK PHI SYMBOL (ϕ): used in mathematical and technical contexts^[2]
  • U+0278 LATIN SMALL LETTER PHI (ɸ): used in IPA to symbolise a voiceless bilabial fricative

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 (), and \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:

Character	Name	Correct appearance	Your browser
U+03C6	GREEK SMALL LETTER PHI		φ
U+03D5	GREEK PHI SYMBOL		ϕ

See also

• F, f - Ef (Latin)
• Ф, ф - Ef (Cyrillic)

References

Look up Phi in Wiktionary, the free dictionary.

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