Phi - Revision history

Beza 1598 at 05:38, 11 March 2016

2016-03-11T05:38:42Z

← Older revision		Revision as of 05:38, 11 March 2016
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	{{DEFAULTSORT:Phi (Letter)}}		{{DEFAULTSORT:Phi (Letter)}}
	[[Category:Greek letters]]		[[Category:Greek letters]]

			{{Donate}}

Nick: /* Use as a symbol */

2012-03-09T10:35:19Z

Use as a symbol

← Older revision		Revision as of 10:35, 9 March 2012
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	'''Phi''' (uppercase Φ, lowercase φ or math symbol ϕ), pronounced ˈfaɪ or sometimes /ˈfiː/ in English,<sup>[1]</sup> and ˈfi in [[Modern Greek language\|modern Greek]], 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 [[Aspiration (phonetics)\|aspirated]] [[voiceless bilabial plosive]] (from which English ultimately inherits the spelling "[[ph (digraph)\|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 (Cyrillic)\|Ef]] (Ф, ф) arose from Φ.		'''Phi''' (uppercase Φ, lowercase φ or math symbol ϕ), pronounced ˈfaɪ or sometimes /ˈfiː/ in English,<sup>[1]</sup> and ˈfi in [[Modern Greek language\|modern Greek]], 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 [[Aspiration (phonetics)\|aspirated]] [[voiceless bilabial plosive]] (from which English ultimately inherits the spelling "[[ph (digraph)\|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 (Cyrillic)\|Ef]] (Ф, ф) arose from Φ.

	~~== Use as a symbol ==~~
	~~The lower-case letter <math>\varphi \,</math> (or often its variant, <math>\phi \,</math>) is often used to represent the following:~~
	*The [[golden ratio]] <math>\tfrac{1 + \sqrt{5}}{2} \approx 1.61803\ldots</math> in mathematics, art, and architecture.
	*[[Euler's totient function]] ''φ''(''n'') in number theory; also called ''Euler's phi function''.
	*In algebra, [[Group (mathematics)\|group]] or [[Ring (mathematics)\|ring]] [[homomorphism]]s
	* In [[probability theory]], {{nowrap\|1=''ϕ''(''x'') = (2π)<sup>−½</sup>''e''<sup>−''x''<sup>2</sup>/2</sup>}} is the [[probability density function]] of the [[normal distribution]].
	* In [[probability theory]], {{nowrap\|1=''φ''<sub>''X''</sub>(''t'') = E[ ''e''<sup>''itX''</sup> ]}} is the [[characteristic function (probability theory)\|characteristic function]] of a random variable ''X''.
	*An [[angle]], typically the second angle mentioned, after ''θ'' ([[theta]]). Especially:
	**The argument of a [[complex number]].
	**The [[phase (waves)\|phase of a wave]] in signal processing.
	**In [[spherical coordinates]], mathematicians usually refer to phi as the polar angle (from the ''z''-[[Coordinate axis\|axis]]). The convention in physics is to use phi as the azimuthal angle (from the ''x''-axis).
	**One of the [[dihedral angle]]s in the backbones of [[protein]]s.
	**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 [[Thermodynamic free energy\|free energy]] destabilizations of protein [[mutant]]s in [[phi value analysis]].
	*In [[cartography]] and [[navigation]], [[latitude]].
	*In combustion engineering, equivalence ratio. The ratio between the actual fuel air ratio to the stoichiometric fuel air ratio.
	*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 the [[International Phonetic Alphabet]] (using the straight line variant character)
	*In economics, this is usually an additive term.
	*In [[flight dynamics]], the roll angle.

	~~The upper-case letter Φ is used as a symbol for:~~
	*The [[Golden_ratio#Golden_ratio_conjugate\|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]].
	*A common symbol for the parametrization of a surface in vector [[calculus]].
	*In [[Lacanian algebra]], Φ stands for the imaginary phallus and also represents phallic signification. -Φ stands in for castration.<sup>[2]</sup>
	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 of measurement\|units]].

	== See also ==		== See also ==

Nick at 12:48, 11 October 2011

2011-10-11T12:48:27Z

← Older revision		Revision as of 12:48, 11 October 2011
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	*Strength (or resistance) reduction factor in [[structural engineering]], used to account for statistical variabilities in materials and construction methods.		*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 the [[International Phonetic Alphabet]] (using the straight line variant character)		*The symbol for a [[voiceless bilabial fricative]] in the [[International Phonetic Alphabet]] (using the straight line variant character)
	*In economics, this is usually an additive term.~~{{Clarify\|date=October 2009}}~~		*In economics, this is usually an additive term.
	*In [[flight dynamics]], the roll angle.		*In [[flight dynamics]], the roll angle.

Nick at 03:56, 2 April 2011

2011-04-02T03:56:22Z

← Older revision		Revision as of 03:56, 2 April 2011
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	[[Image:Phi.png\|thumb\|150px\|Phi]]		[[Image:Phi.png\|thumb\|150px\|Phi]]
	'''Phi''' (uppercase Φ, lowercase φ or math symbol ϕ), pronounced ˈfaɪ or sometimes /ˈfiː/ in English,<sup>[]</sup> and ˈfi in [[Modern Greek language\|modern Greek]], 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 [[Aspiration (phonetics)\|aspirated]] [[voiceless bilabial plosive]] (from which English ultimately inherits the spelling "[[ph (digraph)\|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 (Cyrillic)\|Ef]] (Ф, ф) arose from Φ.		'''Phi''' (uppercase Φ, lowercase φ or math symbol ϕ), pronounced ˈfaɪ or sometimes /ˈfiː/ in English,<sup>[1]</sup> and ˈfi in [[Modern Greek language\|modern Greek]], 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 [[Aspiration (phonetics)\|aspirated]] [[voiceless bilabial plosive]] (from which English ultimately inherits the spelling "[[ph (digraph)\|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 (Cyrillic)\|Ef]] (Ф, ф) arose from Φ.

	== Use as a symbol ==		== Use as a symbol ==
Line 36:		Line 36:
	*The number of phases in a power system in [[electrical engineering]], for example 1Φ for [[single phase]], 3Φ for [[three phase]].		*The number of phases in a power system in [[electrical engineering]], for example 1Φ for [[single phase]], 3Φ for [[three phase]].
	*A common symbol for the parametrization of a surface in vector [[calculus]].		*A common symbol for the parametrization of a surface in vector [[calculus]].
	*In [[Lacanian algebra]], Φ stands for the imaginary phallus and also represents phallic signification. -Φ stands in for castration.<sup>[]</sup>		*In [[Lacanian algebra]], Φ stands for the imaginary phallus and also represents phallic signification. -Φ stands in for castration.<sup>[2]</sup>
	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 of measurement\|units]].		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 of measurement\|units]].

Nick at 03:55, 2 April 2011

2011-04-02T03:55:49Z

← Older revision		Revision as of 03:55, 2 April 2011
Line 1:		Line 1:
	Φφ Phi		[[Image:Phi.png\|thumb\|150px\|Phi]]
			'''Phi''' (uppercase Φ, lowercase φ or math symbol ϕ), pronounced ˈfaɪ or sometimes /ˈfiː/ in English,<sup>[]</sup> and ˈfi in [[Modern Greek language\|modern Greek]], 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 [[Aspiration (phonetics)\|aspirated]] [[voiceless bilabial plosive]] (from which English ultimately inherits the spelling "[[ph (digraph)\|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 (Cyrillic)\|Ef]] (Ф, ф) arose from Φ.

			== Use as a symbol ==
			The lower-case letter <math>\varphi \,</math> (or often its variant, <math>\phi \,</math>) is often used to represent the following:
			*The [[golden ratio]] <math>\tfrac{1 + \sqrt{5}}{2} \approx 1.61803\ldots</math> in mathematics, art, and architecture.
			*[[Euler's totient function]] ''φ''(''n'') in number theory; also called ''Euler's phi function''.
			*In algebra, [[Group (mathematics)\|group]] or [[Ring (mathematics)\|ring]] [[homomorphism]]s
			* In [[probability theory]], {{nowrap\|1=''ϕ''(''x'') = (2π)<sup>−½</sup>''e''<sup>−''x''<sup>2</sup>/2</sup>}} is the [[probability density function]] of the [[normal distribution]].
			* In [[probability theory]], {{nowrap\|1=''φ''<sub>''X''</sub>(''t'') = E[ ''e''<sup>''itX''</sup> ]}} is the [[characteristic function (probability theory)\|characteristic function]] of a random variable ''X''.
			*An [[angle]], typically the second angle mentioned, after ''θ'' ([[theta]]). Especially:
			**The argument of a [[complex number]].
			**The [[phase (waves)\|phase of a wave]] in signal processing.
			**In [[spherical coordinates]], mathematicians usually refer to phi as the polar angle (from the ''z''-[[Coordinate axis\|axis]]). The convention in physics is to use phi as the azimuthal angle (from the ''x''-axis).
			**One of the [[dihedral angle]]s in the backbones of [[protein]]s.
			**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 [[Thermodynamic free energy\|free energy]] destabilizations of protein [[mutant]]s in [[phi value analysis]].
			*In [[cartography]] and [[navigation]], [[latitude]].
			*In combustion engineering, equivalence ratio. The ratio between the actual fuel air ratio to the stoichiometric fuel air ratio.
			*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 the [[International Phonetic Alphabet]] (using the straight line variant character)
			*In economics, this is usually an additive term.{{Clarify\|date=October 2009}}
			*In [[flight dynamics]], the roll angle.

			The upper-case letter Φ is used as a symbol for:
			*The [[Golden_ratio#Golden_ratio_conjugate\|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]].
			*A common symbol for the parametrization of a surface in vector [[calculus]].
			*In [[Lacanian algebra]], Φ stands for the imaginary phallus and also represents phallic signification. -Φ stands in for castration.<sup>[]</sup>
			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 of measurement\|units]].

			== See also ==
			*[[F\|F, f - Ef (Latin)]]
			*[[Ef (Cyrillic)\|Ф, ф - Ef (Cyrillic)]]
			*[[Psi and phi type figurine]]
			* [[Փ]] ([[Armenian alphabet\|Armenian letter]])

			==References==

			{{DEFAULTSORT:Phi (Letter)}}
			[[Category:Greek letters]]

Nick: Protected "Phi" [edit=autoconfirmed:move=autoconfirmed]

2009-03-01T03:38:37Z

Protected "Phi" [edit=autoconfirmed:move=autoconfirmed]

← Older revision	Revision as of 03:38, 1 March 2009
(No difference)

Nick: New page: Φφ Phi

2009-03-01T03:38:32Z

New page: Φφ Phi

New page

Φφ Phi