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Phi (letter)
 
 
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Phi (uppercase F, lowercase f or ), pronounced [] in modern Greek and as [] in English, is the 21st letter of the Greek alphabet
Greek alphabet

The Greek alphabet is a set of twenty-four letters that has been used to write the Greek language since the late 9th century BC or early 8th century BCE....
. In modern Greek, it represents [], a voiceless labiodental fricative
Voiceless labiodental fricative

The voiceless labiodental fricative is a type of consonantal sound, used in some Speech communication languages. The symbol in the International Phonetic Alphabet that represents this sound is , and the equivalent X-SAMPA symbol is f....
. In Ancient Greek it represented [], an aspirated
Aspiration (phonetics)

In phonetics, aspiration is the strong burst of Earth's atmosphere that accompanies either the release or, in the case of preaspiration, the closure of some obstruents....
 voiceless bilabial plosive
Voiceless bilabial plosive

The voiceless bilabial plosive is a type of consonantal sound used in many Speech communication languages. The symbol in the International Phonetic Alphabet that represents this sound is , and the equivalent X-SAMPA symbol is p....
 (from which English ultimately inherits the spelling "ph
Ph (digraph)

Ph is a digraph in the English Language and many other languages that represents the sound // . Ph in English generally occurs in words derived from Greek language, due to Latin transcription of Greek Phi as ph....
" in words derived from Greek). In the system of Greek numerals
Greek numerals

Greek numerals are a numeral system using letters of the Greek alphabet. They are also known by the names Milesian numerals, Alexandrian numerals, or alphabetic numerals....
 it has a value of 500 (f') or 500,000 (?f). The Cyrillic letter Ef (?, ?) arose from phi.

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

The upper-case letter F is used as a symbol for: The diameter
Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle....
 symbol in engineering
Engineering

Engineering is the discipline and profession of applying Technology and science knowledge and utilizing natural laws and physical resources in order to design and implement materials, structures, machines, devices, systems, and process that safely realize a desired objective and meet specified criteria....
, ?
?

or is a letter derived from the Latin alphabet. Both glyphs of the majuscule and Lower case forms of this letter are based on the rotated form of a minuscule e; a similar letter with identical minuscule is used in the Pan-Nigerian Alphabet, but has the capital form majuscule , based on a horizontally flipped majuscule E....
, is often incorrectly referred to as "phi".






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Phi (uppercase F, lowercase f or ), pronounced [] in modern Greek and as [] in English, is the 21st letter of the Greek alphabet
Greek alphabet

The Greek alphabet is a set of twenty-four letters that has been used to write the Greek language since the late 9th century BC or early 8th century BCE....
. In modern Greek, it represents [], a voiceless labiodental fricative
Voiceless labiodental fricative

The voiceless labiodental fricative is a type of consonantal sound, used in some Speech communication languages. The symbol in the International Phonetic Alphabet that represents this sound is , and the equivalent X-SAMPA symbol is f....
. In Ancient Greek it represented [], an aspirated
Aspiration (phonetics)

In phonetics, aspiration is the strong burst of Earth's atmosphere that accompanies either the release or, in the case of preaspiration, the closure of some obstruents....
 voiceless bilabial plosive
Voiceless bilabial plosive

The voiceless bilabial plosive is a type of consonantal sound used in many Speech communication languages. The symbol in the International Phonetic Alphabet that represents this sound is , and the equivalent X-SAMPA symbol is p....
 (from which English ultimately inherits the spelling "ph
Ph (digraph)

Ph is a digraph in the English Language and many other languages that represents the sound // . Ph in English generally occurs in words derived from Greek language, due to Latin transcription of Greek Phi as ph....
" in words derived from Greek). In the system of Greek numerals
Greek numerals

Greek numerals are a numeral system using letters of the Greek alphabet. They are also known by the names Milesian numerals, Alexandrian numerals, or alphabetic numerals....
 it has a value of 500 (f') or 500,000 (?f). The Cyrillic letter Ef (?, ?) arose from phi.

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

    In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller....
      in mathematics, art, and architecture.
  • Euler's totient function
    Euler's totient function

    In number theory, the totient of a positive integer n is defined to be the number of positive integers less than or equal to n that are coprime to n....
     f(n) in number theory; also called Euler's phi function.
  • The probability density function
    Probability density function

    In mathematics, a probability density function is a function that represents a probability distribution in terms of integrals.Formally, a probability distribution has density ƒ, if ƒ is a non-negative Lebesgue integration function such that the probability of the interval [a, b] is given by...
     of the normal distribution
    Normal distribution

    The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields....
     in mathematics
    Mathematics

    Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
     and statistics
    Statistics

    Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data....
    .
  • An angle
    Angle

    In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
    , typically the second angle mentioned, after ? (theta
    Theta

    Theta is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth. In the system of Greek numerals it has a value of 9....
    ). Especially:
    • The argument of a complex number
      Complex number

      In mathematics, the complex numbers are an extension of the real numbers obtained by adjoining an imaginary unit, denoted i, which satisfies:...
      .
    • The phase of a wave
      Phase (waves)

      The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0....
       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 angle
      Dihedral angle

      In geometry, the angle between two Plane s is called their dihedral or torsion angle.The dihedral angle of two planes can be seen by looking at the planes "edge on", i.e., along their line of intersection....
      s in the backbones of protein
      Protein

      Proteins are organic compounds made of amino acids arranged in a linear chain and joined together by peptide bonds between the carboxyl and amino groups of adjacent amino acid Residue ....
      s.
    • Internal or effective angle of friction
  • Electric potential
    Electric potential

    At a point in space, the electric potential is the potential energy per unit of electric charge that is associated with a static electric field....
     in physics.
  • The work function
    Work function

    In solid state physics, the work function is the minimum energy needed to remove an electron from a solid to a point immediately outside the solid surface ....
     in electronics.
  • A shorthand
    Shorthand

    Shorthand is an abbreviated symbolic writing method that increases speed or brevity of writing as compared to a normal method of writing a language....
     representation for an aromatic functional group
    Functional group

    In organic chemistry, functional groups are specific groups of atoms within molecules that are responsible for the characteristic chemical reactions of those molecules....
     in organic chemistry
    Organic chemistry

    Organic chemistry is a discipline within chemistry which involves the science study of the structure, properties, composition, chemical reaction, and preparation of chemical compounds that contain carbon....
  • The fugacity
    Fugacity

    Fugacity is a measure of a chemical potential in the form of 'adjusted pressure.' It reflects the tendency of a substance to prefer one phase over another, and can be literally defined as ?the tendency to flee or escape?....
     coefficient in thermodynamics
    Thermodynamics

    In physics, thermodynamics is the study of the conversion of heat energy into different forms of energy ; different energy conversions into heat energy; and its relation to macroscopic variables such as temperature, pressure, and volume....
  • The ratio of free energy
    Thermodynamic free energy

    In thermodynamics, the term thermodynamic free energy refers to the amount of Work that can be extracted from a system, and is helpful in engineering applications....
     destabilizations of protein mutant
    Mutant

    A mutant is an individual, organism, or new genetic character arising or resulting from an instance of mutation, which is a base-pair sequence change within the DNA of a gene or chromosome of an organism resulting in the creation of a new character or Trait not found in the wild type....
    s in phi value analysis
    Phi value analysis

    Phi value analysis is an experimental protein engineering method used to study the structure of the folding transition state in small protein domains that protein folding in a two-state manner....
  • In cartography
    Cartography

    File:Mediterranean chart fourteenth century2.jpgCartography is the study and practice of making Geography Map. Combining science, aesthetics, and technique, cartography builds on the premise that we can model reality in ways that communicate spatial information effectively....
     and navigation
    Navigation

    Navigation is the process of reading, and controlling the movement of a craft or vehicle from one place to another. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks....
    , latitude
    Latitude

    Latitude, usually denoted symbolically by the Greek letter phi gives the location of a place on Earth north or south of the equator. Lines of Latitude are the horizontal lines shown running east-to-west on maps ....
    .
  • A sentence in first-order logic
    First-order logic

    First-order logic is a formal deductive system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus , the lower predicate calculus, the language of first-order logic or predicate logic....
    .
  • Porosity
    Porosity

    Porosity is a measure of the void spaces in a material, and is measured as a fraction, between 0?1, or as a percentage between 0?100%. The term is used in multiple fields including ceramics, metallurgy, materials, manufacturing, earth sciences and construction....
     in geology and hydrology
    Hydrology

    Hydrology is the study of the movement, distribution, and quality of water throughout the Earth, and thus addresses both the hydrologic cycle and water resources....
    .
  • Strength (or resistance) reduction factor in structural engineering
    Structural engineering

    Structural engineering is a field of engineering dealing with the analysis and design of structures that support or resist structural loads. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right....
    , used to account for statistical variabilities in materials and construction methods.


The upper-case letter F is used as a symbol for:
  • The golden ratio conjugate
    Golden ratio

    In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller....
     0.618... in mathematics.
  • The magnetic flux
    Magnetic flux

    Magnetic flux, represented by the Greek letter F , is a measure of quantity of magnetism, taking into account the strength and the extent of a magnetic field....
     and electric flux
    Electric flux

    In electromagnetism, electric flux is the flux of the electric field. Electric flux is proportional to the number of electric field lines going through a virtual surface....
     in physics, with subscripts distinguishing the two.
  • The cumulative distribution function
    Cumulative distribution function

    In probability theory and statistics, the cumulative distribution function or just distribution function, completely describes the probability distribution of a real-valued random variable X....
     of the normal distribution
    Normal distribution

    The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields....
     in mathematics
    Mathematics

    Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
     and statistics
    Statistics

    Statistics is a Mathematics pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It also provides tools for prediction and forecasting based on data....
    .
  • Philosophy
    Philosophy

    Philosophy is the study of general problems concerning matters such as existence, knowledge, truth, beauty, justice, validity, mind, and language....
    .
  • The number of phases in a power system in electrical engineering
    Electrical engineering

    Electrical engineering, sometimes referred to as electrical and electronic engineering, is a field of engineering that deals with the study and application of electricity, electronics and electromagnetism....
    , for example 1F for single phase, 3F for three phase.
  • The symbol of the voiceless bilabial fricative
    Voiceless bilabial fricative

    The voiceless bilabial fricative is a type of consonantal sound, used in some Speech communication languages. The symbol in the International Phonetic Alphabet that represents this sound is , and the equivalent X-SAMPA symbol is p....
     in the international phonetic alphabet
    International Phonetic Alphabet

    The International Phonetic Alphabet "The acronym 'IPA' strictly refers [...] to the 'International Phonetic Association'. But it is now such a common practice to use the acronym also to refer to the alphabet itself that resistance seems pedantic....
    .
The diameter
Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle....
 symbol in engineering
Engineering

Engineering is the discipline and profession of applying Technology and science knowledge and utilizing natural laws and physical resources in order to design and implement materials, structures, machines, devices, systems, and process that safely realize a desired objective and meet specified criteria....
, ?
?

or is a letter derived from the Latin alphabet. Both glyphs of the majuscule and Lower case forms of this letter are based on the rotated form of a minuscule e; a similar letter with identical minuscule is used in the Pan-Nigerian Alphabet, but has the capital form majuscule , based on a horizontally flipped majuscule E....
, 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
Circle

A circle is a simple shape of Euclidean geometry consisting of those point in a plane which are the same distance from a given point called the center....
 is 14 units
Units of measurement

The definition, agreement and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day....
.

Computing

In Unicode
Unicode

Unicode is a computing industry standard allowing computers to consistently represent and manipulate Character expressed in most of the world's writing systems....
, there are multiple forms of the phi letter:
  • Uppercase:
    • U+03A6 GREEK CAPITAL LETTER PHI (Φ): used in Greek texts
  • Lowercase:
  • GREEK SMALL LETTER PHI (f): used in Greek texts
    • U+03D5 GREEK PHI SYMBOL : used in mathematical and technical contexts
  • LATIN SMALL LETTER PHI: used in IPA to symbolise a voiceless bilabial fricative
    Voiceless bilabial fricative

    The voiceless bilabial fricative is a type of consonantal sound, used in some Speech communication languages. The symbol in the International Phonetic Alphabet that represents this sound is , and the equivalent X-SAMPA symbol is p....


In HTML/XHTML
XHTML

The Extensible Hypertext Markup Language, or XHTML, is a markup language that has the same depth of expression as HTML, but also conforms to XML syntax....
, the upper and lower case phi character entity reference
Character entity reference

In the markup languages SGML, HTML, XHTML and XML, a character entity reference is a reference to a particular kind of named SGML entity that has been predefined or explicitly declared in a Document Type Definition ....
s are Φ (F) and φ (f) respectively.

In LaTeX
LaTeX

LaTeX is a document markup language and Word processor for the TeX typesetting program. Within the typesetting system, its name is styled as ....
, the math symbols are \Phi , \phi , and \varphi .

In some browsers (e.g. Internet Explorer 6
Internet Explorer 6

Microsoft Internet Explorer 6 , is a graphical user interface web browser developed by Microsoft and included as part of the Microsoft Windows XP and Windows Server 2003 lines of operating systems....
), 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
U+03D5 GREEK PHI SYMBOL


See also

  • F, f - Ef (Latin)
    F

    F is the sixth letter in the Latin alphabet. Its name in English language is spelled ef or eff ....
  • ?, ? - Ef (Cyrillic)