Phi (letter)
From Wikipedia, the free encyclopedia
Phi (uppercase Φ, lowercase φ or ϕ), pronounced [fi] 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. In the system of Greek numerals it has a value of 500 (φʹ) or 500,000 (͵φ).
The lower-case letter φ (or often its variant, ) 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
- Any function in mathematics.
- 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
- A sentence in first-order logic.
The upper-case letter Φ is used as a symbol for:
- 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 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.
See also phi phenomenon.
[edit] Computing
In Unicode, there are multiple forms of the phi letter:
- lower case:
- upper case:
- U+03A6 GREEK CAPITAL LETTER PHI (Φ): Greek capital letter phi
In HTML/XHTML, the upper and lower case phi character entity references are Φ (Φ in your browser) and φ (φ) respectively. In LaTeX, the math symbols are \Phi (Φ), \phi (φ), and \varphi ().