|Use in other languages|
Mu /ˈm(j)uː/ (uppercase Μ, lowercase μ; Ancient Greek μῦ [mŷː], Greek: μι or μυ—both [mi]) is the 12th letter of the Greek alphabet, representing the voiced bilabial nasal IPA: [m]. In the system of Greek numerals it has a value of 40. Mu was derived from the Egyptian hieroglyphic symbol for water, which had been simplified by the Phoenicians and named after their word for water, to become 𐤌img (mem). Letters that derive from mu include the Roman M and the Cyrillic М.
In Ancient Greek, the name of the letter was written μῦ and pronounced [mŷː]
In Modern Greek, the letter is spelled μι and pronounced [mi]. In polytonic orthography, it is written with an acute accent: μί.
Use as symbol
The lowercase letter mu (μ) is used as a special symbol in many academic fields. Uppercase mu is not used, because it appears identical to Latin M.
- the SI prefix micro-, which represents one millionth, or 10−6. Lowercase letter "u" is often substituted for "μ" when the Greek character is not typographically available; for example the unit "microfarad", correctly "μF", is often rendered as "uF" or "ufarad" in technical documents.
- the micron "μ", an old unit now named the micrometre and denoted "μm"
"μ" is conventionally used to denote certain things; however, any Greek letter or other symbol may be used freely as a variable name.
- a measure in measure theory
- minimalization in computability theory and Recursion theory
- the integrating factor in ordinary differential equations
- the degree of membership in a fuzzy set
- the Möbius function in number theory
- the population mean or expected value in probability and statistics
- the Ramanujan–Soldner constant
Physics and engineering
In classical physics and engineering:
- the coefficient of friction (also used in aviation as braking coefficient (see Braking action))
- reduced mass in the two-body problem
- Standard gravitational parameter in celestial mechanics
- linear density, or mass per unit length, in strings and other one-dimensional objects
- permeability in electromagnetism
- the magnetic dipole moment of a current-carrying coil
- dynamic viscosity in fluid mechanics
- the amplification factor or voltage gain of a triode vacuum tube
- the electrical mobility of a charged particle
- the rotor advance ratio, the ratio of aircraft airspeed to rotor-tip speed in rotorcraft
- the pore water pressure in saturated soil
In particle physics:
- the elementary particles called the muon and antimuon
- the proton-to-electron mass ratio
- the chemical potential of a system or component of a system
- μ, population size from which in each generation λ offspring will generate (the terms μ and λ originate from evolution strategy notation)
In type theory:
- Used to introduce a recursive data type. For example, is the type of lists with elements of type (a type variable): a sum of unit, representing nil, with a pair of a and another (represented by ). In this notation, is a binding form, where the variable () introduced by is bound within the following term () to the term itself. Via substitution and arithmetic, the type expands to , an infinite sum of ever-increasing products of (that is, a is any -tuple of values of type for any ). Another way to express the same type is .
- the prefix given in IUPAC nomenclature for a bridging ligand
- the mutation rate in population genetics
- A class of Immunoglobulin heavy chain that defines IgM type Antibodies
- an important opiate receptor
- Standard gravitational parameter of a celestial body, the product of the gravitational constant G and the mass M
- planetary discriminant, represents an experimental measure of the actual degree of cleanliness of the orbital zone, a criterion for defining a planet. The value of μ is calculated by dividing the mass of the candidate body by the total mass of the other objects that share its orbital zone.
- Mu chord
- Electronic musician Mike Paradinas runs the label Planet Mu which utilizes the letter as its logo, and releases music under the pseudonym μ-Ziq, pronounced "music"
- Used as the name of the school idol group μ's, pronounced "muse", consisting of nine singing idols in the anime Love Live! School Idol Project
- Official fandom name of Kpop group f(x), appearing as either MeU or 'μ'
- Hip-hop artist Muonboy has taken inspiration from the particle for his stage name and his first EP named Mu uses the letter as its title.
The Olympus Corporation manufactures a series of digital cameras called Olympus μ [mju:] (known as Olympus Stylus in North America)
- μP (mu phrase) can be used as the name for a functional projection.
In Celtic linguistics:
- /μ/ can represent an Old Irish nasalized labial fricative of uncertain articulation, the ancestor of the sound represented by Modern Irish mh.
This section needs additional citations for verification. (June 2015)
- Greek Mu / Coptic Mu
|Unicode name||GREEK CAPITAL LETTER MU||GREEK SMALL LETTER MU||MICRO SIGN||COPTIC CAPITAL LETTER MI||COPTIC SMALL LETTER MI|
|UTF-8||206 156||CE 9C||206 188||CE BC||194 181||C2 B5||226 178 152||E2 B2 98||226 178 153||E2 B2 99|
|Numeric character reference||Μ
|Named character reference||Μ||μ||µ|
|Code page 437, 850||230||E6||230||E6|
|Code page 737||139||8B||163||A3|
|Code page 851, 869||183||B7||230||E6|
|Code page 1253||204||CC||236||EC|
- Mathematical Mu
|Unicode name||MATHEMATICAL BOLD
|MATHEMATICAL BOLD ITALIC
|MATHEMATICAL BOLD ITALIC|
|UTF-8||240 157 154 179||F0 9D 9A B3||240 157 155 141||F0 9D 9B 8D||240 157 155 173||F0 9D 9B AD||240 157 156 135||F0 9D 9C 87||240 157 156 167||F0 9D 9C A7||240 157 157 129||F0 9D 9D 81|
|UTF-16||55349 57011||D835 DEB3||55349 57037||D835 DECD||55349 57069||D835 DEED||55349 57095||D835 DF07||55349 57127||D835 DF27||55349 57153||D835 DF41|
|Numeric character reference||𝚳
|Unicode name||MATHEMATICAL SANS-SERIF
BOLD CAPITAL MU
BOLD SMALL MU
BOLD ITALIC CAPITAL MU
BOLD ITALIC SMALL MU
|UTF-8||240 157 157 161||F0 9D 9D A1||240 157 157 187||F0 9D 9D BB||240 157 158 155||F0 9D 9E 9B||240 157 158 181||F0 9D 9E B5|
|UTF-16||55349 57185||D835 DF61||55349 57211||D835 DF7B||55349 57243||D835 DF9B||55349 57269||D835 DFB5|
|Numeric character reference||𝝡
These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.
Image list for readers with font problems
- ^ "mu". The Chambers Dictionary (9th ed.). Chambers. 2003. ISBN 0-550-10105-5.
- ^ "mu". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
- ^ Hadley, James (1884). A Greek Grammar for Schools and Colleges. New York: American Book. p. 79.
- ^ Neoelliniki Grammatiki (Tis Dimotikis).
- ^ Grammatiki tis Dimotikis Glossas.
- ^ Albert Flack (19 April 2010). "US20130038341A1 - Contactor health monitor circuit and method". Google Patents. Retrieved 10 September 2018. Example of document using both "ufarad" and "microFarad"
- ^ Ballou, Glen (1987). Handbook for Sound Engineers: The New Audio Cyclopedia (1 ed.). Howard W. Sams Co. p. 250. ISBN 0-672-21983-2.
Amplification factor or voltage gain is the amount the signal at the control grid is increased in amplitude after passing through the tube, which is also referred to as the Greek letter μ (mu) or voltage gain (Vg) of the tube.
- ^ "Nomenclature" NASA
- ^ Definition
- ^ "Olympus History : μ[mju:] (Stylus) Series".
- ^ Johnson, Kyle (1991). "Object Positions". Natural Language and Linguistic Theory. 9 (4): 577–636. doi:10.1007/BF00134751. S2CID 189901613.
- ^ Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)