Mu (letter)
Mu (uppercase Μ, lowercase μ; Ancient Greek μῦ [mŷː], Greek: μι or μυ—both [mi]) or my[1] is the 12th letter of the Greek alphabet. In the system of Greek numerals it has a value of 40.[2] 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 𐤌^{img} (mem). Letters that derive from mu include the Roman M and the Cyrillic М. It is also used as coefficient of friction.
Greek alphabet  



History  
Use in other languages  
Related topics  
 
Names
Ancient Greek
In Ancient Greek, the name of the letter was written μῦ and pronounced [mŷː].
Modern Greek
In Modern Greek, the letter is spelled μι and pronounced [mi]. In polytonic orthography, it is written with an acute accent: μί.[3][4]
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.
Measurement
 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.[5]
 the micron "μ", an old unit now named the micrometre and denoted "µm"
Mathematics
"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 learning rate in artificial neural networks
 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)
 reduced mass in the twobody problem
 Standard gravitational parameter in celestial mechanics
 linear density, or mass per unit length, in strings and other onedimensional objects
 permeability in electromagnetism
 the magnetic dipole moment of a currentcarrying coil
 dynamic viscosity in fluid mechanics
 the amplification factor or voltage gain of a triode vacuum tube[6]
 the electrical mobility of a charged particle
 a.k.a. rotor advance ratio, the ratio of aircraft airspeed to rotor tip speed in rotorcraft[7][8]
In particle physics:
 the elementary particles called the muon and antimuon
In thermodynamics:
 the chemical potential of a system or component of a system
Computer science
 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 everincreasing products of (that is, a is any tuple of values of type for any ). Another way to express the same type is .
Orbital mechanics
 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.
Music
 Mu major chord
 Electronic musician Mike Paradinas runs the label Planet Mu which utilizes the letter as its logo, and releases music under the pseudonym µZiq, 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'
Cameras
The Olympus Corporation manufactures a series of digital cameras called Olympus µ [mju:][9] (known as Olympus Stylus in North America)
Linguistics
In phonology, it often stands for mora. In syntax, μP (mu phrase) can be used as the name for a functional projection.[10]. Celtic specialists sometimes use /µ/ to represent an Old Irish nasalized labial fricative of uncertain articulation, the ancestor of the sound represented by Modern Irish mh.
Character encodings
 Greek Mu / Coptic Mu[11]
Character  Μ  μ  µ  Ⲙ  ⲙ  

Unicode name  GREEK CAPITAL LETTER MU  GREEK SMALL LETTER MU  MICRO SIGN  COPTIC CAPITAL LETTER MI  COPTIC SMALL LETTER MI  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  924  U+039C  956  U+03BC  181  U+00B5  11416  U+2C98  11417  U+2C99 
UTF8  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  Μ  μ  μ  µ  µ  Ⲙ  Ⲙ  ⲙ  ⲙ 
Named character reference  Μ  μ  µ  
ISO/IEC 88591  181  B5  
ISO/IEC 88597  204  CC  236  EC  
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  
Roman8, Roman9  243  F3  243  F3  
TeX  \mu  \micro 
 Mathematical Mu
Character  𝚳  𝛍  𝛭  𝜇  𝜧  𝝁  

Unicode name  MATHEMATICAL BOLD CAPITAL MU  MATHEMATICAL BOLD SMALL MU  MATHEMATICAL ITALIC CAPITAL MU  MATHEMATICAL ITALIC SMALL MU  MATHEMATICAL BOLD ITALIC CAPITAL MU  MATHEMATICAL BOLD ITALIC SMALL MU  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120499  U+1D6B3  120525  U+1D6CD  120557  U+1D6ED  120583  U+1D707  120615  U+1D727  120641  U+1D741 
UTF8  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 
UTF16  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  𝚳  𝛍  𝛍  𝛭  𝛭  𝜇  𝜇  𝜧  𝜧  𝝁  𝝁 
Character  𝝡  𝝻  𝞛  𝞵  

Unicode name  MATHEMATICAL SANSSERIF BOLD CAPITAL MU  MATHEMATICAL SANSSERIF BOLD SMALL MU  MATHEMATICAL SANSSERIF BOLD ITALIC CAPITAL MU  MATHEMATICAL SANSSERIF BOLD ITALIC SMALL MU  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120673  U+1D761  120699  U+1D77B  120731  U+1D79B  120757  U+1D7B5 
UTF8  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 
UTF16  55349 57185  D835 DF61  55349 57211  D835 DF7B  55349 57243  D835 DF9B  55349 57269  D835 DFB5 
Numeric character reference  𝝡  𝝡  𝝻  𝝻  𝞛  𝞛  𝞵  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
References
 http://www.oed.com/view/Entry/123122
 Hadley, James (1884). A Greek Grammar for Schools and Colleges. New York: American Book. p. 79.
 http://elibrary.iep.edu.gr/iep/collection/browse/item.html?code=0117160&tab=02&start=40#i
 http://elibrary.iep.edu.gr/iep/collection/browse/item.html?code=0118549&tab=01
 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 0672219832.
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 (V_{g}) 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.
 Unicode Code Charts: Greek and Coptic (Range: 037003FF)