Mu (letter)

Mu (Template:IPAc-en;<ref>Template:Cite book</ref><ref>Template:OED</ref> uppercase Μ, lowercase μ; Ancient Greek Template:Lang Template:IPA, Template:Langx or μυ—both Template:IPA) is the twelfth letter of the Greek alphabet, representing the voiced bilabial nasal Template:IPA. In the system of Greek numerals it has a value of 40.<ref>Template:Cite book</ref> 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 Template:Ref (mem). Letters that derive from mu include the Roman M and the Cyrillic М, though the lowercase resembles a small Latin U (u).

Greek letter mu

Names

Ancient Greek

In Greek, the name of the letter was written Template:Lang and pronounced Template:IPA.

Modern Greek

In Modern Greek, the letter is spelled Template:Lang and pronounced Template:IPA. In polytonic orthography, it is written with an acute accent: Template:Lang.<ref>Template:Cite book</ref><ref>Template:Cite book</ref>

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.

Prefix for units of measurement

"μ" is used as a unit prefix denoting a factor of 10⁻⁶ (one millionth), in this context, the symbol's name is "micro".

• Metric prefix
• International System of Units prefix, also known as "SI prefix"
• The micrometre with a symbol of "μm" can also be referred to as the non-SI term "micron".

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 degree of membership in a fuzzy set<ref>Template:Cite book</ref>
• the Möbius function in number theory<ref>Template:Cite web</ref><ref>Template:Cite web</ref>
• the population mean or expected value in probability and statistics<ref>Template:Cite web</ref>
• the service or departure rate in queueing theory<ref>M/M/1 queues and queueing networks, Oxford University lecture notes</ref>
• the Ramanujan–Soldner constant<ref>Template:Cite web</ref>

Physics and engineering

In classical physics and engineering:

• the coefficient of friction<ref>Template:Cite book</ref> (also used in aviation as braking coefficient (see Braking action))
• reduced mass in the two-body problem<ref>Template:Cite book</ref>
• Standard gravitational parameter in celestial mechanics<ref>Template:Cite book</ref>
• linear density, or mass per unit length, in strings and other one-dimensional objects<ref>Template:Cite book</ref>
• permeability in electromagnetism<ref>Template:Cite book</ref>
• the magnetic dipole moment of a current-carrying coil<ref>Template:Cite journal</ref>
• dynamic viscosity in fluid mechanics
• the amplification factor or voltage gain of a triode vacuum tube<ref>Template:Cite book</ref>
• the electrical mobility of a charged particle
• the rotor advance ratio, the ratio of aircraft airspeed to rotor-tip speed in rotorcraft<ref>"Nomenclature" NASA</ref><ref>Template:Cite web</ref>
• the pore water pressure in saturated soil

In particle physics:

• elementary particles: muon and antimuon (Template:Subatomic particle, Template:Subatomic particle), muon neutrino and antineutrino (Template:Subatomic particle, Template:Subatomic particle)
• the proton-to-electron mass ratio<ref>Template:Cite journal</ref>

In thermodynamics:

• the chemical potential of a system or component of a system

Computer science

In evolutionary algorithms:

• 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, <math>\text{list}(\tau) = \mu{}\alpha{}.1 + \tau{}\alpha</math> is the type of lists with elements of type <math>\tau</math> (a type variable): a sum of unit, representing Template:Mono, with a pair of a <math>\tau</math> and another <math>\text{list}(\tau)</math> (represented by <math>\alpha</math>). In this notation, <math>\mu</math> is a binding form, where the variable (<math>\alpha</math>) introduced by <math>\mu</math> is bound within the following term (<math>1 + \tau{}\alpha</math>) to the term itself. Via substitution and arithmetic, the type expands to <math> 1 + \tau + \tau^2 + \tau^3 + \cdots</math>, an infinite sum of ever-increasing products of <math>\tau</math> (that is, a <math>\tau{}\text{ list}</math> is any <math>k</math>-tuple of values of type <math>\tau</math> for any <math>k \ge 0</math>). Another way to express the same type is <math>\text{list}(\tau) = 1 + \tau{}\text{list}(\tau)</math>.

Chemistry

In chemistry:

• the prefix given in IUPAC nomenclature for a bridging ligand

Biology

In biology:

• the mutation rate in population genetics
• A class of Immunoglobulin heavy chain that defines IgM type Antibodies

Pharmacology

In pharmacology:

• an important opiate receptor

Orbital mechanics

In 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 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.

Cameras

The Olympus Corporation manufactures a series of digital cameras called Olympus μ Template:IPA<ref>Template:Cite web</ref> (known as Olympus Stylus in North America).

Linguistics

In phonology:

• mora

In syntax:

• μP (mu phrase) can be used as the name for a functional projection.<ref>Template:Cite journal</ref>

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.

Unicode

The lowercase mu (as "micro sign") appeared at Template:Tt in the 8-bit ISO-8859-1 encoding, from which Unicode and many other encodings inherited it. It was also at Template:Tt in the popular CP437 on the IBM PC. Unicode designates mu as is the compatibility equivalent of the micro sign.<ref>Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)</ref>

• Template:Unichar
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• Template:UnicharTemplate:Efn
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See also

• Greek letters used in mathematics, science, and engineering
• Fraser alphabet#Consonants