Mu (letter)
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.
Names
Ancient Greek
In Ancient Greek, the name of the letter was written μῦ and pronounced [mŷː].
Modern Greek
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 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[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
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, 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 .
Chemistry
In chemistry:
the prefix given in IUPAC nomenclature for a bridging ligand
Biology
In biology:
the mutation rate in population genetics
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 major 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 in the name of the school idol group μ's, pronounced "muse", consisting of nine singing teen girls 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 |
| 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 | Μ | μ | μ | µ | µ | Ⲙ | Ⲙ | ⲙ | ⲙ |
| Named character reference | Μ | μ | µ | |||||||
| ISO/IEC 8859-1 | 181 | B5 | ||||||||
| ISO/IEC 8859-7 | 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 | ||||||
| Roman-8, Roman-9 | 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 |
| 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 | 횳 | 횳 | 훍 | 훍 | 훭 | 훭 | 휇 | 휇 | 휧 | 휧 | 흁 | 흁 |
| Character | 𝝡 | 𝝻 | 𝞛 | 𝞵 | ||||
|---|---|---|---|---|---|---|---|---|
| Unicode name | MATHEMATICAL SANS-SERIF BOLD CAPITAL MU | MATHEMATICAL SANS-SERIF BOLD SMALL MU | MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL MU | MATHEMATICAL SANS-SERIF 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 |
| 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 | 흡 | 흡 | 흻 | 흻 | 힛 | 힛 | ힵ | ힵ |
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
^ [[INLINE_IMAGE|//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Phoenician_mem.svg/50px-Phoenician_mem.svg.png|//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Phoenician_mem.svg/75px-Phoenician_mem.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/Phoenician_mem.svg/100px-Phoenician_mem.svg.png 2x|Phoenician mem.svg|h50|w50]]
See also
Greek letters used in mathematics, science, and engineering
Fraser alphabet#Consonants