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 𐤌img (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

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 106. 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.

Physics and engineering

In classical physics and engineering:

In particle physics:

In thermodynamics:

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:

Biology

In biology:

  • the mutation rate in population genetics

Pharmacology

In pharmacology:

Orbital mechanics

In orbital mechanics:

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 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]
CharacterΜμµ
Unicode nameGREEK CAPITAL LETTER MUGREEK SMALL LETTER MUMICRO SIGNCOPTIC CAPITAL LETTER MICOPTIC SMALL LETTER MI
Encodingsdecimalhexdecimalhexdecimalhexdecimalhexdecimalhex
Unicode924U+039C956U+03BC181U+00B511416U+2C9811417U+2C99
UTF-8206 156CE 9C206 188CE BC194 181C2 B5226 178 152E2 B2 98226 178 153E2 B2 99
Numeric character referenceΜΜμμµµⲘⲘⲙⲙ
Named character referenceΜμµ
ISO/IEC 8859-1181B5
ISO/IEC 8859-7204CC236EC
Code page 437, 850230E6230E6
Code page 7371398B163A3
Code page 851, 869183B7230E6
Code page 1253204CC236EC
Roman-8, Roman-9243F3243F3
TeX\mu\micro
  • Mathematical Mu
Character𝚳𝛍𝛭𝜇𝜧𝝁
Unicode nameMATHEMATICAL 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
Encodingsdecimalhexdecimalhexdecimalhexdecimalhexdecimalhexdecimalhex
Unicode120499U+1D6B3120525U+1D6CD120557U+1D6ED120583U+1D707120615U+1D727120641U+1D741
UTF-8240 157 154 179F0 9D 9A B3240 157 155 141F0 9D 9B 8D240 157 155 173F0 9D 9B AD240 157 156 135F0 9D 9C 87240 157 156 167F0 9D 9C A7240 157 157 129F0 9D 9D 81
UTF-1655349 57011D835 DEB355349 57037D835 DECD55349 57069D835 DEED55349 57095D835 DF0755349 57127D835 DF2755349 57153D835 DF41
Numeric character reference𝚳𝚳𝛍𝛍𝛭𝛭𝜇𝜇𝜧𝜧𝝁𝝁
Character𝝡𝝻𝞛𝞵
Unicode nameMATHEMATICAL 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
Encodingsdecimalhexdecimalhexdecimalhexdecimalhex
Unicode120673U+1D761120699U+1D77B120731U+1D79B120757U+1D7B5
UTF-8240 157 157 161F0 9D 9D A1240 157 157 187F0 9D 9D BB240 157 158 155F0 9D 9E 9B240 157 158 181F0 9D 9E B5
UTF-1655349 57185D835 DF6155349 57211D835 DF7B55349 57243D835 DF9B55349 57269D835 DFB5
Numeric character reference𝝡𝝡𝝻𝝻𝞛𝞛𝞵𝞵

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

  1. ^

See also

References

  1. http://www.oed.com/view/Entry/123122
  2. Hadley, James (1884). A Greek Grammar for Schools and Colleges. New York: American Book. p. 79.
  3. http://e-library.iep.edu.gr/iep/collection/browse/item.html?code=01-17160&tab=02&start=40#i
  4. http://e-library.iep.edu.gr/iep/collection/browse/item.html?code=01-18549&tab=01
  5. 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"
  6. 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.
  7. "Nomenclature" NASA
  8. Definition
  9. Olympus History : µ[mju:] (Stylus) Series
  10. Johnson, Kyle (1991). "Object Positions". Natural Language and Linguistic Theory. 9 (4): 577–636. doi:10.1007/BF00134751.
  11. Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)
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