Mu (letter)

Mu (letter)

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Mu Modern Greek
Modern Greek
Modern Greek refers to the varieties of the Greek language spoken in the modern era. The beginning of the "modern" period of the language is often symbolically assigned to the fall of the Byzantine Empire in 1453, even though that date marks no clear linguistic boundary and many characteristic...

 μι or μυ mi) is the 12th letter of the Greek alphabet
Greek alphabet
The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . The alphabet in its classical and modern form consists of 24 letters ordered in sequence from alpha to omega...

. In the system of Greek numerals
Greek numerals
Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Ionian numerals, Milesian numerals , Alexandrian numerals, or alphabetic numerals...

 it has a value of 40. Mu was derived from the Egyptian hieroglyphic symbol for water (𓈖) which had been simplified by the Phoenicia
Phoenicia
Phoenicia , was an ancient civilization in Canaan which covered most of the western, coastal part of the Fertile Crescent. Several major Phoenician cities were built on the coastline of the Mediterranean. It was an enterprising maritime trading culture that spread across the Mediterranean from 1550...

ns and named after their word for water, to become 𐤌
Mem
Mem is the thirteenth letter of many Semitic abjads, including Phoenician, Aramaic, Hebrew and Arabic...

. Letters that arose from mu include the Roman M
M
M is the thirteenth letter of the basic modern Latin alphabet.-History:The letter M is derived from the Phoenician Mem, via the Greek Mu . Semitic Mem probably originally pictured water...

 and the Cyrillic М
Em (Cyrillic)
Em is a letter of the Cyrillic alphabet.Em commonly represents the bilabial nasal consonant , like the pronunciation of ⟨m⟩ in "him".It is derived from the Greek letter Mu ....

.

Ancient Greek


In Ancient Greek
Ancient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...

, the name of the letter is written and pronounced mŷː.

Modern Greek


In Modern Greek
Modern Greek
Modern Greek refers to the varieties of the Greek language spoken in the modern era. The beginning of the "modern" period of the language is often symbolically assigned to the fall of the Byzantine Empire in 1453, even though that date marks no clear linguistic boundary and many characteristic...

, the name of the letter is spelled μι and pronounced mi. In monotonic orthography, the ancient version is written with an acute accent
Acute accent
The acute accent is a diacritic used in many modern written languages with alphabets based on the Latin, Cyrillic, and Greek scripts.-Apex:An early precursor of the acute accent was the apex, used in Latin inscriptions to mark long vowels.-Greek:...

 instead of a circumflex
Circumflex
The circumflex is a diacritic used in the written forms of many languages, and is also commonly used in various romanization and transcription schemes. It received its English name from Latin circumflexus —a translation of the Greek περισπωμένη...

: μύ.

Symbol


The lower-case letter mu (μ) is used as a special symbol in many academic fields. The upper case mu is not used, since it is normally identical to Latin M
M
M is the thirteenth letter of the basic modern Latin alphabet.-History:The letter M is derived from the Phoenician Mem, via the Greek Mu . Semitic Mem probably originally pictured water...

.

Mathematics


In mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

:
  • the µ-roots of a complex number
    Complex number
    A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...

     z = a + bi
  • the Möbius function
    Möbius function
    The classical Möbius function μ is an important multiplicative function in number theory and combinatorics. The German mathematician August Ferdinand Möbius introduced it in 1832...

     in number theory
    Number theory
    Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

  • the integrating factor
    Integrating factor
    In mathematics, an integrating factor is a function that is chosen to facilitate the solving of a given equation involving differentials. It is commonly used to solve ordinary differential equations, but is also used within multivariable calculus, in this case often multiplying through by an...

     in ordinary differential equations
  • the population mean
    Mean
    In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....

     or expected value
    Expected value
    In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...

     in probability
    Probability
    Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

     and statistics
    Statistics
    Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

  • a measure
    Measure (mathematics)
    In mathematical analysis, a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization of the concepts of length, area, and volume...

     in measure theory
  • minimalization
    Mu operator
    In computability theory, the μ operator, minimization operator, or unbounded search operator searches for the least natural number with a given property.- Definition :...

     in computability theory
    Computability theory (computer science)
    Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science...

     and Recursion theory
    Recursion theory
    Computability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability and definability...

  • the learning rate as used in artificial neural networks

Measurement


In measurement:
  • the SI prefix
    SI prefix
    The International System of Units specifies a set of unit prefixes known as SI prefixes or metric prefixes. An SI prefix is a name that precedes a basic unit of measure to indicate a decadic multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol...

     micro-, which represents one millionth, or 10−6.
  • the micron, an old unit which corresponds to the micrometre
    Micrometre
    A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...

     (which is now denoted "µm")

Physics and engineering


In classical physics
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...

 and engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

:
  • the coefficient of friction (also used in aviation as braking coefficient)
  • reduced mass
    Reduced mass
    Reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. This is a quantity with the unit of mass, which allows the two-body problem to be solved as if it were a one-body problem. Note however that the mass determining the gravitational force is not...

     in the two-body problem
    Two-body problem
    In classical mechanics, the two-body problem is to determine the motion of two point particles that interact only with each other. Common examples include a satellite orbiting a planet, a planet orbiting a star, two stars orbiting each other , and a classical electron orbiting an atomic nucleus In...

  • linear density
    Linear density
    Linear density, linear mass density or linear mass is a measure of mass per unit of length, and it is a characteristic of strings or other one-dimensional objects. The SI unit of linear density is the kilogram per metre...

     or mass per unit length in strings and other one-dimensional objects.
  • permeability
    Permeability (electromagnetism)
    In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...

     in electromagnetism
    Electromagnetism
    Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

  • the magnetic dipole moment of a current-carrying coil
  • dynamic viscosity in fluid mechanics
    Fluid mechanics
    Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...

  • the amplification
    Amplifier
    Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...

     factor or voltage gain of a triode
    Triode
    A triode is an electronic amplification device having three active electrodes. The term most commonly applies to a vacuum tube with three elements: the filament or cathode, the grid, and the plate or anode. The triode vacuum tube was the first electronic amplification device...

     vacuum tube
    Vacuum tube
    In electronics, a vacuum tube, electron tube , or thermionic valve , reduced to simply "tube" or "valve" in everyday parlance, is a device that relies on the flow of electric current through a vacuum...

  • the electrical mobility
    Electrical mobility
    Electrical mobility is the ability of charged particles to move through a medium in response to an electric field that is pulling them...

     of a charged particle
  • the airspeed
    Airspeed
    Airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are: indicated airspeed , calibrated airspeed , true airspeed , equivalent airspeed and density airspeed....

     relative to rotor tip speed, in rotorcraft
    Rotorcraft
    A rotorcraft or rotary wing aircraft is a heavier-than-air flying machine that uses lift generated by wings, called rotor blades, that revolve around a mast. Several rotor blades mounted to a single mast are referred to as a rotor. The International Civil Aviation Organization defines a rotorcraft...



In particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

:
  • the elementary particle
    Elementary particle
    In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...

    s called the muon
    Muon
    The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...

     and antimuon


In thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

:
  • the chemical potential
    Chemical potential
    Chemical potential, symbolized by μ, is a measure first described by the American engineer, chemist and mathematical physicist Josiah Willard Gibbs. It is the potential that a substance has to produce in order to alter a system...

     of a system or component of a system.

Chemistry


In chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

:
  • the prefix given in IUPAC nomenclature for a bridging ligand
    Bridging ligand
    A bridging ligand is a ligand that connects two or more atoms, usually metal ions. The ligand may be atomic or polyatomic. Virtually all complex organic compounds can serve as bridging ligands, so the term is usually restricted to small ligands such as pseudohalides or to ligands that are...

    .

Orbital mechanics


In orbital mechanics:
  • Standard gravitational parameter
    Standard gravitational parameter
    In astrodynamics, the standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of the body.\mu=GM \ The SI units of the standard gravitational parameter are m3s−2....

     of a celestial body
    Celestial Body
    Celestial Body is a Croatian film directed by Lukas Nola. It was released in 2000....

    , the product of the gravitational constant
    Gravitational constant
    The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...

     G and the mass
    Mass
    Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

     M.
  • planetary discriminant, represents an experimental measure of the actual degree of cleanliness
    Clearing the neighbourhood
    "Clearing the neighbourhood of its orbit" is a criterion for a celestial body to be considered a planet in the Solar System. This was one of the three criteria adopted by the International Astronomical Union in its 2006 definition of planet....

     of the orbital zone, a criterion for defining a planet
    Planet
    A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

    . µ is calculated by dividing the mass of the candidate body by the total mass of the other objects that share its orbital zone.

Cameras


The Olympus Corporation
Olympus Corporation
is a Japan-based manufacturer of optics and reprography products. Olympus was established on 12 October 1919, initially specializing in microscope and thermometer businesses. Its global headquarters are in Shinjuku, Tokyo, Japan, while its USA operations are based in Center Valley, Pennsylvania,...

 manufactures a series of digital cameras called Olympus µ[mju:] or Olympus Stylus.

Computing



In Unicode, the upper and lower case mu are encoded at and respectively. In ISO 8859-7 they are encoded at CCHEX
Hexadecimal
In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...

and ECHEX. In HTML code, the μ character is represented by "μ", "μ" and the entity "μ".

The micro sign or micron
Micron
Micron can refer to:*Micron, a non-SI name for micrometre*Micron , is the measurement used to express the diameter of a wool fibre.*A small curved diacritic mark above some letters, used to indicate shortness, e.g...

 is considered a distinct character
Character (word)
A character may refer to any sign or symbol.-History:Greek is a nomen agentis of the verb with a meaning "to sharpen, to whet", and also "to make cake ", from a PIE root "cut" also continued in Irish gearr and English gash, which is perhaps an early loan ultimately from...

 from the Greek alphabet letter by Unicode for historical reasons (although it is a homoglyph
Homoglyph
In typography, a homoglyph is one of two or more characters, or glyphs, with shapes that either appear identical or cannot be differentiated by quick visual inspection. This designation is also applied to sequences of characters sharing these properties....

) and is found at U+00B5 as well as position B5HEX in ISO 8859-1, 3, 8, 9, 13 and 15, and thus in the corresponding Windows code pages Windows-1252
Windows-1252
Windows-1252 or CP-1252 is a character encoding of the Latin alphabet, used by default in the legacy components of Microsoft Windows in English and some other Western languages. It is one version within the group of Windows code pages...

 etc. In HTML code, the µ symbol is represented by "µ", "µ" and the entity "µ". When Alt-0181 or the DOS legacy
Code page 437
IBM PC or MS-DOS code page 437 is the character set of the original IBM PC. It is also known as CP 437, OEM 437, PC-8, MS-DOS Latin US or sometimes misleadingly referred to as the OEM font, High ASCII or Extended ASCII....

 Alt+230 is typed into an editable field using the numeric keypad
Numeric keypad
A numeric keypad, numpad or tenkey for short, is the small, palm-sized, seventeen key section of a computer keyboard, usually on the very far right. The numeric keypad features digits 0 to 9, addition , subtraction , multiplication and division symbols, a decimal point and Num Lock and Enter keys...

 in Microsoft Windows
Microsoft Windows
Microsoft Windows is a series of operating systems produced by Microsoft.Microsoft introduced an operating environment named Windows on November 20, 1985 as an add-on to MS-DOS in response to the growing interest in graphical user interfaces . Microsoft Windows came to dominate the world's personal...

, the µ symbol appears. Also pressing AltGr + M results in a µ on some keyboard layouts.

Because µ is the abbreviation for the metric system
Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

 prefix micro-, the symbol is used in many word plays about the field of micro-computing. For example, the symbol is used in the name and logo of the popular bittorrent client
BitTorrent client
BitTorrent is a peer-to-peer program developed by Bram Cohen and BitTorrent, Inc. used for uploading and downloading files via the BitTorrent protocol. BitTorrent was the first client written for the protocol. It is often nicknamed Mainline by developers denoting its official origins. Since version...

, µTorrent. Also, the microcontrollers are commonly represented in schematics as µC. It is sometimes simply substituted with a u, the most similar-looking ASCII
ASCII
The American Standard Code for Information Interchange is a character-encoding scheme based on the ordering of the English alphabet. ASCII codes represent text in computers, communications equipment, and other devices that use text...

glyph, e.g. uTorrent.