Omega

Template:Short description Template:Redirect Template:About {{#invoke:other uses|otheruses}} Template:More citations needed Template:Use dmy dates Template:Greek AlphabetOmega (Template:IPAc-en, Template:IPAc-en;<ref>Template:Cite LPD</ref> uppercase Ω, lowercase ω) is the twenty-fourth and last letter in the Greek alphabet. In the Greek numeric system/isopsephy (gematria), it has a value of 800. The name of the letter was originally Template:Lang (Template:Transliteration Template:IPA), but it was later changed to Template:Wikt-lang (Template:Transliteration 'big o') in the Middle Ages to distinguish it from omicron Template:Angbr, whose name means 'small o', as both letters had come to be pronounced Template:IPA.<ref>Template:Cite web</ref> In modern Greek, its name has fused into Template:Lang (Template:Transliteration).

In phonetic terms, the Ancient Greek Ω represented a long open-mid back rounded vowel Template:IPA, in contrast to omicron, which represented the close-mid back rounded vowel Template:IPA, and the digraph Template:Angbr, which represented the long close back rounded vowel Template:IPA. In modern Greek, both omega and omicron represent the mid back rounded vowel Template:IPA. The letter omega is transliterated into a Latin-script alphabet as Template:Transliteration or simply Template:Transliteration.

As the final letter in the Greek alphabet, omega is often used to denote the last, the end, or the ultimate limit of a set, in contrast to alpha, the first letter of the Greek alphabet; see Alpha and Omega.

History

Ω was not part of the early (8th century BC) Greek alphabets. It was introduced in the late 7th century BC in the Ionian cities of Asia Minor to denote a long open-mid back rounded vowel Template:IPA. It is a variant of omicron (Ο), broken up at the side (File:Greek Omega 09.svg), with the edges subsequently turned outward (Template:GrGl, Template:GrGl, Template:GrGl, Template:GrGl).<ref name="Jeffery37f">Anne Jeffery (1961), The Local Scripts of Archaic Greece, pp. 37–38.</ref> The Dorian city of Knidos as well as a few Aegean islands, namely Paros, Thasos and Melos, chose the exact opposite innovation, using a broken-up circle for the short and a closed circle for the long Template:IPA.<ref name=Jeffery37f/>

The name Ωμέγα is Byzantine; in Classical Greek, the letter was called ō (Template:Lang) (pronounced /ɔ̂ː/), whereas the omicron was called ou (Template:Lang) (pronounced /ôː/).<ref>Herbert Weir Smyth A Greek Grammar for Colleges §1.</ref> The modern lowercase shape goes back to the uncial form File:Greek uncial Omega.svg, a form that developed during the 3rd century BC in ancient handwriting on papyrus, from a flattened-out form of the letter (File:Greek Omega 08.svg) that had its edges curved even further upward.<ref>Edward M. Thompson (1912), Introduction to Greek and Latin Paleography, Oxford: Clarendon, p. 144.</ref>

In addition to the Greek alphabet, Omega was also adopted into the early Cyrillic alphabet (see Cyrillic omega (Ѡ, ѡ)). A Raetic variant is conjectured to be at the origin or parallel evolution of the Elder Futhark ᛟ.

Omega was also adopted into the Latin alphabet, as a letter of the 1982 revision to the African reference alphabet. It is in sparse use (see Latin omega).

The symbol Ω (uppercase letter)

File:Kos città, piazza eleftherias, edificio razionalista, targa.JPG

Plaque in Kos with "underlined O" form of omega

The uppercase letter Ω is used as a symbol:

• In chemistry:
  • For oxygen-18, a natural, stable isotope of oxygen<ref name="geoENV2012">Template:Cite web</ref>
  • For omega loop, a protein structural motif consisting of a loop of six or more amino acid residues in any sequence, a structure named for its resemblance to the Greek letter.<ref>Template:Cite journal</ref>
• In physics:
  • For ohm – SI unit of electrical resistance.<ref>Template:Cite web</ref> Unicode has a separate code point Template:Unichar (HTML entity Ω), but it is included only for backward compatibility, and the canonically equivalent code point Template:Unichar (Ω) is preferred. Also formerly also used upside down (Template:Unichar) to represent mho, the old name for the inverse of an ohm (now siemens with symbol S), the SI unit of electrical conductance.<ref>Excerpts from The Unicode Standard, Version 4.0. Retrieved 11 October 2006.</ref>
  • In statistical mechanics, Ω refers to the multiplicity (number of microstates) in a system.
  • The solid angle<ref>Template:Cite web</ref><ref>Template:Cite journal</ref> or the rate of precession in a gyroscope
  • In particle physics to represent the Omega baryons
  • In astronomy (cosmology), Ω refers to the average density of the universe, also called the density parameter.
  • In astronomy (orbital mechanics), Ω refers to the longitude of the ascending node of an orbit.<ref name=":0">Template:Cite web</ref>
• In mathematics and computer science:
  • In complex analysis, the Omega constant, a solution of Lambert's W function<ref>Template:Cite web</ref>
  • In differential geometry, the space of differential forms on a manifold (of a certain degree, usually with a superscript).
  • A variable for a 2-dimensional region in calculus, usually corresponding to the domain of a double integral.
  • In topos theory, the (codomain of the) subobject classifier of an elementary topos.
  • In combinatory logic, the looping combinator, (S I I (S I I))
  • In group theory, the omega and agemo subgroups of a p-group, Ω(G) and ℧(G)
  • In group theory, Cayley's Ω process as a partial differential operator.
  • In statistics, it is used as the symbol for the sample space, or total set of possible outcomes.
  • In triangle geometry, Brocard points<ref>Template:Cite web</ref>
  • In number theory, Ω(n) is the number of prime divisors of n (counting multiplicity).<ref>Template:Cite web</ref>
  • In notation related to Big O notation to describe the asymptotic behavior of functions.<ref>Template:Cite web</ref>
  • Chaitin's constant.<ref>Template:Cite web</ref>
  • In set theory, the first uncountable ordinal number, ω₁ or Ω
  • The absolute infinite proposed by Georg Cantor.
• As part of a logo or trademark:
  • The logo of Omega Watches SA<ref>Template:Cite web</ref>
  • Part of the original Pioneer logo<ref>Template:Cite web</ref>
  • Part of the Badge of the Supreme Court of the United Kingdom<ref>Template:Cite web</ref>
  • Part of the mission patch for STS-135, as it was the last mission of the Space Shuttle program<ref>Template:Cite web</ref>
  • The logo of the God of War video game series based on Greek mythology. In God of War (2018), it is revealed it stands as the symbol of war in Greece.
  • The logo of E-123 Omega, a Sonic the Hedgehog character.
  • The logo of the Heroes of Olympus series, based on Greek mythology.
  • the logo of the Ultramarines in Warhammer 40,000
  • The logo of Primal Groudon, the version mascot of Pokémon Omega Ruby.
  • The logo of Darkseid in DC comics
  • One of the logos of professional wrestler Kenny Omega
  • The logo for Meow Wolf's Omega Mart in Area15, Las Vegas, Nevada
  • The logo of Lalaji Memorial Omega International School

File:Fachada de Panteón de la Cruz.jpg

Omega-shaped entrance to the Panteón de la Cruz in Aguascalientes, representing the end of life<ref>Template:Cite web</ref>

• Other:
  • In eschatology, the symbol for the end of everything
  • In molecular biology, the symbol is used as shorthand to signify a genetic construct introduced by a two-point crossover
  • Omega Particle in the Star Trek universe<ref>Template:Cite web</ref>
  • The final form of NetNavi bosses in some of the Mega Man Battle Network games
  • A secret boss in the Final Fantasy series called Omega ( Ω ) Weapon.
  • A character from the series Doctor Who called Omega, believed to be one of the creators of the Time Lords of Gallifrey.
  • The symbol for the highest power level of a PSI attack in the Mother/EarthBound games
  • A symbol used by U.S. citizens in the 1960s & 1970s to denote resistance to the U.S. war in Viet Nam. Adapted from the SI unit for electrical resistance.<ref>Template:Cite web</ref>
  • It is used along with Alpha in the Alpha and Omega, a Christian symbol.<ref>Template:CathEncy</ref>
  • Used as the highest tier of equipment in the flash game, Learn to Fly
  • Appears in galaxy quest as the Omega 13 device

The symbol ω (lowercase letter)

The minuscule letter ω is used as a symbol:

• Biology, biochemistry and chemistry:
  • In biochemistry, for one of the RNA polymerase subunits
  • In biology, for fitness
  • In chemistry, for denoting the carbon atom furthest from the carboxyl group of a fatty acid
  • In genomics, as a measure of molecular evolution in protein-coding genes (also denoted as d_N/d_S or K_a/K_s ratio)
• Physics:
  • Angular velocity or angular frequency<ref>Template:Citation</ref>
  • Rotation velocity (bold), rotational speed or frequency<ref>Template:Citation</ref>
  • In computational fluid dynamics, the specific turbulence dissipation rate
  • In meteorology, the change of pressure with respect to time of a parcel of air
  • In circuit analysis and signal processing to represent angular frequency, related to frequency f by ω = 2πf
  • In astronomy, as a ranking of a star's brightness within a constellation<ref>Template:Cite web</ref>
  • In orbital mechanics, as designation of the argument of periapsis of an orbit<ref name=":0" />
  • In particle physics to represent the omega meson<ref>Template:Cite journal</ref>
• Computer science:
  • In notation related to Big O notation, the asymptotically dominant nature of functions
  • In relational database theory to represent NULL, a missing or inapplicable value
  • In APL, to represent the right parameter to a function
• Mathematics:
  • The first and smallest transfinite ordinal number, often identified with the set of natural numbers including 0 (sometimes written <math>\omega_0</math>)<ref>Template:Cite web</ref><ref>Template:Citation</ref>
  • In set theory, ω is the ordinal number<ref>Template:Cite web</ref>
  • A primitive root of unity, like the complex cube roots of 1
  • The Wright Omega function<ref>Template:Cite web</ref>
  • A generic differential form
  • In number theory, ω(n) is the number of distinct prime divisors of n<ref>Template:Cite web</ref>
  • In number theory, an arithmetic function
  • In combinatory logic, the self-application combinator, (λ x. x x)
  • In triangle geometry, a Brocard angle<ref>Template:Cite web</ref>
  • Clique number in Graph theory<ref>Template:Cite web</ref>
• Finance:
  • In finance, the elasticity of options
  • In analytical investment management, the tracking error of an investment manager
• Other:
  • Used in place of ん in Japanese typing shorthand.
  • In linguistics, the phonological word
  • In textual criticism, the archetype of a manuscript tradition
  • In sociology, used to refer to the lowest ranking member of a group<ref>Template:Cite web</ref>
  • In economics (specifically like in general equilibrium theory), the endowments of agents
  • In shift_JIS art, used to represent the cat's mouth. (e.g. Template:Lang)
  • In actuarial sciences, used to represent the maximum life span that characterizes a mortality table<ref>Template:Cite web</ref>

Unicode

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External links

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