Editing Epsilon

[[image:Epsilon.jpg|thumb]]
'''Epsilon''' ([[uppercase]] '''Ε''', [[lowercase]] '''ε'''; Έψιλον) is the fifth letter of the [[Greek alphabet]], corresponding phonetically to a [[close-mid front unrounded vowel]] /e/. In the system of [[Greek numerals]] it has a value of 5. It was derived from the [[Phoenician alphabet|Phoenician letter]] [[He (letter)|He]] [[image:Phoenician he.png|20px|He]]. Letters that arose from Epsilon include the Roman [[E]] and Cyrillic [[Ye (Cyrillic)|Ye]].

The name "epsilon" (ἒ ψιλόν, "simple e") was coined in the Middle Ages to distinguish the letter from the [[Digraph (orthography)|digraph]] αι, a former [[diphthong]] that had come to be pronounced the same as epsilon. 

The uppercase form of epsilon looks essentially identical to Latin E. The lowercase version has two typographical variants, both inherited from [[History of the Greek alphabet|medieval Greek handwriting]]. One, the most common in modern typography and inherited from medieval minuscule, looks like an inverted "3". The other, also known as [[lunate]] or uncial epsilon and inherited from earlier uncial writing,<sup>[1]</sup><sup>[2]</sup> looks like a semicircle crossed by a horizontal bar. While in normal typography these are just alternate font variants, both may have different meanings as mathematical symbols. Computer systems therefore offer distinct encodings for both.<sup>[1]</sup> In [[Unicode]], the character U+03F5 "Greek lunate epsilon symbol" (ϵ) is provided specifically for the lunate form. In [[TeX]],  ([[image:49bfd9e448b2ac27ea9a754bd7a7ada4.png]]) denotes the lunate form, while ([[image:36a0ee3562f26da26c60dac5dbae18c4.png]]) denotes the inverted-3 form. 

There is also a [[Latin epsilon]] or "open e", which looks similar to the Greek lowercase epsilon. It is encoded in Unicode as U+025B ("Latin small letter open e", ɛ) and U+0190 ("Latin capital letter open e", Ɛ) and is used as an [[IPA]] phonetic symbol. The lunate or uncial epsilon has also provided inspiration for the euro sign ([[€]]).

The lunate epsilon (ϵ) is not to be confused with the [[set membership]] symbol (∈), nor should the Latin uppercase epsilon (Ɛ) be confused with the Greek uppercase sigma ([[Σ]]).

==History==
===Origin===
The letter Ε was taken over from the [[Phoenician alphabet|Phonician]] letter [[He (letter)|He]] ([[image:Phoenician he.png|inline|x12px]]) when Greeks first adopted alphabetic writing. In archaic Greek writing, its shape is often still identical to the Phoenician letter. Like other Greek letters, it could face either leftwards or rightwards ([[image:Greek Epsilon left.png|inline|x14px]][[image:Greek Epsilon archaic.png|inline|x14px]]), depending on the current writing direction, but just like in Phoenician, the horizontal bars always faced in the direction of writing. Archaic writing often preserves the Phoenician form with a vertical stem extending slightly below the lowest horizontal bar. In the classical era, through the influence of more cursive writing styles, the shape was simplified to the current E glyph.<sup>[3]</sup>

===Sound value===
The initial sound value of Ε was determined by the vowel occurring in the Phoenician letter name ''He'', which made it a natural choice for being reinterpreted from a consonant symbol to a vowel symbol denoting an [e] sound.<sup>[4]</sup> Besides its classical Greek sound value, the short /e/ phoneme, it could initially also be used for other [e]-like sounds. For instance, in early [[Attic Greek|Attic]] before c.500 B.C., it was used also both for the long, [[open-mid vowel|open]] /ɛː/, and for the long [[close-mid vowel|close]] /eː/. In the former role, it was later replaced in the classic Greek alphabet by [[Eta]] (Η), which was taken over from eastern [[Ionic Greek|Ionic]] alphabets, while in the latter role it was replaced by the [[digraph (orthography)|digraph]] spelling ΕΙ.

===Epichoric alphabets===
Some dialects used yet other ways of distinguishing between various e-like sounds.

In [[Ancient Corinth|Corinth]], the normal function of Ε to denote /e/ and /ɛː/ was taken by a glyph resembling a pointed B ([[image:Greek Beta archaic.png|inline|x14px]]), while Ε was used only for long close /eː/.<sup>[5]</sup> The letter [[Beta]], in turn, took the deviant shape [[image:Greek Beta Corinth 1.png|inline|x14px]].

In [[Sicyon]], a variant glyph resembling an X ([[image:Greek Epsilon X-shaped.png|inline|x14px]]) was used in the same function as Corinthian [[image:Greek Beta archaic.png|inline|x14px]].<sup>[6]</sup>

In [[Thespiai]] ([[Boeotia]]), a special letter form consisting of a vertical stem with a single rightward-pointing horizontal bar ([[image:Greek Eta tack.png|inline|x12px]]) was used for what was probably a [[close vowel|raised]] variant of /e/ in pre-vocalic environments.<sup>[7]</sup><sup>[1]</sup> This tack glyph was used elsewhere also as a form of "[[Heta]]", i.e. for the sound /h/.

===Glyph variants===
After the establishment of the canonical classic Greek alphabet, new glyph variants for Ε were introduced through handwriting. In the [[uncial script]] (used for literary [[papyrus]] manuscripts in late antiquity and then in early medieval [[vellum]] codices), the "lunate" shape ([[image:Greek uncial Epsilon.png|inline|x12px]]) became predominant. In [[cursive]] handwriting, a large number of shorthand glyphs came to be used, where the cross-bar and the curved stroke were linked in various ways.<sup>[8]</sup> Some of them resembled a modern lowercase Latin "e", some a "6" with a connecting stroke to the next letter starting from the middle, and some a combination of two small "c"-like curves. Several of these shapes were later taken over into [[minuscule Greek|minuscule]] book hand. Of the various minuscule letter shapes, the inverted-3 form became the basis for lower-case Epsilon in Greek typography during the modern era.

{|class="wikitable"
!Uncial
!Uncial variants
!Cursive variants
!Minuscule
!Minuscule with ligatures
|-
|[[image:Greek uncial Epsilon.png|inline|x20px]]
|[[image:Greek uncial variants Epsilon.png|inline|x30px]]
|[[image:Greek cursive variants Epsilon.png|inline|x30px]]
|[[image:Greek minuscule Epsilon.png|inline|x40px]]
|[[image:Greek minuscule Epsilon with ligatures.png|inline|x40px]]
|}

==Uses==
===International Phonetic Alphabet===
In the [[International Phonetic Alphabet]], the Latin epsilon ɛ represents [[open-mid front unrounded vowel]], as in the English word "pet" ˈpɛt.

===Symbol===
The uppercase Epsilon is not commonly used outside of the Greek language because of its similarity to the [[Latin]] letter [[E]].

====Lower case====
The Greek lowercase epsilon '''[[ε]]''', the lunate epsilon symbol '''[[ϵ]]''', or the Latin lowercase epsilon '''[[ɛ]]''' (see above) is used as the symbol for:

=====Math and science=====
*In mathematics (particularly [[calculus]]), an arbitrarily small positive quantity is commonly denoted ε; see [[(ε, δ)-definition of limit|(ε,&nbsp;δ)-definition of limit]].
**By analogy with this, the late mathematician [[Paul Erdős]] also used the term "epsilons" to refer to children ([[Paul Hoffman (science writer)|Hoffman]] 1998, p.&nbsp;4).
*In mathematics, [[David Hilbert|Hilbert]] introduced epsilon terms εx.φ as an extension to [[first order logic]]; see [[epsilon calculus]].
*In mathematics, the [[Levi-Civita symbol]].
*In mathematics, to represent the [[dual number]]s: ''a''&nbsp;+&nbsp;''bε'', with ''ε''<sup>2</sup>&nbsp;=&nbsp;0 and&nbsp;''ε''&nbsp;≠&nbsp;0.
*In mathematics, sometimes used to denote the [[Heaviside step function]].
*In [[set theory]], the [[epsilon nought|limit ordinal]] of the sequence [[image:4c44a89bb33a6b5219e5863cb2ccb32.png]].
*In computing, the [[Precision (computer science)|precision]] of a numeric data type and floating-point [[machine epsilon]].
*In [[computer science]], the [[empty string]], though different writers use a variety of other symbols for the empty string as well, including the lower case Greek letter [[lambda]].
*In physics, the [[permittivity]] of a medium.
*In physics and electronics, the [[Electromotive force|emf]] of a circuit
*In physics, the [[Strain (materials science)|strain]] of a material (a ratio of extensions).
*In [[automata theory]], a transition that involves no shifting of an input symbol.
*In [[astronomy]], the fifth-brightest star in a [[constellation]] (see [[Bayer designation]]).
*In [[astronomy]], Epsilon is the name for Uranus' most distant and most visible ring.
*In [[chemistry]], the [[molar extinction coefficient]] of a [[chromophore]].
*In [[economics]], ε refers to [[elasticity (economics)|elasticity]].
*In [[statistics]], to refer to [[Errors and residuals in statistics|error terms]].
*In agriculture, to represent the "[[photosynthetic]] efficiency" of a particular plant or crop.

===Fictional names===
*In the popular web series "[[Red vs. Blue]]", Epsilon is the name of Agent Washington's AI, possessing memories from the breaking of the Alpha AI by Project Freelancer.
*''Epsilon in Malaysian Pale'' is the name of the second solo album released by [[Tangerine Dream]] leader [[Edgar Froese]] in 1975.
*Epsilon is also an [[Australian]] light-powered female-looking [[robot]] that fought [[Pluto (manga)|Pluto]] in an episode of [[Astro Boy (2003)|Astro Boy]].
*''[[Epsilon Eridani]] III'' is the planet that the spacestation [[Babylon 5]] orbited in the eponymous [[science fiction|sci-fi]] television series.
*[[E-104 Epsilon]] is also the name of a robot in [[Sonic Adventure]].
*Epsilon is an otherworldy being in the book [[The Riddles of Epsilon]] by Christine Morton-Shaw.
*"Epsilon 9" is the name of the Federation space station consumed by the V'ger cloud in [[Star Trek: The Motion Picture]].
*Epsilon is the name of an unlockable creature in the game [[Monster Rancher 2]].
*In Greek it is used for [[Epsilon Team]].
*"Epsilon Mirror" is the name of one of Aika's moves in the video game [[Skies of Arcadia]].
*''Epsilon'' is the leader of the Rebellion in [[Mega Man X: Command Mission]].
*"The Epsilon Program" is a mysterious [[cult]] in the video game [[Grand Theft Auto: San Andreas]] by Game Developer [[Rockstar North]]. This cult is thought to be based on [[Scientology]].
*The Epsilon Project is a fictional experiment mentioned in the [[Dreamcast]] and [[Xbox]] versions of [[Dead or Alive 2]] and is based on cloning.
*Epsilon is the lowest of five social [[caste]]s in the [[Aldous Huxley]] novel ''[[Brave New World]]''.
*"Plan Epsilon" was one of many plans to restore [[Doctor Doom]] to life in the event of his death, as shown in [[Fantastic Four]] issue no. 246, written by [[Stan Lee]].
*Epsilon-Eagle is the name of the protagonist in the [[Sega Mega Drive]] game [[Alien Soldier]].
*Epsilon was the name given to one of the ground support teams in the [[Sony Playstation]] game [[G-Police]].
*Epsilon is the name of the newly resurrected Yuri Faction in the [[Yuri's Revenge]] mod [[Mental Omega]].
*Epsilon was one of the warriors of Asgard in the Anime series [[Saint Seiya]], Fenrir Epsilon, The Northern Wolf, when [[Dragon Shiryu]] had to fight for his life against him on his way to rescue Hilda.
*Epsilon was the name of the chef dog in the [[Pixar]] movie [[Up (2009 film)|Up]] when Carl and Russell are in Muntz's lair.
*"Epsilon Knight" is the name of a racer in the Extreme-G racing game series who, if controlled by the computer, always happened to finish 5th.
*Epsilon was a man-made God in the game [[AdventureQuest]].

===Other uses===
*"Epsilon" is the name used by [[General Motors]] for the post-2003 [[GM Epsilon platform|Epsilon platform]].
*[[Epsilon Euskadi]], a carmaker and [[EpsilonEuskadi LMP1]] car.
*[[Barazi-Epsilon]], a manufacturer in the [[2009 Superleague Formula season]] for the [[Olympique Lyonnais]] car.
*[[Hurricane Epsilon (2005)|Hurricane Epsilon]], a storm of the [[2005 Atlantic hurricane season]].
*Epsilon TB-30 is a training aircraft made by Socata and used by the French, Portuguese, Senegalese and Togo airforces.  Introduced in 1984 it provides basic and intermediate training, and has a 300&nbsp;hp lycoming engine.
*Stars [[Epsilon Eridani]] and [[40 Epsilon]].
*[[Epsilon (text editor)|Epsilon]] is a multi-platform [[Emacs]]-like programmer's text editor by [http://lugaru.com/ Lugaru Software Ltd]
*Epsilon is used in the "reverse cat-face" [[emoticon]].



==Initial==
[[image:Lectionary 226 GA 0020b Epsilon.JPG|50px|[[Initial]] epsilon in [[Lectionary 226]], folio 20 [[recto and verso|verso]]]]

[[image:Lectionary_226_(GA)_Epsilon_0064b.JPG|50px|folio 64 verso]]

[[image:Lectionary_226_GA_0125b_Epsilon.JPG|50px|folio 125 verso]]

==References==

* 1. Nick Nicholas: Letters, 2003–2008. (Greek Unicode Issues)
* 2. Colwell, Ernest C. (1969). "A chronology for the letters Ε, Η, Λ, Π in the Byzantine minuscule book hand". Studies in methodology in textual criticism of the New Testament. Leiden: Brill. pp. 127. 
* 3. Jeffery, Lilian H. (1961). The local scripts of archaic Greece. Oxford: Clarendon. pp. 63–64. 
* 4. Jeffery, Local scripts, p.24.
* 5. Jeffery, Local scripts, p.114.
* 6. Jeffery, Local scripts, p.138.
* 7. Jeffery, Local scripts, p.89.
* 8. Thompson, Edward M. (1911). An introduction to Greek and Latin palaeography. Oxford: Clarendon. pp. 191–194.

== Further reading ==
*[[Paul Hoffman (science writer)|Hoffman, Paul]]; ''[[The Man Who Loved Only Numbers]]''. Hyperion, 1998. ISBN 0-7868-6362-5.

==External Links==
* [http://en.wikipedia.org/wiki/Epsilon Wikipedia article on Epsilon]

{{Greek Lexicon}}
[[Category:Greek letters]]
[[Category:Vowel letters]]

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