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{{about|the Greek letter|other uses|Epsilon (disambiguation)}}
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{{Wiktionary|Ε|ε}}
{{Greek Alphabet|letter=epsilon}}
'''Epsilon''' ([[uppercase]] '''{{lang|el|Ε}}''', [[lowercase]] '''{{lang|el|ε}}''' or [[Epsilon#Glyph variants|lunate]] '''{{lang|el|ϵ}}'''; {{lang-el|έψιλον}}) is the fifth letter of the [[Greek alphabet]], corresponding phonetically to a [[close-mid front unrounded vowel]] {{IPA|/e/}}. In the system of [[Greek numerals]] it has the value five. It was derived from the [[Phoenician alphabet|Phoenician letter]] [[He (letter)|He]] [[File:Phoenician he.svg|20px|He]]. Letters that arose from epsilon include the Roman [[E]] and Cyrillic [[Ye (Cyrillic)|Е]].


The name "epsilon" ({{lang|grc|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.
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In essence, the uppercase form of epsilon looks 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 a reversed "3". The other, also known as [[lunate]] or uncial epsilon and inherited from earlier uncial writing,<ref name="nicholas">Nick Nicholas: [http://www.tlg.uci.edu/~opoudjis/unicode/letters.html Letters], 2003–2008. (''Greek Unicode Issues'')</ref><ref name="colwell">{{cite book|last=Colwell|first=Ernest C.|chapter=A chronology for the letters Ε, Η, Λ, Π in the Byzantine minuscule book hand|title=Studies in methodology in textual criticism of the New Testament|year=1969|place=Leiden|publisher=Brill|pages=127}}</ref> looks like a semicircle crossed by a horizontal bar. While in normal typography these are just alternative font variants, they may have different meanings as mathematical symbols. Computer systems therefore offer distinct encodings for them.<ref name="nicholas"/> In [[Unicode]], the character U+03F5 "Greek lunate epsilon symbol" ({{unicode|ϵ}}) is provided specifically for the lunate form. In [[TeX]], <code>\epsilon</code> (<math>\epsilon\!</math>) denotes the lunate form, while <code>\varepsilon</code> (<math>\varepsilon\!</math>) 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", {{unicode|ɛ}}) and U+0190 ("Latin capital-letter open e", {{unicode|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|Phoenician]] letter [[He (letter)|He]] ([[File:Phoenician he.svg|inline|x12px]]) when Greeks first adopted alphabetic writing. In archaic Greek writing, its shape is often still identical to that of the Phoenician letter. Like other Greek letters, it could face either leftward or rightward ([[File:Greek Epsilon left.svg|inline|x14px]][[File:Greek Epsilon archaic.svg|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.<ref name="jeffery63">{{cite book|last=Jeffery|first=Lilian H.|title=The local scripts of archaic Greece|place=Oxford|publisher=Clarendon|year=1961|pages=63–64}}</ref>
 
===Sound value===
While the original pronunciation of the Phoenician letter ''He'' was {{IPA|[h]}}, the earliest Greek sound value of Ε was determined by the vowel occurring in the Phoenician letter name, which made it a natural choice for being reinterpreted from a consonant symbol to a vowel symbol denoting an {{IPA|[e]}} sound.<ref name="jeffery24">Jeffery, ''Local scripts'', p.24.</ref> Besides its classical Greek sound value, the short {{IPA|/e/}} phoneme, it could initially also be used for other {{IPA|[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]] {{IPA|/ɛː/}}, and for the long [[close-mid vowel|close]] {{IPA|/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 {{IPA|/e/}} and {{IPA|/ɛː/}} was taken by a glyph resembling a pointed B ([[File:Greek Beta archaic.svg|inline|x14px]]), while Ε was used only for long close {{IPA|/eː/}}.<ref name="jeffery114">Jeffery, ''Local scripts'', p.114.</ref> The letter [[Beta]], in turn, took the deviant shape [[File:Greek Beta Corinth 1.svg|inline|x14px]].
 
In [[Sicyon]], a variant glyph resembling an X ([[File:Greek Epsilon X-shaped.svg|inline|x14px]]) was used in the same function as Corinthian [[File:Greek Beta archaic.svg|inline|x14px]].<ref name="jeffery138">Jeffery, ''Local scripts'', p.138.</ref>
 
In [[Thespiai]] ([[Boeotia]]), a special letter form consisting of a vertical stem with a single rightward-pointing horizontal bar ([[File:Greek Eta tack.svg|inline|x12px]]) was used for what was probably a [[close vowel|raised]] variant of {{IPA|/e/}} in pre-vocalic environments.<ref name="nicholas">{{cite web|last=Nicholas|first=Nick|title=Proposal to add Greek epigraphical letters to the UCS|url=http://www.tlg.uci.edu/~opoudjis/unicode/epigraphical.pdf|accessdate=2010-08-12|year=2005}}</ref><ref name="jeffery89">Jeffery, ''Local scripts'', p.89.</ref> This tack glyph was used elsewhere also as a form of "[[Heta]]", i.e. for the sound {{IPA|/h/}}.
 
===Glyph variants===
After the establishment of the {{cl-span|canonical classic Greek alphabet|date=March 2013}}, 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 ([[File:Greek uncial Epsilon.svg|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.<ref name="thompson">{{cite book|last=Thompson|first=Edward M.|title=An introduction to Greek and Latin palaeography|place=Oxford|publisher=Clarendon|year=1911|pages=191–194}}</ref> 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
|-
|[[File:Greek uncial Epsilon.svg|inline|x20px]]
|[[File:Greek uncial variants Epsilon.svg|inline|x30px]]
|[[File:Greek cursive variants Epsilon.svg|inline|x30px]]
|[[File:Greek minuscule Epsilon.svg|inline|x40px]]
|[[File:Greek minuscule Epsilon with ligatures.svg|inline|x40px]]
|}
 
==Uses==
 
===International Phonetic Alphabet===
In the [[International Phonetic Alphabet]], the Latin epsilon {{IPAc-en|ɛ}} represents [[open-mid front unrounded vowel]], as in the English word "pet" {{IPAc-en|ˈ|p|ɛ|t}}.
 
===Symbol===
The uppercase Epsilon is not commonly used outside of the Greek language because of its similarity to the [[Latin alphabet|Latin]] letter [[E]].
 
The Greek lowercase epsilon '''[[ε]]''', the lunate epsilon symbol '''[[ϵ]]''', or the Latin lowercase epsilon '''[[ɛ]]''' (see above) is used as the symbol for:
 
*In mathematics (in particular [[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 <math>\epsilon x.\phi</math> 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]].{{Citation needed|date=March 2010}}
*In [[set theory]], the [[epsilon numbers (mathematics)|limit ordinal]] of the sequence <math>\omega,\omega^\omega,\omega^{\omega^\omega},\dots</math>.
*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, usually the lower-case Greek letter [[lambda]] (λ).
*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 [[planetary science]], ε is the denotion of [[axial tilt]].
*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 [[agronomy]], to represent the "[[photosynthetic]] efficiency" of a particular plant or crop.
 
==Unicode==
 
* Greek Epsilon
 
{{charmap
|0395|name1=Greek capital letter epsilon
|03B5|name2=Greek small letter epsilon
|03F5|name3=Greek lunate epsilon symbol
|03F6|name4=Greek reversed lunate epsilon symbol
|map2=DOS Greek|map2char1=84|map2char2=9C
|map3=DOS Greek-2|map3char1=A8|map3char2=DE
|map4=Windows 1253|map4char1=C5|map4char2=E5
|namedref1=TeX|ref1char2=\varepsilon|ref1char3=\epsilon
}}
 
* Coptic Eie
 
{{charmap
|2C88|name1=Coptic Capital Letter Eie
|2C89|name2=Coptic Small Letter Eie
}}
 
* Latin Open E
 
{{charmap
|0190|name1=Latin Capital Letter<br />Open E
|025B|name2=Latin Small Letter<br />Open E
|1D93|name3=Latin Small Letter<br />Open E with Retroflex Hook
|1D4B|name4=Modifier Letter<br />Small Open E
}}
 
{{charmap
|025C|name1=Latin Small Letter<br />Reversed Open E
|025D|name2=Latin Small Letter<br />Reversed Open E with Hook
|1D94|name3=Latin Small Letter Reversed<br />Open E with Retroflex Hook
|1D9F|name4=Modifier Letter<br />Small Reversed Open E
}}
 
{{charmap
|1D08|name1=Latin Small Letter<br />Turned Open E
|1D4C|name2=Modifier Letter Small<br />Turned Open E
|029A|name3=Latin Small Letter<br />Closed Open E
|025E|name4=Latin Small Letter<br />Closed Reversed Open E
}}
 
* Mathematical Epsilon
 
{{charmap
|1D6AC|name1=Mathematical Bold<br />Capital Epsilon
|1D6C6|name2=Mathematical Bold<br />Small Epsilon
|1D6E6|name3=Mathematical Italic<br />Capital Epsilon
|1D700|name4=Mathematical Italic<br />Small Epsilon
|1D720|name5=Mathematical Bold Italic<br />Capital Epsilon
|1D73A|name6=Mathematical Bold Italic<br />Small Epsilon
}}
 
{{charmap
|1D75A|name1=Mathematical Sans-Serif<br />Bold Capital Epsilon
|1D774|name2=Mathematical Sans-Serif<br />Bold Small Epsilon
|1D794|name3=Mathematical Sans-Serif<br />Bold Italic Capital Epsilon
|1D7AE|name4=Mathematical Sans-Serif<br />Bold Italic Small Epsilon
}}
 
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.
 
==Initial==
<gallery>
File:Lectionary 226 GA 0020b Epsilon.JPG|[[Initial]] epsilon in [[Lectionary 226]], folio 20 [[recto and verso|verso]]
File:Lectionary 226 (GA) Epsilon 0064b.JPG|folio 64 verso
File:Lectionary 226 GA 0125b Epsilon.JPG|folio 125 verso
</gallery>
 
==References==
{{Reflist}}
<References/>
 
== Further reading ==
*[[Paul Hoffman (science writer)|Hoffman, Paul]]; ''[[The Man Who Loved Only Numbers]]''. Hyperion, 1998. ISBN 0-7868-6362-5.
 
[[Category:Greek letters]]
[[Category:Vowel letters]]

Latest revision as of 01:41, 6 January 2015

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