Epsilon
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Epsilon (US: /ˈɛpsɪlɒn/,[1] UK: /ɛpˈsaɪlən/;[2] uppercase Ε, lowercase ε or ϵ; Greek: έψιλον) is the fifth letter of the Greek alphabet, corresponding phonetically to a mid front unrounded vowel IPA: [e̞] or IPA: [ɛ̝]. In the system of Greek numerals it also has the value five. It was derived from the Phoenician letter He . Letters that arose from epsilon include the Roman E, Ë and Ɛ, and Cyrillic Е, È, Ё, Є and Э.
The name of the letter was originally εἶ ( that had come to be pronounced the same as epsilon.
The
\epsilon
( ) denotes the lunate form, while \varepsilon
( ) denotes the reversed-3 form. Unicode versions 2.0.0 and onwards use ɛ as the lowercase Greek epsilon letter,[5] but in version 1.0.0, ϵ was used.[6] The lunate or uncial epsilon provided inspiration for the euro sign, €.[7]
There is also a 'Latin epsilon', ⟨ɛ⟩ or "open e", which looks similar to the Greek lowercase epsilon. It is encoded in Unicode as U+025B ɛ LATIN SMALL LETTER OPEN E and U+0190 Ɛ LATIN CAPITAL LETTER OPEN E and is used as an IPA phonetic symbol. This Latin uppercase epsilon, Ɛ, is not to be confused with the Greek uppercase Σ (sigma)
The lunate epsilon, ⟨ϵ⟩, is not to be confused with the
History
Origin
The letter ⟨Ε⟩ was adopted from the Phoenician letter He () 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 (), depending on the current writing direction, but, just as 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.[9]
Sound value
While the original pronunciation of the Phoenician letter He was [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 [e] sound.[10] 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 before c. 500 BC, it was used also both for the long, open /ɛː/, and for the long 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 alphabets, while in the latter role it was replaced by the digraph spelling ΕΙ.
Epichoric alphabets
Some dialects used yet other ways of distinguishing between various e-like sounds.
In Corinth, the normal function of ⟨Ε⟩ to denote /e/ and /ɛː/ was taken by a glyph resembling a pointed B (), while ⟨Ε⟩ was used only for long close /eː/.[11] The letter Beta, in turn, took the deviant shape .
In Sicyon, a variant glyph resembling an ⟨X⟩ () was used in the same function as Corinthian .[12]
In
Glyph variants
After the establishment of the canonical classical Ionian (Euclidean)
Uncial | Uncial variants | Cursive variants | Minuscule | Minuscule with ligatures |
---|---|---|---|---|
Uses
International Phonetic Alphabet
Despite its pronunciation as mid, in the International Phonetic Alphabet, the Latin epsilon /ɛ/ represents open-mid front unrounded vowel, as in the English word pet /pɛt/.
Symbol
The uppercase Epsilon is not commonly used outside of the Greek language because of its similarity to the
The Greek lowercase epsilon ε
, the lunate epsilon symbol ϵ
, and the Latin lowercase epsilon ɛ
(see above) are used in a variety of places:
- In engineering mechanics, strain calculations ϵ = increase of length / original length. Usually this relates to extensometer testing of metallic materials.
- In mathematics
- (particularly (ε, δ)-definition of limit.
- Hilbert introduced epsilon terms as an extension to first-order logic; see epsilon calculus.
- it is used to represent the Levi-Civita symbol.
- it is used to represent dual numbers: , with and .
- it is sometimes used to denote the Heaviside step function.[16]
- in epsilon numbers are ordinal numbers that satisfy the fixed point ε = ωε. The first epsilon number, ε0, is the limit ordinalof the set {ω, ωω, ωωω, ...}.
- in numerical analysis and statistics it is used as the error term
- in idempotentgroup when e is in use as a variable name
- (particularly
- In computer science
- it often represents 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).
- the machine epsilon indicates the upper bound on the relative error due to rounding in floating point arithmetic.
- In physics,
- it indicates the permittivity of free space.
- it can also indicate the strainof a material (a ratio of extensions).
- it indicates the
- In automata theory, it shows a transition that involves no shifting of an input symbol.
- In astronomy,
- it stands for the fifth-brightest star in a constellation (see Bayer designation).
- Epsilon is the name for the most distant and most visible ring of Uranus.
- In planetary science, ε denotes the axial tilt.
- In molar extinction coefficient of a chromophore.
- In economics, ε refers to elasticity.
- In statistics,
- it is used to refer to error terms.
- it also can to refer to the degree of sphericity in repeated measures ANOVAs.
- it is used to refer to
- In photosyntheticefficiency" of a particular plant or crop.
Unicode
- Greek Epsilon
Preview | Ε | ε | ϵ | ϶ | ||||
---|---|---|---|---|---|---|---|---|
Unicode name | GREEK CAPITAL LETTER EPSILON | GREEK SMALL LETTER EPSILON | GREEK LUNATE EPSILON SYMBOL | GREEK REVERSED LUNATE EPSILON SYMBOL | ||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex |
Unicode | 917 | U+0395 | 949 | U+03B5 | 1013 | U+03F5 | 1014 | U+03F6 |
UTF-8 | 206 149 | CE 95 | 206 181 | CE B5 | 207 181 | CF B5 | 207 182 | CF B6 |
Numeric character reference | Ε |
Ε |
ε |
ε |
ϵ |
ϵ |
϶ |
϶ |
Named character reference | Ε | ε, ε | ϵ, ϵ, ϵ | ϶, ϶ | ||||
DOS Greek | 132 | 84 | 156 | 9C | ||||
DOS Greek-2 | 168 | A8 | 222 | DE | ||||
Windows 1253 | 197 | C5 | 229 | E5 | ||||
TeX | \varepsilon | \epsilon |
- Coptic Eie
Preview | Ⲉ | ⲉ | ||
---|---|---|---|---|
Unicode name | COPTIC CAPITAL LETTER EIE | COPTIC SMALL LETTER EIE | ||
Encodings | decimal | hex | dec | hex |
Unicode | 11400 | U+2C88 | 11401 | U+2C89 |
UTF-8 | 226 178 136 | E2 B2 88 | 226 178 137 | E2 B2 89 |
Numeric character reference | Ⲉ |
Ⲉ |
ⲉ |
ⲉ |
Preview | Ɛ | ɛ | ᶓ | ᵋ | ||||
---|---|---|---|---|---|---|---|---|
Unicode name | LATIN CAPITAL LETTER OPEN E |
LATIN SMALL LETTER OPEN E |
LATIN SMALL LETTER OPEN E WITH RETROFLEX HOOK |
MODIFIER LETTER SMALL OPEN E | ||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex |
Unicode | 400 | U+0190 | 603 | U+025B | 7571 | U+1D93 | 7499 | U+1D4B |
UTF-8 | 198 144 | C6 90 | 201 155 | C9 9B | 225 182 147 | E1 B6 93 | 225 181 139 | E1 B5 8B |
Numeric character reference | Ɛ |
Ɛ |
ɛ |
ɛ |
ᶓ |
ᶓ |
ᵋ |
ᵋ |
Preview | ɜ | ɝ | ᶔ | ᶟ | ||||
---|---|---|---|---|---|---|---|---|
Unicode name | LATIN SMALL LETTER REVERSED OPEN E |
LATIN SMALL LETTER REVERSED OPEN E WITH HOOK |
LATIN SMALL LETTER REVERSED OPEN E WITH RETROFLEX HOOK |
MODIFIER LETTER SMALL REVERSED OPEN E | ||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex |
Unicode | 604 | U+025C | 605 | U+025D | 7572 | U+1D94 | 7583 | U+1D9F |
UTF-8 | 201 156 | C9 9C | 201 157 | C9 9D | 225 182 148 | E1 B6 94 | 225 182 159 | E1 B6 9F |
Numeric character reference | ɜ |
ɜ |
ɝ |
ɝ |
ᶔ |
ᶔ |
ᶟ |
ᶟ |
Preview | ᴈ | ᵌ | ʚ | ɞ | ||||
---|---|---|---|---|---|---|---|---|
Unicode name | LATIN SMALL LETTER TURNED OPEN E |
MODIFIER LETTER SMALL TURNED OPEN E |
LATIN SMALL LETTER CLOSED OPEN E |
LATIN SMALL LETTER CLOSED REVERSED OPEN E | ||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex |
Unicode | 7432 | U+1D08 | 7500 | U+1D4C | 666 | U+029A | 606 | U+025E |
UTF-8 | 225 180 136 | E1 B4 88 | 225 181 140 | E1 B5 8C | 202 154 | CA 9A | 201 158 | C9 9E |
Numeric character reference | ᴈ |
ᴈ |
ᵌ |
ᵌ |
ʚ |
ʚ |
ɞ |
ɞ |
- Mathematical Epsilon
Preview | 𝚬 | 𝛆 | 𝛦 | 𝜀 | 𝜠 | 𝜺 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Unicode name | MATHEMATICAL BOLD CAPITAL EPSILON |
MATHEMATICAL BOLD SMALL EPSILON |
MATHEMATICAL ITALIC CAPITAL EPSILON |
MATHEMATICAL ITALIC SMALL EPSILON |
MATHEMATICAL BOLD ITALIC CAPITAL EPSILON |
MATHEMATICAL BOLD ITALIC SMALL EPSILON | ||||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 120492 | U+1D6AC | 120518 | U+1D6C6 | 120550 | U+1D6E6 | 120576 | U+1D700 | 120608 | U+1D720 | 120634 | U+1D73A |
UTF-8 | 240 157 154 172 | F0 9D 9A AC | 240 157 155 134 | F0 9D 9B 86 | 240 157 155 166 | F0 9D 9B A6 | 240 157 156 128 | F0 9D 9C 80 | 240 157 156 160 | F0 9D 9C A0 | 240 157 156 186 | F0 9D 9C BA |
UTF-16 | 55349 57004 | D835 DEAC | 55349 57030 | D835 DEC6 | 55349 57062 | D835 DEE6 | 55349 57088 | D835 DF00 | 55349 57120 | D835 DF20 | 55349 57146 | D835 DF3A |
Numeric character reference | 𝚬 |
𝚬 |
𝛆 |
𝛆 |
𝛦 |
𝛦 |
𝜀 |
𝜀 |
𝜠 |
𝜠 |
𝜺 |
𝜺 |
Preview | 𝛜 | 𝜖 | 𝝐 | |||
---|---|---|---|---|---|---|
Unicode name | MATHEMATICAL BOLD EPSILON SYMBOL |
MATHEMATICAL ITALIC EPSILON SYMBOL |
MATHEMATICAL BOLD ITALIC EPSILON SYMBOL | |||
Encodings | decimal | hex | dec | hex | dec | hex |
Unicode | 120540 | U+1D6DC | 120598 | U+1D716 | 120656 | U+1D750 |
UTF-8 | 240 157 155 156 | F0 9D 9B 9C | 240 157 156 150 | F0 9D 9C 96 | 240 157 157 144 | F0 9D 9D 90 |
UTF-16 | 55349 57052 | D835 DEDC | 55349 57110 | D835 DF16 | 55349 57168 | D835 DF50 |
Numeric character reference | 𝛜 |
𝛜 |
𝜖 |
𝜖 |
𝝐 |
𝝐 |
Preview | 𝝚 | 𝝴 | 𝞔 | 𝞮 | ||||
---|---|---|---|---|---|---|---|---|
Unicode name | MATHEMATICAL SANS-SERIF BOLD CAPITAL EPSILON |
MATHEMATICAL SANS-SERIF BOLD SMALL EPSILON |
MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL EPSILON |
MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL EPSILON | ||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex |
Unicode | 120666 | U+1D75A | 120692 | U+1D774 | 120724 | U+1D794 | 120750 | U+1D7AE |
UTF-8 | 240 157 157 154 | F0 9D 9D 9A | 240 157 157 180 | F0 9D 9D B4 | 240 157 158 148 | F0 9D 9E 94 | 240 157 158 174 | F0 9D 9E AE |
UTF-16 | 55349 57178 | D835 DF5A | 55349 57204 | D835 DF74 | 55349 57236 | D835 DF94 | 55349 57262 | D835 DFAE |
Numeric character reference | 𝝚 |
𝝚 |
𝝴 |
𝝴 |
𝞔 |
𝞔 |
𝞮 |
𝞮 |
Preview | 𝞊 | 𝟄 | ||
---|---|---|---|---|
Unicode name | MATHEMATICAL SANS-SERIF BOLD EPSILON SYMBOL |
MATHEMATICAL SANS-SERIF BOLD ITALIC EPSILON SYMBOL | ||
Encodings | decimal | hex | dec | hex |
Unicode | 120714 | U+1D78A | 120772 | U+1D7C4 |
UTF-8 | 240 157 158 138 | F0 9D 9E 8A | 240 157 159 132 | F0 9D 9F 84 |
UTF-16 | 55349 57226 | D835 DF8A | 55349 57284 | D835 DFC4 |
Numeric character reference | 𝞊 |
𝞊 |
𝟄 |
𝟄 |
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
-
folio 64 verso
-
folio 125 verso
See also
- е, the letter Ye of the Cyrillic alphabet
- Є є, Ukrainian Ye
- Ԑ ԑ, Reversed Ze
- E (disambiguation)
References
- ISBN 0582053838.
- ^ "epsilon". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
- ^ a b Nick Nicholas: Letters Archived 2012-12-15 at archive.today, 2003–2008. (Greek Unicode Issues)
- ^ 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. p. 127.
- ISBN 0-201-48345-9.
- ISBN 0-201-56788-1.
- ^ "European Commission – Economic and Financial Affairs – How to use the euro name and symbol". Ec.europa.eu. Retrieved 7 April 2010.
Inspiration for the € symbol itself came from the Greek epsilon, ϵ – a reference to the cradle of European civilization – and the first letter of the word Europe, crossed by two parallel lines to 'certify' the stability of the euro.
- ISBN 978-1614271314.
- ^ Jeffery, Lilian H. (1961). The local scripts of archaic Greece. Oxford: Clarendon. pp. 63–64.
- ^ Jeffery, Local scripts, p. 24.
- ^ Jeffery, Local scripts, p. 114.
- ^ Jeffery, Local scripts, p. 138.
- ^ Nicholas, Nick (2005). "Proposal to add Greek epigraphical letters to the UCS" (PDF). Archived from the original (PDF) on February 17, 2006. Retrieved 2010-08-12.
- ^ Jeffery, Local scripts, p. 89.
- ^ Thompson, Edward M. (1911). An introduction to Greek and Latin palaeography. Oxford: Clarendon. pp. 191–194.
- ^ Weisstein, Eric W. "Delta Function". mathworld.wolfram.com. Retrieved 2019-02-19.
Further reading
- ISBN 0-7868-6362-5.