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Eighteenth letter of the Greek alphabet From Wikipedia, the free encyclopedia
Sigma (/ˈsɪɡmə/ SIG-mə;[1] uppercase Σ, lowercase σ, lowercase in word-final position ς; Greek: σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as an operator for summation. When used at the end of a letter-case word (one that does not use all caps), the final form (ς) is used. In Ὀδυσσεύς (Odysseus), for example, the two lowercase sigmas (σ) in the center of the name are distinct from the word-final sigma (ς) at the end. The Latin letter S derives from sigma while the Cyrillic letter Es derives from a lunate form of this letter.
The shape (Σς) and alphabetic position of sigma is derived from the Phoenician letter (shin).
Sigma's original name may have been san, but due to the complicated early history of the Greek epichoric alphabets, san came to be identified as a separate letter in the Greek alphabet, represented as Ϻ.[2] Herodotus reports that "san" was the name given by the Dorians to the same letter called "sigma" by the Ionians.[lower-roman 1][3]
According to one hypothesis,[4] the name "sigma" may continue that of Phoenician samekh (), the letter continued through Greek xi, represented as Ξ. Alternatively, the name may have been a Greek innovation that simply meant 'hissing', from the root of σίζω (sízō, from Proto-Greek *sig-jō 'I hiss').[2]
In handwritten Greek during the Hellenistic period (4th–3rd century BC), the epigraphic form of Σ was simplified into a C-like shape,[5] which has also been found on coins from the 4th century BC onward.[6] This became the universal standard form of sigma during late antiquity and the Middle Ages.
Today, it is known as lunate sigma (uppercase Ϲ, lowercase ϲ), because of its crescent-like shape, and is still widely used in decorative typefaces in Greece, especially in religious and church contexts, as well as in some modern print editions of classical Greek texts.
A dotted lunate sigma (sigma periestigmenon, Ͼ) was used by Aristarchus of Samothrace (220–143 BC) as an editorial sign indicating that the line marked as such is at an incorrect position. Similarly, a reversed sigma (antisigma, Ͻ), may mark a line that is out of place. A dotted antisigma (antisigma periestigmenon, Ͽ) may indicate a line after which rearrangements should be made, or to variant readings of uncertain priority.
In Greek inscriptions from the late first century BC onwards, Ͻ was an abbreviation indicating that a man's father's name is the same as his own name, thus Dionysodoros son of Dionysodoros would be written Διονυσόδωρος Ͻ (Dionysodoros Dionysodorou).[7][8]
In Unicode, the above variations of lunate sigma are encoded as U+03F9 Ϲ GREEK CAPITAL LUNATE SIGMA SYMBOL; U+03FD Ͻ GREEK CAPITAL REVERSED LUNATE SIGMA SYMBOL, U+03FE Ͼ GREEK CAPITAL DOTTED LUNATE SIGMA SYMBOL, and U+03FF Ͽ GREEK CAPITAL REVERSED DOTTED LUNATE SIGMA SYMBOL.
Sigma was adopted in the Old Italic alphabets beginning in the 8th century BC. At that time a simplified three-stroke version, omitting the lowermost stroke, was already found in Western Greek alphabets, and was incorporated into classical Etruscan and Oscan, as well as in the earliest Latin epigraphy (early Latin S), such as the Duenos inscription. The alternation between three and four (and occasionally more than four) strokes was also adopted into the early runic alphabet (early form of the s-rune). Both the Anglo-Saxon runes and the Younger Futhark consistently use the simplified three-stroke version.
The letter С of Cyrillic script originates in the lunate form of Sigma.
Preview | Σ | σ | ς | Ϲ | ϲ | |||||
---|---|---|---|---|---|---|---|---|---|---|
Unicode name | GREEK CAPITAL LETTER SIGMA | GREEK SMALL LETTER SIGMA | GREEK SMALL LETTER FINAL SIGMA | GREEK CAPITAL LUNATE SIGMA SYMBOL | GREEK LUNATE SIGMA SYMBOL | |||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 931 | U+03A3 | 963 | U+03C3 | 962 | U+03C2 | 1017 | U+03F9 | 1010 | U+03F2 |
UTF-8 | 206 163 | CE A3 | 207 131 | CF 83 | 207 130 | CF 82 | 207 185 | CF B9 | 207 178 | CF B2 |
Numeric character reference | Σ | Σ | σ | σ | ς | ς | Ϲ | Ϲ | ϲ | ϲ |
Named character reference | Σ | σ | ς, ς, ς | |||||||
DOS Greek | 145 | 91 | 169 | A9 | 170 | AA | ||||
DOS Greek-2 | 207 | CF | 236 | EC | 237 | ED | ||||
Windows 1253 | 211 | D3 | 243 | F3 | 242 | F2 | ||||
TeX | \Sigma | \sigma | \varsigma |
Preview | Ͻ | ͻ | Ͼ | ͼ | Ͽ | ͽ | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Unicode name | GREEK CAPITAL REVERSED LUNATE SIGMA SYMBOL | GREEK SMALL REVERSED LUNATE SIGMA SYMBOL | GREEK CAPITAL DOTTED LUNATE SIGMA SYMBOL | GREEK SMALL DOTTED LUNATE SIGMA SYMBOL | GREEK CAPITAL REVERSED DOTTED LUNATE SIGMA SYMBOL | GREEK SMALL REVERSED DOTTED LUNATE SIGMA SYMBOL | ||||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 1021 | U+03FD | 891 | U+037B | 1022 | U+03FE | 892 | U+037C | 1023 | U+03FF | 893 | U+037D |
UTF-8 | 207 189 | CF BD | 205 187 | CD BB | 207 190 | CF BE | 205 188 | CD BC | 207 191 | CF BF | 205 189 | CD BD |
Numeric character reference | Ͻ | Ͻ | ͻ | ͻ | Ͼ | Ͼ | ͼ | ͼ | Ͽ | Ͽ | ͽ | ͽ |
Preview | Ⲥ | ⲥ | ||
---|---|---|---|---|
Unicode name | COPTIC CAPITAL LETTER SIMA | COPTIC SMALL LETTER SIMA | ||
Encodings | decimal | hex | dec | hex |
Unicode | 11428 | U+2CA4 | 11429 | U+2CA5 |
UTF-8 | 226 178 164 | E2 B2 A4 | 226 178 165 | E2 B2 A5 |
Numeric character reference | Ⲥ | Ⲥ | ⲥ | ⲥ |
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.
Preview | ∑ | 𝚺 | 𝛔 | 𝛓 | 𝛴 | 𝜎 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Unicode name | N-ARY SUMMATION | MATHEMATICAL BOLD CAPITAL SIGMA |
MATHEMATICAL BOLD SMALL SIGMA |
MATHEMATICAL BOLD SMALL FINAL SIGMA |
MATHEMATICAL ITALIC CAPITAL SIGMA |
MATHEMATICAL ITALIC SMALL SIGMA | ||||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 8721 | U+2211 | 120506 | U+1D6BA | 120532 | U+1D6D4 | 120531 | U+1D6D3 | 120564 | U+1D6F4 | 120590 | U+1D70E |
UTF-8 | 226 136 145 | E2 88 91 | 240 157 154 186 | F0 9D 9A BA | 240 157 155 148 | F0 9D 9B 94 | 240 157 155 147 | F0 9D 9B 93 | 240 157 155 180 | F0 9D 9B B4 | 240 157 156 142 | F0 9D 9C 8E |
UTF-16 | 8721 | 2211 | 55349 57018 | D835 DEBA | 55349 57044 | D835 DED4 | 55349 57043 | D835 DED3 | 55349 57076 | D835 DEF4 | 55349 57102 | D835 DF0E |
Numeric character reference | ∑ | ∑ | 𝚺 | 𝚺 | 𝛔 | 𝛔 | 𝛓 | 𝛓 | 𝛴 | 𝛴 | 𝜎 | 𝜎 |
Named character reference | ∑, ∑ |
Preview | 𝜍 | 𝜮 | 𝝈 | 𝝇 | 𝝨 | |||||
---|---|---|---|---|---|---|---|---|---|---|
Unicode name | MATHEMATICAL ITALIC SMALL FINAL SIGMA |
MATHEMATICAL BOLD ITALIC CAPITAL SIGMA |
MATHEMATICAL BOLD ITALIC SMALL SIGMA |
MATHEMATICAL BOLD ITALIC SMALL FINAL SIGMA |
MATHEMATICAL SANS-SERIF BOLD CAPITAL SIGMA | |||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 120589 | U+1D70D | 120622 | U+1D72E | 120648 | U+1D748 | 120647 | U+1D747 | 120680 | U+1D768 |
UTF-8 | 240 157 156 141 | F0 9D 9C 8D | 240 157 156 174 | F0 9D 9C AE | 240 157 157 136 | F0 9D 9D 88 | 240 157 157 135 | F0 9D 9D 87 | 240 157 157 168 | F0 9D 9D A8 |
UTF-16 | 55349 57101 | D835 DF0D | 55349 57134 | D835 DF2E | 55349 57160 | D835 DF48 | 55349 57159 | D835 DF47 | 55349 57192 | D835 DF68 |
Numeric character reference | 𝜍 | 𝜍 | 𝜮 | 𝜮 | 𝝈 | 𝝈 | 𝝇 | 𝝇 | 𝝨 | 𝝨 |
Preview | 𝞂 | 𝞁 | 𝞢 | 𝞼 | 𝞻 | |||||
---|---|---|---|---|---|---|---|---|---|---|
Unicode name | MATHEMATICAL SANS-SERIF BOLD SMALL SIGMA |
MATHEMATICAL SANS-SERIF BOLD SMALL FINAL SIGMA |
MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL SIGMA |
MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL SIGMA |
MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL FINAL SIGMA | |||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex | dec | hex |
Unicode | 120706 | U+1D782 | 120705 | U+1D781 | 120738 | U+1D7A2 | 120764 | U+1D7BC | 120763 | U+1D7BB |
UTF-8 | 240 157 158 130 | F0 9D 9E 82 | 240 157 158 129 | F0 9D 9E 81 | 240 157 158 162 | F0 9D 9E A2 | 240 157 158 188 | F0 9D 9E BC | 240 157 158 187 | F0 9D 9E BB |
UTF-16 | 55349 57218 | D835 DF82 | 55349 57217 | D835 DF81 | 55349 57250 | D835 DFA2 | 55349 57276 | D835 DFBC | 55349 57275 | D835 DFBB |
Numeric character reference | 𝞂 | 𝞂 | 𝞁 | 𝞁 | 𝞢 | 𝞢 | 𝞼 | 𝞼 | 𝞻 | 𝞻 |
The Miscellaneous Technical Unicode block also has two characters that represent the top and bottom of a double-height sigma: U+23B2 ⎲ SUMMATION TOP and U+23B3 ⎳ SUMMATION BOTTOM.