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Omicron

For other uses, see Omicron (disambiguation).

Omicron (uppercase Ο, lowercase ο, literally 'small o':όμικρον <ὂ μικρόν - ò mikrón, micron meaning 'small' in contrast to omega) is the 15th letter of the Greek alphabet. In the system of Greek numerals it has a value of 70. This letter is derived from the Phoenician letter ayin . In classical Greek, omicron represented the sound[o] in contrast to omega[ɔː] and ου[oː]. In modern Greek, omicron represents the mid back rounded vowel/o̞/, the same sound as omega. Letters that arose from omicron include Roman O and Cyrillic O.

Contents

In addition to its use as an alphabetic letter, omicron is occasionally used in technical notation, but its use is limited since both upper case and lower case (Ο ο) are indistinguishable from the Latin letter "oh" (O o) and difficult to distinguish from the Hindu-Arabic numeral "zero" (0).

Mathematics

The upper-case letter of omicron (O) was originally used in mathematics as a symbol for Big O notation (representing a function's asymptotic growth rate), but has fallen out of favor because omicron is indistinguishable from the Latin letter O and easily confused with the digit zero (0). Where "Big O" notation is still used, Omicron is generally replaced with a script- or calligraphic-form Latin letter "Oh" ( O {\displaystyle {\mathcal {O}}} ).

Greek numerals

Main article: Greek numerals

There were several systems for writing numbers in Greek; the most common form used in late classical era used omicron (either upper or lower case) to represent the value 70.

More generally, the letter omicron is used to mark the fifteenth ordinal position in any Greek-alphabet marked list. So for example, in Euclid's Elements, when various points in a geometric diagram are marked with letters, it is effectively the same as marking them with numbers, each letter representing the number of its place in the standard alphabet.

Astronomy

Omicron is used to designate the fifteenth star in a constellation group, its ordinal placement an irregular function of both magnitude and position. Such stars include Omicron Andromedae, Omicron Ceti, and Omicron Persei.

In Claudius Ptolemy's (c. 100–170) Almagest, tables of sexagesimal numbers 1 ... 59 are represented in the conventional manner for Greek numbers:′α ...′νθ . Since the letter omicron [which represents 70 (′ο) in the standard system] is not used in sexagesimal, it is re-purposed to represent an empty number cell. In some renditions the cell was just left blank (nothing there = value is zero), but to avoid copying errors, positively marking a zero cell with omicron was preferred, in the same way that blank cells in modern tables are filled with a dash (—). Both an omicron and a dash imply that "this isn't a mistake, the cell is actually supposed to be empty". By coincidence, the ancient zero-value omicron (ο) resembles a modern Hindu-Arabic zero (0).

  • Greek Omicron / Coptic O
Character information
Preview Ο ο
Unicode name GREEK CAPITAL LETTER OMICRON GREEK SMALL LETTER OMICRON COPTIC CAPITAL LETTER O COPTIC SMALL LETTER O
Encodings decimal hex decimal hex decimal hex decimal hex
Unicode 927 U+039F 959 U+03BF 11422 U+2C9E 11423 U+2C9F
UTF-8 206 159 CE 9F 206 191 CE BF 226 178 158 E2 B2 9E 226 178 159 E2 B2 9F
Numeric character reference &#927; &#x39F; &#959; &#x3BF; &#11422; &#x2C9E; &#11423; &#x2C9F;
Named character reference &Omicron; &omicron;
DOS Greek 142 8E 166 A6
DOS Greek-2 190 BE 233 E9
Windows 1253 207 CF 239 EF
  • Mathematical Omicron

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.


Character information
Preview 𝚶 𝛐 𝛰 𝜊 𝜪 𝝄
Unicode name MATHEMATICAL BOLD
CAPITAL OMICRON
MATHEMATICAL BOLD
SMALL OMICRON
MATHEMATICAL ITALIC
CAPITAL OMICRON
MATHEMATICAL ITALIC
SMALL OMICRON
MATHEMATICAL BOLD ITALIC
CAPITAL OMICRON
MATHEMATICAL BOLD ITALIC
SMALL OMICRON
Encodings decimal hex decimal hex decimal hex decimal hex decimal hex decimal hex
Unicode 120502 U+1D6B6 120528 U+1D6D0 120560 U+1D6F0 120586 U+1D70A 120618 U+1D72A 120644 U+1D744
UTF-8 240 157 154 182 F0 9D 9A B6 240 157 155 144 F0 9D 9B 90 240 157 155 176 F0 9D 9B B0 240 157 156 138 F0 9D 9C 8A 240 157 156 170 F0 9D 9C AA 240 157 157 132 F0 9D 9D 84
UTF-16 55349 57014 D835 DEB6 55349 57040 D835 DED0 55349 57072 D835 DEF0 55349 57098 D835 DF0A 55349 57130 D835 DF2A 55349 57156 D835 DF44
Numeric character reference &#120502; &#x1D6B6; &#120528; &#x1D6D0; &#120560; &#x1D6F0; &#120586; &#x1D70A; &#120618; &#x1D72A; &#120644; &#x1D744;


Character information
Preview 𝝤 𝝾 𝞞 𝞸
Unicode name MATHEMATICAL SANS-SERIF
BOLD CAPITAL OMICRON
MATHEMATICAL SANS-SERIF
BOLD SMALL OMICRON
MATHEMATICAL SANS-SERIF
BOLD ITALIC CAPITAL OMICRON
MATHEMATICAL SANS-SERIF
BOLD ITALIC SMALL OMICRON
Encodings decimal hex decimal hex decimal hex decimal hex
Unicode 120676 U+1D764 120702 U+1D77E 120734 U+1D79E 120760 U+1D7B8
UTF-8 240 157 157 164 F0 9D 9D A4 240 157 157 190 F0 9D 9D BE 240 157 158 158 F0 9D 9E 9E 240 157 158 184 F0 9D 9E B8
UTF-16 55349 57188 D835 DF64 55349 57214 D835 DF7E 55349 57246 D835 DF9E 55349 57272 D835 DFB8
Numeric character reference &#120676; &#x1D764; &#120702; &#x1D77E; &#120734; &#x1D79E; &#120760; &#x1D7B8;
  1. Greek letters-as-numbers used an older Greek alphabet with three more otherwise unused letters, two of them re‑instated in their old locations, early in the alphabet. So positions higher than 5th place (ε) were shifted from the standard alphabet; 5th place was marked with normal fifth letter epsilon (ε). The 6th letter in the conventional alphabet, that normally followsε isζ (zeta) but the number 6 was represented a revived ancient letterϝ (digamma), followed byζ which was pushed up from 6th to its ancient position (7th) to represent the number 7. All of the letters afterζ were likewise shifted up one place, until the second ancient letter koppa, (ϙ), was reached; it fell betweenπ andρ. Ever letter from ρ to ω was shifted two places past its conventional ordinal position. Last place coming right after omega (ω, 800) was sampi (ϡ) which represented 900. (From that point, the system restarted, with a new tick-mark, at͵α. The tick-mark was put in a different place (͵α rather thanα) to show that the letter represented a multiple of 1,000 rather than 1.)[citation needed]
  2. From Euclid up to the 19th century, mathematical and technical diagrams were habitually marked sequentially with letters (or numbers),[citation needed] whereas in modern mathematical and scientific diagrams, it is much more common to choose for markers letters that might remind readers of the word used to describe the item in question.[citation needed] For example, Feynman diagrams in particle physics label the positions of particles with the first letter of their name, either in the Latin or Greek alphabet. Sop,n, ande , represent the position on a diagram of a proton, neutron, and electron, respectively. The neutrino is represented byν (Greek "nu"), since the Latin letter "n" is reserved for the neutron.[citation needed]
  3. Sexagesimal Greek numbers in the Almagest are conventional: 1 2 3 4 5 6 7 8 9 = ′α ′β ′γ ′δ ′ε ′ϝ ′ζ ′η ′θ . Notice that ancient digamma (ϝ) is used for 6 instead of zeta (ζ, which is used for 7) ; 10 20 30 40 50 = ′ι ′κ ′λ ′μ ′ν . Adjacent number-letters add, so all the other numbers are made by letter pairs, such as 29 30 31 = ′κθ ′λ ′λα . The number 59 (′νθ) is the largest value used in a single cell in sexagesimal. That leaves xi (ξ) and the letters following it ξ ο π ϙ ρ σ τ υ φ χ ψ ω ϡ free for other use: Ptolemy picked ο, which normally was used for 70, to mark empty (zero) cells, perhaps because the word for "nothing",οὐδέν starts with an omicron.
Look up Ο or ο in Wiktionary, the free dictionary.
  1. "omicron". Oxford English Dictionary (Online ed.). Oxford University Press.(Subscription or participating institution membership required.)
  2. Martin, Martha Evans (1907). The Friendly Stars (1st ed.). New York: Harper & Brothers Publishers. p. 135. Retrieved8 February 2016.
  3. Wilk, Stephen R. (2007). Medusa: Solving the Mystery of the Gorgon (1st ed.). New York, NY; London, UK: Oxford University Press. p. 201. ISBN 9780199887736. Retrieved8 February 2016.
  4. "Greek and Coptic (Range: 0370–03FF)"(PDF). The Unicode Standard, Ver. 8.0. Unicode, Inc. 2015. Retrieved8 February 2016.
  5. "Mathematical Alphanumeric Symbols (Range: 1D400–1D7FF)"(PDF). The Unicode Standard, Ver. 8.0. Unicode, Inc. 2015. Retrieved8 February 2016.

Omicron
Omicron Language Watch Edit 160 160 Redirected from O For other uses see Omicron disambiguation Omicron ˈ ɒ m ɪ k r ɒ n oʊ ˈ m aɪ k r ɒ n 1 uppercase O lowercase o literally small o omikron lt ὂ mikron o mikron micron meaning small in contrast to omega is the 15th letter of the Greek alphabet In the system of Greek numerals it has a value of 70 This letter is derived from the Phoenician letter ayin In classical Greek omicron represented the sound o in contrast to omega ɔː and oy oː In modern Greek omicron represents the mid back rounded vowel o the same sound as omega Letters that arose from omicron include Roman O and Cyrillic O Contents 1 Use 1 1 Mathematics 1 2 Greek numerals 1 3 Astronomy 2 Character encodings 3 Footnotes 4 ReferencesUse EditIn addition to its use as an alphabetic letter omicron is occasionally used in technical notation but its use is limited since both upper case and lower case O o are indistinguishable from the Latin letter oh O o and difficult to distinguish from the Hindu Arabic numeral zero 0 Mathematics Edit The upper case letter of omicron O was originally used in mathematics as a symbol for Big O notation representing a function s asymptotic growth rate but has fallen out of favor because omicron is indistinguishable from the Latin letter O and easily confused with the digit zero 0 Where Big O notation is still used Omicron is generally replaced with a script or calligraphic form Latin letter Oh O displaystyle mathcal O Greek numerals Edit Main article Greek numerals There were several systems for writing numbers in Greek the most common form used in late classical era used omicron either upper or lower case to represent the value 70 More generally the letter omicron is used to mark the fifteenth ordinal position in any Greek alphabet marked list So for example in Euclid s Elements when various points in a geometric diagram are marked with letters it is effectively the same as marking them with numbers each letter representing the number of its place in the standard alphabet a b Astronomy Edit Omicron is used to designate the fifteenth star in a constellation group its ordinal placement an irregular function of both magnitude and position 2 3 Such stars include Omicron Andromedae Omicron Ceti and Omicron Persei In Claudius Ptolemy s c 100 170 Almagest tables of sexagesimal numbers 1 59 are represented in the conventional manner c for Greek numbers a n8 Since the letter omicron which represents 70 o in the standard system is not used in sexagesimal it is re purposed to represent an empty number cell In some renditions the cell was just left blank nothing there value is zero but to avoid copying errors positively marking a zero cell with omicron was preferred in the same way that blank cells in modern tables are filled with a dash Both an omicron and a dash imply that this isn t a mistake the cell is actually supposed to be empty By coincidence the ancient zero value omicron o resembles a modern Hindu Arabic zero 0 Character encodings EditGreek Omicron Coptic O 4 Character information Preview O o Ⲟ ⲟUnicode name GREEK CAPITAL LETTER OMICRON GREEK SMALL LETTER OMICRON COPTIC CAPITAL LETTER O COPTIC SMALL LETTER OEncodings decimal hex decimal hex decimal hex decimal hexUnicode 927 U 039F 959 U 03BF 11422 U 2C9E 11423 U 2C9FUTF 8 206 159 CE 9F 206 191 CE BF 226 178 158 E2 B2 9E 226 178 159 E2 B2 9FNumeric character reference amp 927 wbr amp x39F wbr amp 959 wbr amp x3BF wbr amp 11422 wbr amp x2C9E wbr amp 11423 wbr amp x2C9F wbr Named character reference amp Omicron amp omicron DOS Greek 142 8E 166 A6DOS Greek 2 190 BE 233 E9Windows 1253 207 CF 239 EFMathematical Omicron 5 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 Character information Preview 𝚶 𝛐 𝛰 𝜊 𝜪 𝝄Unicode name MATHEMATICAL BOLD CAPITAL OMICRON MATHEMATICAL BOLD SMALL OMICRON MATHEMATICAL ITALIC CAPITAL OMICRON MATHEMATICAL ITALIC SMALL OMICRON MATHEMATICAL BOLD ITALIC CAPITAL OMICRON MATHEMATICAL BOLD ITALIC SMALL OMICRONEncodings decimal hex decimal hex decimal hex decimal hex decimal hex decimal hexUnicode 120502 U 1D6B6 120528 U 1D6D0 120560 U 1D6F0 120586 U 1D70A 120618 U 1D72A 120644 U 1D744UTF 8 240 157 154 182 F0 9D 9A B6 240 157 155 144 F0 9D 9B 90 240 157 155 176 F0 9D 9B B0 240 157 156 138 F0 9D 9C 8A 240 157 156 170 F0 9D 9C AA 240 157 157 132 F0 9D 9D 84UTF 16 55349 57014 D835 DEB6 55349 57040 D835 DED0 55349 57072 D835 DEF0 55349 57098 D835 DF0A 55349 57130 D835 DF2A 55349 57156 D835 DF44Numeric character reference amp 120502 wbr amp x1D6B6 wbr amp 120528 wbr amp x1D6D0 wbr amp 120560 wbr amp x1D6F0 wbr amp 120586 wbr amp x1D70A wbr amp 120618 wbr amp x1D72A wbr amp 120644 wbr amp x1D744 wbr Character information Preview 𝝤 𝝾 𝞞 𝞸Unicode name MATHEMATICAL SANS SERIF BOLD CAPITAL OMICRON MATHEMATICAL SANS SERIF BOLD SMALL OMICRON MATHEMATICAL SANS SERIF BOLD ITALIC CAPITAL OMICRON MATHEMATICAL SANS SERIF BOLD ITALIC SMALL OMICRONEncodings decimal hex decimal hex decimal hex decimal hexUnicode 120676 U 1D764 120702 U 1D77E 120734 U 1D79E 120760 U 1D7B8UTF 8 240 157 157 164 F0 9D 9D A4 240 157 157 190 F0 9D 9D BE 240 157 158 158 F0 9D 9E 9E 240 157 158 184 F0 9D 9E B8UTF 16 55349 57188 D835 DF64 55349 57214 D835 DF7E 55349 57246 D835 DF9E 55349 57272 D835 DFB8Numeric character reference amp 120676 wbr amp x1D764 wbr amp 120702 wbr amp x1D77E wbr amp 120734 wbr amp x1D79E wbr amp 120760 wbr amp x1D7B8 wbr Footnotes Edit Greek letters as numbers used an older Greek alphabet with three more otherwise unused letters two of them re instated in their old locations early in the alphabet So positions higher than 5th place e were shifted from the standard alphabet 5th place was marked with normal fifth letter epsilon e The 6th letter in the conventional alphabet that normally follows e is z zeta but the number 6 was represented a revived ancient letter ϝ digamma followed by z which was pushed up from 6th to its ancient position 7th to represent the number 7 All of the letters after z were likewise shifted up one place until the second ancient letter koppa ϙ was reached it fell between p and r Ever letter from r to w was shifted two places past its conventional ordinal position Last place coming right after omega w 800 was sampi ϡ which represented 900 From that point the system restarted with a new tick mark at a The tick mark was put in a different place a rather than a to show that the letter represented a multiple of 1 000 rather than 1 citation needed From Euclid up to the 19th century mathematical and technical diagrams were habitually marked sequentially with letters or numbers citation needed whereas in modern mathematical and scientific diagrams it is much more common to choose for markers letters that might remind readers of the word used to describe the item in question citation needed For example Feynman diagrams in particle physics label the positions of particles with the first letter of their name either in the Latin or Greek alphabet So p n and e represent the position on a diagram of a proton neutron and electron respectively The neutrino is represented by n Greek nu since the Latin letter n is reserved for the neutron citation needed Sexagesimal Greek numbers in the Almagest are conventional 1 2 3 4 5 6 7 8 9 a b g d e ϝ z h 8 Notice that ancient digamma ϝ is used for 6 instead of zeta z which is used for 7 10 20 30 40 50 i k l m n Adjacent number letters add so all the other numbers are made by letter pairs such as 29 30 31 k8 l la The number 59 n8 is the largest value used in a single cell in sexagesimal That leaves xi 3 and the letters following it 3 o p ϙ r s t y f x ps w ϡ free for other use Ptolemy picked o which normally was used for 70 to mark empty zero cells perhaps because the word for nothing oὐden starts with an omicron References EditLook up O or o in Wiktionary the free dictionary omicron Oxford English Dictionary Online ed Oxford University Press Subscription or participating institution membership required Martin Martha Evans 1907 The Friendly Stars 1st ed New York Harper amp Brothers Publishers p 135 Retrieved 8 February 2016 Wilk Stephen R 2007 Medusa Solving the Mystery of the Gorgon 1st ed New York NY London UK Oxford University Press p 201 ISBN 9780199887736 Retrieved 8 February 2016 Greek and Coptic Range 0370 03FF PDF The Unicode Standard Ver 8 0 Unicode Inc 2015 Retrieved 8 February 2016 Mathematical Alphanumeric Symbols Range 1D400 1D7FF PDF The Unicode Standard Ver 8 0 Unicode Inc 2015 Retrieved 8 February 2016 Retrieved from https en wikipedia org w index php title Omicron amp oldid 1044858223, wikipedia, wiki, book,

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