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Theta

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Eighth letter of the Greek alphabet
"θ" redirects here. For the letter used in Latin scripts, seeLatin theta. For the letter used in IPA, seeVoiceless dental fricative. For other uses, seeTheta (disambiguation).Not to be confused with the Cyrillic lettersFita orOe.
See also:Ø and similar symbols
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Greek alphabet
ΑαAlpha ΝνNu
ΒβBeta ΞξXi
ΓγGamma ΟοOmicron
ΔδDelta ΠπPi
ΕεEpsilon ΡρRho
ΖζZeta ΣσςSigma
ΗηEta ΤτTau
ΘθTheta ΥυUpsilon
ΙιIota ΦφPhi
ΚκKappa ΧχChi
ΛλLambda ΨψPsi
ΜμMu ΩωOmega
History
ϜDigamma ͰHeta
ϺSan ϘKoppa
Ͷ ͲSampi
Diacritics and other symbols
Related topics

Theta (UK:/ˈθtə/ ,US:/ˈθtə/ ) uppercaseΘ; lowercaseθ;Ancient Greek:θῆταthē̂ta[tʰɛ̂ːta];Modern:θήταthī́ta[ˈθita]) is the eighth letter of theGreek alphabet, derived from thePhoenician letterTeth 𐤈. In the system ofGreek numerals, it has a value of 9.

Greek

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InAncient Greek, θ represented theaspiratedvoiceless dental plosiveIPA:[t̪ʰ], but inModern Greek it represents thevoiceless dental fricativeIPA:[θ].

Forms

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Modern print theta, in a typical uppercase and two different lowercase glyph forms.

In itsarchaic form, θ was written as a cross within a circle (as in the EtruscanA symbol of a cross within a circle orAnother symbol of a cross within a circle), and later, as a line or point in circle (The symbol of a line within a circle orThe symbol of a point within a circle).

In modern print, lowercase theta may appear in two different forms: one resembling the uppercase form, like a zero with a horizontal bar through it, and one more cursive style featuring an open loop, resembling a nine. For use as a mathematical symbol, where the difference between the two forms may be significant, a dedicated Unicode symbolU+03D1 ϑGREEK THETA SYMBOL was introduced, which always displays the open-loop form. There is alsoU+03F4 ϴGREEK CAPITAL THETA SYMBOL, which differs from most realizations of the normal textual uppercase letter by having a cross-bar that goes all the way across, touching the outer O-shape on both sides.

Latin

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Further information:Latin theta
The name ARAÐÐOVNA on a Gaulish tombstone

In the Latin script used for theGaulish language, theta inspired thetau gallicum (Ꟈ ꟈ). The phonetic value of thetau gallicum is thought to have been[t͡s].[1] In addition, multiple modern languages written in Latin script useLatin theta.

Cyrillic

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Theearly Cyrillic letterfita (Ѳ, ѳ) developed from θ. This letter existed in theRussian alphabet until the1918 Russian orthography reform.

International Phonetic Alphabet

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In theInternational Phonetic Alphabet (IPA),[θ] represents thevoiceless dental fricative, as inthick orthin.[2] It does not represent the consonant inthe, which is thevoiced dental fricative counterpart, represented in the IPA by[ð] (cf.Eth). A similar-looking lower-case symbol,[ɵ], which is calledbarred o, is the IPA symbol for theclose-mid central rounded vowel.

Mathematics and science

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Lower case

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The lowercase letter θ is used as a symbol for:

Upper case

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The uppercase letter Θ is used as a symbol for:

Symbolism

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θ (θάνατος, death) in a mosaic

In ancient times,Tau was used as a symbol forlife orresurrection, whereas the eighth letter of the Greek alphabet (ninth in the archaic form anciently used for numeration), theta, was considered the symbol ofdeath.[21] A quotation attributed to the ancient Roman authorEnnius (though possibly spuriously) said of it: "oh, theta, a letter much unluckier than the others".[22]

According toPorphyry of Tyros, theEgyptians used an X within a circle as asymbol of the soul; having a value of nine, it was used as a symbol forEnnead.Johannes Lydus says that theEgyptians used a symbol forKosmos in the form of theta, with a fiery circle representing the world, and a snake spanning the middle representingAgathos Daimon (literally:good spirit).[23]

Abbreviation

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Main article:Theta nigrum

In classical Athens, it was used as an abbreviation for theGreek θάνατος (Thanatos, "death") and as it vaguely resembles a human skull,[23] theta was used as a warning symbol ofdeath, in the same way thatskull and crossbones are used in modern times.[23] It survives onpotsherds used by Athenians when voting for thedeath penalty.[23]Petrus de Dacia in a document from 1291 relates the idea that theta was used to brand criminals as empty ciphers, and the branding rod was affixed to the crossbar spanning the circle.[24] For this reason, the use of the number 9 was sometimes avoided where the connotation was felt to be unlucky—the mint marks of some Late Imperial Roman coins famously have the sum ΔΕ or ΕΔ (delta and epsilon, that is 4 and 5) substituted as aeuphemism where a Θ (9) would otherwise be expected.

Unicode

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  • U+0398 ΘGREEK CAPITAL LETTER THETA (Θ)
  • U+03B8 θGREEK SMALL LETTER THETA (θ)
  • U+03D1 ϑGREEK THETA SYMBOL (ϑ, ϑ, ϑ)
  • U+03F4 ϴGREEK CAPITAL THETA SYMBOL
  • U+0472 ѲCYRILLIC CAPITAL LETTER FITA
  • U+0473 ѳCYRILLIC SMALL LETTER FITA
  • U+1DBF ᶿMODIFIER LETTER SMALL THETA
  • U+2C2A GLAGOLITIC CAPITAL LETTER FITA
  • U+2C5A GLAGOLITIC SMALL LETTER FITA
  • U+2C90 COPTIC CAPITAL LETTER THETHE
  • U+2C91 COPTIC SMALL LETTER THETHE
  • U+2DF4 ◌ⷴCOMBINING CYRILLIC LETTER FITA
  • U+1CF83 𜾃ZNAMENNY NEUME FITA
  • U+1D6AF 𝚯MATHEMATICAL BOLD CAPITAL THETA[a]
  • U+1D6B9 𝚹MATHEMATICAL BOLD CAPITAL THETA SYMBOL
  • U+1D6C9 𝛉MATHEMATICAL BOLD SMALL THETA
  • U+1D6DD 𝛝MATHEMATICAL BOLD THETA SYMBOL
  • U+1D6E9 𝛩MATHEMATICAL ITALIC CAPITAL THETA
  • U+1D6F3 𝛳MATHEMATICAL ITALIC CAPITAL THETA SYMBOL
  • U+1D703 𝜃MATHEMATICAL ITALIC SMALL THETA
  • U+1D717 𝜗MATHEMATICAL ITALIC THETA SYMBOL
  • U+1D723 𝜣MATHEMATICAL BOLD ITALIC CAPITAL THETA
  • U+1D72D 𝜭MATHEMATICAL BOLD ITALIC CAPITAL THETA SYMBOL
  • U+1D73D 𝜽MATHEMATICAL BOLD ITALIC SMALL THETA
  • U+1D751 𝝑MATHEMATICAL BOLD ITALIC THETA SYMBOL
  • U+1D75D 𝝝MATHEMATICAL SANS-SERIF BOLD CAPITAL THETA
  • U+1D767 𝝧MATHEMATICAL SANS-SERIF BOLD CAPITAL THETA SYMBOL
  • U+1D777 𝝷MATHEMATICAL SANS-SERIF BOLD SMALL THETA
  • U+1D78B 𝞋MATHEMATICAL SANS-SERIF BOLD THETA SYMBOL
  • U+1D797 𝞗MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL THETA
  • U+1D7A1 𝞡MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL THETA SYMBOL
  • U+1D7B1 𝞱MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL THETA
  • U+1D7C5 𝟅MATHEMATICAL SANS-SERIF BOLD ITALIC THETA SYMBOL
  • U+1E02A ◌𞀪COMBINING GLAGOLITIC LETTER FITA

See also

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Look upΘ orθ in Wiktionary, the free dictionary.
  • ʘ – Consonantal soundPages displaying short descriptions of redirect targets

Notes and references

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Notes

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  1. ^TheMATHEMATICAL characters are used only in math. Stylized Greek text should be encoded using normal Greek letters, with markup and formatting to indicate text style.

References

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  1. ^Everson, Michael; Lilley, Chris (2019-05-26)."L2/19-179: Proposal for the addition of four Latin characters for Gaulish"(PDF).
  2. ^International Phonetic Association (2021).Handbook of the International Phonetic Association: a guide to the use of the international phonetic alphabet (22. printing ed.). Cambridge: Cambridge University Press. p. 177.ISBN 978-0-521-63751-0.θ Theta voiceless dental fricative
  3. ^Weisstein, Eric W."Angle".mathworld.wolfram.com. Retrieved2025-02-01.
  4. ^Elert, Glenn (2023),"Special Symbols",The Physics Hypertextbook, hypertextbook, retrieved2025-02-01,ϴ,φ,ϴ,φ angle, angular displacement, angular separation, rotation angle
  5. ^Weisstein, Eric W."Chebyshev Functions".mathworld.wolfram.com. Retrieved2025-01-24.
  6. ^Holton, James R.; Hakim, Gregory J. (2013).An introduction to dynamic meteorology (Fifth ed.). Amsterdam: Academic Press. p. 87.ISBN 978-0-12-384866-6.Since potential temperature θ is conserved following the motion in adiabatic flow, a parcel of air which movees adiabatically will remain on the same potential temperature surface.
  7. ^Ahsan, Amimul, ed. (2011).Convection and Conduction Heat Transfer. Erscheinungsort nicht ermittelbar: IntechOpen. p. 57.ISBN 978-953-307-582-2.θ dimensionless temperature,...
  8. ^van der Linden, Wim J.; Hambleton, Ronald K. (2018).Handbook of Item Response Theory, Three Volume Set. Chapman & Hall / CRC Statistics in the Social and Behavioral Sciences (1st ed.). Boca Raton: CRC Press. pp. section 10.2.ISBN 978-1-4665-1439-3.θp is test taker p's factor score or latent trait parameter.
  9. ^Bakich, Michael E. (1995).The Cambridge guide to the constellations. Cambridge: Cambridge University Press. p. 109.ISBN 978-0-521-46520-5.To designate the 24 brightest stars in the constellation, Johannes Bayer used the lowercase letters of the Greek alphabet:
  10. ^Casella, George; Berger, Roger W. (2024).Statistical inference. CRC texts in statistical science series (Second ed.). Boca Raton: CRC Press. p. 8.ISBN 978-1-032-59303-6.Likelihood is the most directly accessible inferential element for estimation statements about θ conditional on f...
  11. ^Hösel, Volker (2020).Mathematical population genetics and evolution of bacterial cooperation. New Jersey: World Scientific. p. 75.ISBN 978-981-12-0549-1.
  12. ^Reszat, Beate (2005).European financial systems in the global economy. Chichester, West Sussex, England ; Hoboken, NJ: Wiley. pp. 223–224.ISBN 978-0-470-87056-3.As a consequence, the critical level for joining shifts from θ to θ' -...
  13. ^Damill, Mario; Rapetti, Martín; Rozenwurcel, Guillermo, eds. (2016).Macroeconomics and development: Roberto Frenkel and the economics of Latin America. Initiative for policy dialogue. New York: Columbia University Press.ISBN 978-0-231-17508-1....θ and θ* are reserve ratios in DC and FC...
  14. ^Feferman, Solomon (2010). Schindler, Ralf (ed.)."The proof theory of classical and constructive inductive definitions. A 40 year saga, 1968–2008"(PDF).Ways of Proof Theory:7–30.doi:10.1515/9783110324907.7.
  15. ^Weisstein, Eric W."Heaviside Step Function".mathworld.wolfram.com. Retrieved2025-01-24.
  16. ^Ali Elkordy, Amal, ed. (2013).Applications of Calorimetry in a Wide Context: Differential Scanning Calorimetry, Isothermal Titration Calorimetry and Microcalorimetry. Erscheinungsort nicht ermittelbar: IntechOpen. p. 75.ISBN 978-953-51-0947-1.Saturation fraction, θ. The fraction of the total number of sites of the macromolecule occupied by ligand molecules.
  17. ^Singh, Balwant; Arbestain, Marta Camps; Lehmann, Johannes, eds. (2017).Biochar: a guide to analytical methods. Clayton South: CSIRO Publishing. p. 246.ISBN 978-1-4987-6553-4.θ is the angle between the incident x-ray beam and the diffracting plane
  18. ^"DLMF: Chapter 20 Theta Functions".dlmf.nist.gov. Retrieved2025-01-31.
  19. ^Lemons, Don S. (2017).A student's guide to dimensional analysis. New York: Cambridge University Press. p. 50.ISBN 978-1-107-16115-3.The physics of heat transfer requires two dimensions, temperature Θ and heat H, beyond those that characterize non-equilibrium dynamics.
  20. ^Ursone, Pierino (2015).How to Calculate Options Prices and Their Greeks: Exploring the Black Scholes Model from Delta to Vega. The Wiley Finance Series (1st ed.). Newark: John Wiley & Sons, Incorporated. p. 2.ISBN 978-1-119-01162-0.Θ (time decay): the price change of an option in relation to time;
  21. ^Mednikarova, Iveta (2001). "The Use of Θ in Latin Funerary Inscriptions".Zeitschrift für Papyrologie und Epigraphik.136:267–276.JSTOR 20190914.
  22. ^Ennius, Quintus (2018). Goldberg, Sander M.;Manuwald, Gesine (eds.).Fragmentary Republican Latin, Volume I: Ennius, Testimonia. Epic Fragments. Cambridge, MA: Harvard University Press. pp. 456–457.
  23. ^abcdBarry, Kieren (1998),The Greek Qabalah: Alphabetic Mysticism and Numerology in the Ancient World,Samuel Weiser, p. 73,ISBN 1-57863-110-6.
  24. ^Kaplan, Robert (2000),The Nothing that Is: A Natural History of Zero, Oxford; New York:Oxford University Press, p. 66,Bibcode:2000tnti.book.....K,ISBN 0-19-514237-3.
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