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Tau

From Wikipedia, the free encyclopedia
Nineteenth letter in the Greek alphabet
This article is about the letter of the Greek alphabet. For the mathematical constant, seeTau (mathematical constant). For other uses, seeTau (disambiguation).
Not to be confused withTao or the Latin letterT.
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

Tau (/ˈt,ˈtɔː,ˈtɒ/ ;[1] uppercaseΤ, lowercaseτ orτ;Greek:ταυ[taf]) is the nineteenth letter of theGreek alphabet, representing thevoiceless dental or alveolar plosiveIPA:[t]. In the system ofGreek numerals, it has a value of 300.

The name in English is pronounced/t/ or/tɔː/,[2] but inGreek it is[taf].[3][4] This is because the pronunciation of the combination of Greek letters αυ can have the pronunciation of either[ai],[av] or[af], depending on what follows and if adiaeresis is present on the second vowel (seeGreek orthography).

Tau was derived from thePhoenician lettertaw (𐤕).[5] Letters that arose from tau include RomanT and CyrillicTe (Т, т).

Modern usage

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See also:Greek letters used in mathematics, science, and engineering § Ττ (tau)

The lower-case letter τ is used as a symbol for:

Biology

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Mathematics

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Physics

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Symbolism

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  • In ancient times, tau was used as a symbol forlife orresurrection, whereas the eighth letter of the Greek alphabet,theta, was considered the symbol ofdeath.[citation needed]
  • In Biblical times, thetaw was put on men to distinguish those who lamented sin, although newer versions of the Bible have replaced the ancient termtaw withmark (Ezekiel 9:4) orsignature (Job 31:35). Its original sound value is avoiceless alveolar plosive, IPA /t/[citation needed]
  • The symbolism of thecross was connected not only to the letterchi but also to tau, the equivalent of the last letter in thePhoenician and Old Hebrew alphabets, and which was originally cruciform in shape; seeCross of Tau.[citation needed]
  • An essay written around 160 AD, attributed toLucian, a mock legal prosecution calledThe Consonants at Law - Sigma vs. Tau, in the Court of the Seven Vowels, contains a reference to the cross attribution.Sigma petitions the court to sentence Tau to death by crucifixion, saying:
    Men weep, and bewail their lot, and curse Cadmus with many curses for introducingTau into the family of letters; they say it was his body that tyrants took for a model, his shape that they imitated, when they set up structures on which men are crucified.Stauros (cross) the vile engine is called, and it derives its vile name from him. Now, with all these crimes upon him, does he not deserve death, nay, many deaths? For my part I know none bad enough but that supplied by his own shape — that shape which he gave to thegibbet namedstauros after him by men
  • Tau is usually considered as the symbol ofFranciscan orders due toSt. Francis' love for it, symbol of the redemption and of theCross. Almost all Franciscan churches have painted a tau with two crossing arms, both withstigmata, the one of Jesus and the other of Francis; members of theSecular Franciscan Order usually wear a wooden τ in a string with three knots around the neck
  • The title and symbol of "Tau" is used byneo-Gnostic bishops as it has some symbolism in many of the modern branches of Gnosticism.
  • For the unofficial astronomical symbol ofSaturn’s moon ofTitan, a ringed tau is connected to the crook of Saturn.

Unicode

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For the Greek and Coptic letter tau:[25]

  • U+03A4 ΤGREEK CAPITAL LETTER TAU (Τ)
  • U+03C4 τGREEK SMALL LETTER TAU (τ)
  • U+2CA6 COPTIC CAPITAL LETTER TAU
  • U+2CA7 COPTIC SMALL LETTER TAU
  • U+1D6BB 𝚻MATHEMATICAL BOLD CAPITAL TAU[a]
  • U+1D6D5 𝛕MATHEMATICAL BOLD SMALL TAU
  • U+1D6F5 𝛵MATHEMATICAL ITALIC CAPITAL TAU
  • U+1D70F 𝜏MATHEMATICAL ITALIC SMALL TAU
  • U+1D72F 𝜯MATHEMATICAL BOLD ITALIC CAPITAL TAU
  • U+1D749 𝝉MATHEMATICAL BOLD ITALIC SMALL TAU
  • U+1D769 𝝩MATHEMATICAL SANS-SERIF BOLD CAPITAL TAU
  • U+1D783 𝞃MATHEMATICAL SANS-SERIF BOLD SMALL TAU
  • U+1D7A3 𝞣MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL TAU
  • U+1D7BD 𝞽MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL TAU
  1. ^TheMATHEMATICAL characters are used only in math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

See also

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Notes

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  1. ^abcThe date given on the source is after that of the archive. This is because the original publishing date is unknown, so the latest update date is stated instead.
  2. ^The archived version of this source may take a few minutes to render theTeX math codes properly.

References

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Look upΤ orτ in Wiktionary, the free dictionary.
  1. ^"tau".Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription orparticipating institution membership required.)
    "tau".Dictionary.com Unabridged (Online). n.d.
  2. ^"Oxford Dictionaries Online". Oxford University Press. Archived fromthe original on July 20, 2012.
  3. ^Gaifyllia, Nancy (10 Oct 2016)."The Greek Alphabet".The Spruce.Archived from the original on 28 Oct 2017. Retrieved28 Oct 2017.
  4. ^UNGEGN Working Group on Romanization Systems (1 Mar 2016)."UN Romanization of Greek for Geographical Names (1987)".Institute of the Estonian Language.Archived from the original on 18 Oct 2017. Retrieved28 Oct 2017.
  5. ^Panse, Sonal (1 May 2012). Finn, Wendy (ed.)."The Greek Alphabet: Where did It Come From & How Did It Become Modern Greek?".Bright Hub Education.Archived from the original on 22 Dec 2016. Retrieved28 Oct 2017.
  6. ^McPeak, John (10 Jun 2010)."McPeak, Lecture 4".Syracuse University.Archived from the original on 10 Jun 2010. Retrieved27 Oct 2017.
  7. ^MJ, Shelton; MB, Wire; Y, Lou; B, Adamkiewicz; SS, Min (Mar 2016)."Pharmacokinetic and safety evaluation of high-dose combinations of fosamprenavir and ritonavir".Antimicrobial Agents and Chemotherapy.50 (3):928–934.doi:10.1128/AAC.50.3.928-934.2006.PMC 1426463.PMID 16495253.
  8. ^C, González; G, Farías; RB, Maccioni (1 Nov 1998). "Modification of tau to an Alzheimer's type protein interferes with its interaction with microtubules".Cell Mol Biol (Noisy-le-grand).44 (7):1117–1127.PMID 9846894 – via EuropeMC.
  9. ^M, Sjögren; E, Englund (2004). "Negative neurofilament light and tau immunostaining in frontotemporal dementia".Dementia and Geriatric Cognitive Disorders.17 (4):346–349.doi:10.1159/000077169.PMID 15178951.S2CID 9306507.
  10. ^Weisstein, Eric W. (27 Oct 2017)."Divisor Function".mathworld.wolfram.com.Archived from the original on 29 Jun 2017. Retrieved28 Oct 2017.
  11. ^Weisstein, Eric W."Tau Function".mathworld.wolfram.com. Retrieved2025-01-31.A functionτ(n) related to the divisor functionσ(n), also sometimes called Ramanujan's tau function.
  12. ^"DLMF: §27.14 Unrestricted Partitions ‣ Additive Number Theory ‣ Chapter 27 Functions of Number Theory".dlmf.nist.gov. Retrieved2025-01-31.
  13. ^Weisstein, Eric W. (27 Oct 2017)."Golden Ratio".mathworld.wolfram.com.Archived from the original on 22 Aug 2017. Retrieved28 Oct 2017.
  14. ^Ghent, A. W. (June 1963)."Kendall's "Tau" Coefficient as an Index of Similarity in Comparisons of Plant or Animal Communities".The Canadian Entomologist.95 (6):568–575.Bibcode:1963CaEnt..95..568G.doi:10.4039/ent95568-6.S2CID 84897435 – via Cambridge University Press.
  15. ^Lowther, George (23 Nov 2009)."Sigma Algebras at a Stopping Time".Almost Sure at Wordpress.Archived from the original on 21 Dec 2016. Retrieved28 Oct 2017.
  16. ^Hartl, Michael (28 Jun 2010)."The Tau Manifesto".Tau Day.Archived from the original on 7 Oct 2017. Retrieved28 Oct 2017.
  17. ^Bartholomew, Randyn Charles (June 25, 2014)."Let's Use Tau–It's Easier Than Pi".Scientific American.Archived from the original on September 8, 2017. Retrieved2020-08-31.
  18. ^Weisstein, Eric W."Torsion".Wolfram MathWorld.Archived from the original on 29 Aug 2017. Retrieved28 Oct 2017.
  19. ^Weisstein, Eric W."Thue-Morse Sequence".mathworld.wolfram.com. Retrieved2025-01-31.The Thue–Morse sequence, also called the Morse–Thue sequence or Prouhet–Thue–Morse sequence (Allouche and Cosnard 2000), is one of a number of related sequences of numbers obtained from the parities of the counts of 1's in the binary representation of the nonnegative integers.
  20. ^Elert, Glenn (2023),"Special Symbols",The Physics Hypertextbook, hypertextbook, retrieved2025-02-01,τ shear stress
  21. ^Braslavsky, S. E. (2007-01-01)."Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)".Pure and Applied Chemistry.79 (3): 448.doi:10.1351/pac200779030293.ISSN 1365-3075.S2CID 96601716.lifetime τ
  22. ^Elert, Glenn (2023),"Special Symbols",The Physics Hypertextbook, hypertextbook, retrieved2025-02-01,τ time constant
  23. ^Weisstein, Eric W."Tau".mathworld.wolfram.com. Retrieved2025-02-01.The symbol also has a number of other different meanings in physics, for example the tau particle, tau neutrino, as a symbol for torque, etc.
  24. ^Elert, Glenn (2023),"Special Symbols",The Physics Hypertextbook, hypertextbook, retrieved2025-02-01,τ,τ torque
  25. ^Unicode: "Greek and Coptic (Range: 0370-03FF)".
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