Tau

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Tau /ˈtɔː, ˈt/[1] (uppercase Τ, lowercase τ; Greek: ταυ [taf]) is the 19th letter of the Greek alphabet. In the system of Greek numerals it has a value of 300.

The name in English is pronounced /t/ or /tɔː/,[2] but in modern Greek it is [taf].[3][4] This is because the pronunciation of the combination of Greek letters αυ has changed from ancient to modern times from one of [au] to either [av] or [af], depending on what follows (see Greek orthography).

Tau was derived from the Phoenician letter taw Phoenician taw.svg (𐤕).[5] Letters that arose from tau include Roman T and Cyrillic Te (Т, т).

The letter occupies the Unicode slots U+03C4 (lowercase) and U+03A4 (uppercase). In HTML, they can be produced with named entities (τ and Τ), decimal references (τ and Τ), or hexadecimal references (τ and Τ).

Modern usage[edit]

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

Biology[edit]

Mathematics[edit]

Physics[edit]

Symbolism[edit]

  • In ancient times, tau was used as a symbol for life or resurrection, whereas the eighth letter of the Greek alphabet, theta, was considered the symbol of death.
  • In Biblical times, the taw was put on men to distinguish those who lamented sin, although newer versions of the Bible have replaced the ancient term taw with mark (Ezekiel 9:4) or signature (Job 31:35). Its original sound value is a voiceless alveolar plosive, IPA /t/
  • The symbolism of the cross was connected not only to the letter chi but also to tau, the equivalent of the last letter in the Phoenician and Old Hebrew alphabets, and which was originally cruciform in shape; see Cross of Tau
  • An essay written around 160 AD, attributed to Lucian, a mock legal prosecution called The 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 introducing Tau 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 the gibbet named stauros after him by men
  • Tau is usually considered as the symbol of Franciscan orders due to St. Francis' love for it, symbol of the redemption and of the Cross. Almost all Franciscan churches have painted a tau with two crossing arms, both with stigmata, the one of Jesus and the other of Francis; usually members of the Secular Franciscan Order wear a wooden τ in a string with three knots around the neck

Character encodings[edit]

For the Greek and Coptic letter tau:[17]

Character Τ τ
Unicode name GREEK CAPITAL LETTER TAU GREEK SMALL LETTER TAU COPTIC CAPITAL LETTER TAU COPTIC SMALL LETTER TAU
Encodings decimal hex decimal hex decimal hex decimal hex
Unicode 932 U+03A4 964 U+03C4 11430 U+2CA6 11431 U+2CA7
UTF-8 206 164 CE A4 207 132 CF 84 226 178 166 E2 B2 A6 226 178 167 E2 B2 A7
Numeric character reference Τ Τ τ τ Ⲧ Ⲧ ⲧ ⲧ
Named character reference Τ τ
DOS Greek 147 93 171 AB
DOS Greek-2 208 D0 238 EE
Windows 1253 212 D4 244 F4
TeX \tau

For the mathematical letter tau:[18][19][20][21][22][23][24][25][26][27]

Character 𝚻 𝛕 𝛵 𝜏 𝜯 𝝉
Unicode name MATHEMATICAL BOLD
CAPITAL TAU
MATHEMATICAL BOLD
SMALL TAU
MATHEMATICAL ITALIC
CAPITAL TAU
MATHEMATICAL ITALIC
SMALL TAU
MATHEMATICAL BOLD ITALIC
CAPITAL TAU
MATHEMATICAL BOLD ITALIC
SMALL TAU
Encodings decimal hex decimal hex decimal hex decimal hex decimal hex decimal hex
Unicode 120507 U+1D6BB 120533 U+1D6D5 120565 U+1D6F5 120591 U+1D70F 120623 U+1D72F 120649 U+1D749
UTF-8 240 157 154 187 F0 9D 9A BB 240 157 155 149 F0 9D 9B 95 240 157 155 181 F0 9D 9B B5 240 157 156 143 F0 9D 9C 8F 240 157 156 175 F0 9D 9C AF 240 157 157 137 F0 9D 9D 89
UTF-16 55349 57019 D835 DEBB 55349 57045 D835 DED5 55349 57077 D835 DEF5 55349 57103 D835 DF0F 55349 57135 D835 DF2F 55349 57161 D835 DF49
Numeric character reference 𝚻 𝚻 𝛕 𝛕 𝛵 𝛵 𝜏 𝜏 𝜯 𝜯 𝝉 𝝉
Character 𝝩 𝞃 𝞣 𝞽
Unicode name MATHEMATICAL SANS-SERIF
BOLD CAPITAL TAU
MATHEMATICAL SANS-SERIF
BOLD SMALL TAU
MATHEMATICAL SANS-SERIF
BOLD ITALIC CAPITAL TAU
MATHEMATICAL SANS-SERIF
BOLD ITALIC SMALL TAU
Encodings decimal hex decimal hex decimal hex decimal hex
Unicode 120681 U+1D769 120707 U+1D783 120739 U+1D7A3 120765 U+1D7BD
UTF-8 240 157 157 169 F0 9D 9D A9 240 157 158 131 F0 9D 9E 83 240 157 158 163 F0 9D 9E A3 240 157 158 189 F0 9D 9E BD
UTF-16 55349 57193 D835 DF69 55349 57219 D835 DF83 55349 57251 D835 DFA3 55349 57277 D835 DFBD
Numeric character reference 𝝩 𝝩 𝞃 𝞃 𝞣 𝞣 𝞽 𝞽

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.

Notes[edit]

  1. ^ a b c The 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 the TeX math codes properly.

References[edit]

  1. ^ "tau". Oxford English Dictionary (3rd ed.). Oxford University Press. September 2005. (Subscription or UK public library membership required.)
    "tau". Dictionary.com Unabridged. Random House.
  2. ^ "Oxford Dictionaries Online". Oxford University Press.
  3. ^ Gaifyllia, Nancy (10 Oct 2016). "The Greek Alphabet". The Spruce. Archived from the original on 28 Oct 2017. Retrieved 28 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. Retrieved 28 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. Retrieved 28 Oct 2017.
  6. ^ McPeak, John (10 Jun 2010). "McPeak, Lecture 4". Syracuse University. Archived from the original on 10 Jun 2010. Retrieved 27 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.
  10. ^ Weisstein, Eric W. (27 Oct 2017). "Divisor Function". MathWorld --A Wolfram Web Resource. Archived from the original on 29 Jun 2017. Retrieved 28 Oct 2017.
  11. ^ Weisstein, Eric W. (27 Oct 2017). "Golden Ratio". Mathworld -- A Wolfram Web Resource. Archived from the original on 22 Aug 2017. Retrieved 28 Oct 2017.
  12. ^ 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. doi:10.4039/ent95568-6 – via Cambridge University Press.
  13. ^ Lowther, George (23 Nov 2009). "Sigma Algebras at a Stopping Time". Almost Sure at Wordpress. Archived from the original on 21 Dec 2016. Retrieved 28 Oct 2017.
  14. ^ Bartholomew, Randyn (25 Jun 2014). "Why Tau Trumps Pi". Scientific American. Archived from the original on 8 Sep 2017. Retrieved 28 Oct 2017.
  15. ^ Hartl, Michael (28 Jun 2010). "The Tau Manifesto". Tau Day. Archived from the original on 7 Oct 2017. Retrieved 28 Oct 2017.
  16. ^ Weisstein, Eric W. (27 Oct 2017). "Torsion -- From Wolfram MathWorld - a Wolfram Web Resource". Wolfram MathWorld. Archived from the original on 29 Aug 2017. Retrieved 28 Oct 2017.
  17. ^ Unicode code charts: Greek and Coptic (Range: 0370-03FF)
  18. ^ "Unicode Character 'MATHEMATICAL BOLD CAPITAL TAU' (U+1D6BB)". www.fileformat.info. Retrieved 2017-10-28.
  19. ^ "Unicode Character 'MATHEMATICAL BOLD SMALL TAU' (U+1D6D5)". www.fileformat.info. Retrieved 2017-10-28.
  20. ^ "Unicode Character 'MATHEMATICAL ITALIC CAPITAL TAU' (U+1D6F5)". www.fileformat.info. Retrieved 2017-10-28.
  21. ^ "Unicode Character 'MATHEMATICAL ITALIC SMALL TAU' (U+1D70F)". www.fileformat.info. Retrieved 2017-10-28.
  22. ^ "Unicode Character 'MATHEMATICAL BOLD ITALIC CAPITAL TAU' (U+1D72F)". www.fileformat.info. Retrieved 2017-10-28.
  23. ^ "Unicode Character 'MATHEMATICAL BOLD ITALIC SMALL TAU' (U+1D749)". www.fileformat.info. Retrieved 2017-10-28.
  24. ^ "Unicode Character 'MATHEMATICAL SANS-SERIF BOLD CAPITAL TAU' (U+1D769)". www.fileformat.info. Retrieved 2017-10-28.
  25. ^ "Unicode Character 'MATHEMATICAL SANS-SERIF BOLD SMALL TAU' (U+1D783)". www.fileformat.info. Retrieved 2017-10-28.
  26. ^ "Unicode Character 'MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL TAU' (U+1D7A3)". www.fileformat.info. Retrieved 2017-10-28.
  27. ^ "Unicode Character 'MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL TAU' (U+1D7BD)". www.fileformat.info. Retrieved 2017-10-28.