Theta

From Wikipedia, the free encyclopedia

Template:Short description Template:Hatnote group

Page Module:Message box/ambox.css has no content.

Lua error in package.lua at line 80: module 'Module:Sidebar/configuration' not found.

Theta[a] (uppercase Θ or ϴ; lowercase θ; cursive ϑ) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth 𐤈. In the system of Greek numerals, it has a value of 9.

Greek

In Ancient Greek, θ originally represented the aspirated voiceless dental plosive Script error: No such module "IPA"., but it later became a voiceless dental fricative Script error: No such module "IPA"., which is the value it retains in Modern Greek.

Forms

File:Theta uc lc with variant.svg
Modern print theta, in a typical uppercase and two different lowercase glyph forms.

In its archaic form, θ was written as a cross within a circle (as in the Etruscan A symbol of a cross within a circle or Another symbol of a cross within a circle), and later, as a line or point in circle (The symbol of a line within a circle or The 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 symbol Page Template:Mono/styles.css has no content.U+03D1 ϑ Script error: No such module "Unicode data". was introduced, which always displays the open-loop form. There is also Page Template:Mono/styles.css has no content.U+03F4 ϴ Script error: No such module "Unicode data"., 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

Script error: No such module "labelled list hatnote".

File:Tau gallic CourDOr Metz 3147.jpg
The name ARAÐÐOVNA on a Gaulish tombstone

In the Latin script used for the Gaulish language, theta inspired the tau gallicum (Ꟈ ꟈ). The phonetic value of the tau gallicum is thought to have been Script error: No such module "IPA"..[1] In addition, multiple modern languages written in Latin script use Latin theta.

Cyrillic

The early Cyrillic letter fita (Ѳ, ѳ) developed from θ. This letter existed in the Russian alphabet until the 1918 Russian orthography reform.

International Phonetic Alphabet

In the International Phonetic Alphabet (IPA), Script error: No such module "IPA". represents the voiceless dental fricative, as in thigh (/θaɪ/), thick (/θɪk/), enthuse (/ˈɛnθjuːz/), thing (/θɪŋ/), think (/θɪŋk/), thin (/θɪn/), thang (/θæŋ/), myth (/mɪθ/), smith (/smɪθ/), youth (/juːθ/), bath (/bæθ/), math (/mæθ/), birth (/bɜːrθ/), fourth (/fɔːrθ/), death (/dɛθ/), or health (/hɛlθ/).[2] It does not represent the consonant in the, which is the voiced dental fricative counterpart, represented in the IPA by Script error: No such module "IPA". (cf. Eth). A similar-looking lower-case symbol, Script error: No such module "IPA"., which is called barred o, is the IPA symbol for the close-mid central rounded vowel.

Mathematics and science

Lower case

The lowercase letter θ is used as a symbol for:

Upper case

The uppercase letter Θ is used as a symbol for:

Symbolism

File:Retiarius vs secutor from Borghese mosaic.jpg
θ (θάνατος, death) in a mosaic

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

According to Porphyry of Tyros, the Egyptians used an X within a circle as a symbol of the soul; having a value of nine, it was used as a symbol for Ennead. Johannes Lydus says that the Egyptians used a symbol for Kosmos in the form of theta, with a fiery circle representing the world, and a snake spanning the middle representing Agathos Daimon (literally: good spirit).[23]

Abbreviation

Script error: No such module "Labelled list hatnote". In classical Athens, it was used as an abbreviation for the Greek θάνατος (Thanatos, "death") and as it vaguely resembles a human skull,[23] theta was used as a warning symbol of death, in the same way that skull and crossbones are used in modern times.[23] It survives on potsherds used by Athenians when voting for the death 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 a euphemism where a Θ (9) would otherwise be expected.

Unicode

See also

Page Module:Side box/styles.css has no content.Page Template:Sister project/styles.css has no content.

Page Template:Plainlist/styles.css has no content.
Script error: No such module "Sister project logo".
Look up Θ or θ in Wiktionary, the free dictionary.

Notes and references

Notes

Page Template:Reflist/styles.css has no content.

  1. ^
    1. REDIRECT Template:Unbulleted list citebundle
    Template:Redirect category shell
  2. ^ The Page Template:Smallcaps/styles.css has no content.mathematical characters are used only in math. Stylized Greek text should be encoded using normal Greek letters, with markup and formatting to indicate text style.[citation needed]

Template:NoteFoot

References

Page Template:Reflist/styles.css has no content.

  1. ^ Page Module:Citation/CS1/styles.css has no content.Everson, Michael; Lilley, Chris (2019-05-26). "L2/19-179: Proposal for the addition of four Latin characters for Gaulish" (PDF).
  2. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ Page Module:Citation/CS1/styles.css has no content.Weisstein, Eric W. "Angle". mathworld.wolfram.com. Retrieved 2025-02-01.
  4. ^ Page Module:Citation/CS1/styles.css has no content.Elert, Glenn (2023), "Special Symbols", The Physics Hypertextbook, hypertextbook, retrieved 2025-02-01, ϴ,φ,ϴ,φ angle, angular displacement, angular separation, rotation angle
  5. ^ Page Module:Citation/CS1/styles.css has no content.Weisstein, Eric W. "Chebyshev Functions". mathworld.wolfram.com. Retrieved 2025-01-24.
  6. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ Page Module:Citation/CS1/styles.css has no content.Hösel, Volker (2020). Mathematical population genetics and evolution of bacterial cooperation. New Jersey: World Scientific. p. 75. ISBN 978-981-12-0549-1.
  12. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ Page Module:Citation/CS1/styles.css has no content.Weisstein, Eric W. "Heaviside Step Function". mathworld.wolfram.com. Retrieved 2025-01-24.
  16. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ Page Module:Citation/CS1/styles.css has no content."DLMF: Chapter 20 Theta Functions". dlmf.nist.gov. Retrieved 2025-01-31.
  19. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ Page Module:Citation/CS1/styles.css has no content.Mednikarova, Iveta (2001). "The Use of Θ in Latin Funerary Inscriptions". Zeitschrift für Papyrologie und Epigraphik. 136: 267–276. JSTOR 20190914.
  22. ^ Page Module:Citation/CS1/styles.css has no content.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. ^ a b c d Page Module:Citation/CS1/styles.css has no content.Barry, Kieren (1998), The Greek Qabalah: Alphabetic Mysticism and Numerology in the Ancient World, Samuel Weiser, p. 73, ISBN 1-57863-110-6.
  24. ^ Page Module:Citation/CS1/styles.css has no content.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.
Retrieved from "https://cosmopedia.co/index.php?title=Theta&oldid=120107"