Biology:Theta

Short description: Eighth letter of the Greek alphabet

Theta (UK: /ˈθiːtə/, US: /ˈθeɪtə/; uppercase: Θ or ; lowercase: θ^{[note 1]} or ϑ} θῆτα thē̂ta [tʰɛ̂ːta]; Modern: θήτα thī́ta [ˈθita]) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth . In the system of Greek numerals, it has a value of 9.

Greek

The alphabet on a black figure vessel, with a point-and-circle theta

In Ancient Greek, θ represented the aspirated voiceless dental plosive IPA: [t̪ʰ], but in Modern Greek it represents the voiceless dental fricative IPA: [θ].

Forms

In its archaic form, θ was written as a cross within a circle (as in the Etruscan or 16px|Another symbol of a cross within a circle), and later, as a line or point in circle (16px|The symbol of a line within a circle or ).

The cursive form was retained by Unicode as U+03D1 ϑ GREEK THETA SYMBOL, separate from U+03B8 θ GREEK SMALL LETTER THETA. (There is also U+03F4 ϴ GREEK CAPITAL THETA SYMBOL). For the purpose of writing Greek text, the two can be font variants of a single character, but {{not a typo|θ as distinct symbols in technical and mathematical contexts. Extensive lists of examples follow below at Mathematics and Science. U+03D1 ϑ GREEK THETA SYMBOL (script theta) is also common in biblical and theological usage e.g. πρόϑεσις instead of π in public or laying out a corpse).

Latin

The name ARAÐÐOVNA on a Gaulish tombstone

In Latin script used for the Gaulish language, theta inspired the tau gallicum (). The phonetic value of the tau gallicum is thought to have been [t͡s].^[1] Theta itself is used alongside Latin letters in Halkomelem, an indigenous North American language.

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), [θ] represents the voiceless dental fricative, as in thick or thin. It does not represent the consonant in the, which is the voiced dental fricative, represented in the IPA by [ð] (cf. Eth). A similar-looking lower-case symbol, [ɵ], 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:

A plane angle in geometry
An unknown variable in trigonometry
The voiceless dental fricative, spelled θ
A special function of several complex variables
One of the Chebyshev functions in prime number theory
The potential temperature in meteorology
The score of a test taker in item response theory
Theta Type Replication: a type of bacterial DNA replication specific to circular chromosomes
Threshold value of an artificial neuron
A Bayer designation letter applied to a star in a constellation; usually the eighth star so labelled but not necessarily the eighth-brightest as viewed from Earth
The statistical parameter frequently used in writing the likelihood function
The Watterson estimator for the population mutation rate in population genetics
Indicates a minimum optimum integration level determined by the intersection of GG and LL schedules (The GG-LL schedules are tools used in analyzing the potential benefits of a country pegging their domestic currency to a foreign currency.)
The reserve ratio of banks in economic models
The ordinal collapsing function developed by Solomon Feferman^[2]
Heaviside step function
In pharmacology, the fraction of ligand bound to a macromolecule based on the Hill Equation

Upper case

The uppercase letter Θ is used as a symbol for:

Dimension of temperature, by SI standard (in italics)
Dimensionless temperature in transport phenomena
An asymptotically tight bound in the analysis of algorithms (big O notation)
A certain ordinal number in set theory
Pentaquarks, exotic baryons in particle physics
A brain signal frequency (beta, alpha, theta, delta) ranging from 4–8 Hz
One of the variables known as "Greeks" in finance, representing time decay of options or the change in the intrinsic value of an option divided by the number of days until the option expires
A variable indicating temperature difference in heat transfer
Measuring the angle of incident X-ray beam during XRD

Symbolism

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.^[3] A quotation attributed to the ancient Roman author Ennius (though possibly spuriously) said of it: "oh, theta, a letter much unluckier than the others".^[4]

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).^[5]

Abbreviation

In classical Athens, it was used as an abbreviation for the Greek θάνατος (Thanatos, "death") and as it vaguely resembles a human skull,^[5] theta was used as a warning symbol of death, in the same way that skull and crossbones are used in modern times.^[5] It survives on potsherds used by Athenians when voting for the death penalty.^[5] 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.^[6] 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.

Greek Life

The names of many American fraternities and sororities are named with Greek letters, including Theta.

Character encodings

Greek Theta

Character information
Preview	Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar
Unicode name	GREEK CAPITAL LETTER THETA		GREEK SMALL LETTER THETA		GREEK THETA SYMBOL		GREEK CAPITAL THETA SYMBOL		MODIFIER LETTER SMALL THETA
Encodings	decimal	hex	decimal	hex	decimal	hex	decimal	hex	decimal	hex
Unicode	920 0 0 0	U+0398	952 0 0 0	U+03B8	977 0 0 0	U+03D1	1012 0 0 0	U+03F4	7615 0 0 0	U+1DBF
UTF-8	206 152 0 0 0	CE 98 00 00 00	206 184 0 0 0	CE B8 00 00 00	207 145 0 0 0	CF 91 00 00 00	207 180 0 0 0	CF B4 00 00 00	225 182 191 0 0 0	E1 B6 BF 00 00 00
Numeric character reference	Θ	Θ	θ	θ	ϑ	ϑ	ϴ	ϴ	ᶿ	ᶿ
Named character reference	Θ		θ		&thetasym;
DOS Greek	135	87	159	9F
DOS Greek-2	172	AC	226	E2
Windows 1253	200	C8	232	E8
TeX	\Theta		\theta		\vartheta

Coptic Thethe

Character information
Preview	Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar
Unicode name	COPTIC CAPITAL LETTER THETHE		COPTIC SMALL LETTER THETHE
Encodings	decimal	hex	decimal	hex
Unicode	11408 0 0 0	U+2C90	11409 0 0 0	U+2C91
UTF-8	226 178 144 0 0 0	E2 B2 90 00 00 00	226 178 145 0 0 0	E2 B2 91 00 00 00
Numeric character reference	Ⲑ	Ⲑ	ⲑ	ⲑ

Cyrillic Fita

Character information
Preview	Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar
Unicode name	CYRILLIC CAPITAL LETTER FITA		CYRILLIC SMALL LETTER FITA
Encodings	decimal	hex	decimal	hex
Unicode	1138 0 0 0	U+0472	1139 0 0 0	U+0473
UTF-8	209 178 0 0 0	D1 B2 00 00 00	209 179 0 0 0	D1 B3 00 00 00
Numeric character reference	Ѳ	Ѳ	ѳ	ѳ

Mathematical Theta

Character information
Preview	Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar
Unicode name	MATHEMATICAL BOLD CAPITAL THETA		MATHEMATICAL BOLD SMALL THETA		MATHEMATICAL BOLD CAPITAL THETA SYMBOL		MATHEMATICAL BOLD THETA SYMBOL
Encodings	decimal	hex	decimal	hex	decimal	hex	decimal	hex
Unicode	120495 0 0 0	U+1D6AF	120521 0 0 0	U+1D6C9	120505 0 0 0	U+1D6B9	120541 0 0 0	U+1D6DD
UTF-8	0 157 154 175 0 0 0	Template:UTF-8/4 9D 9A AF 00 00 00	0 157 155 137 0 0 0	Template:UTF-8/4 9D 9B 89 00 00 00	0 157 154 185 0 0 0	Template:UTF-8/4 9D 9A B9 00 00 00	0 157 155 157 0 0 0	Template:UTF-8/4 9D 9B 9D 00 00 00
UTF-16	55349 57007 0 0 0	D835 DEAF 0000 0000 0000	55349 57033 0 0 0	D835 DEC9 0000 0000 0000	55349 57017 0 0 0	D835 DEB9 0000 0000 0000	55349 57053 0 0 0	D835 DEDD 0000 0000 0000
Numeric character reference	𝚯	𝚯	𝛉	𝛉	𝚹	𝚹	𝛝	𝛝

Character information
Preview	Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar
Unicode name	MATHEMATICAL ITALIC CAPITAL THETA		MATHEMATICAL ITALIC SMALL THETA		MATHEMATICAL ITALIC CAPITAL THETA SYMBOL		MATHEMATICAL ITALIC THETA SYMBOL
Encodings	decimal	hex	decimal	hex	decimal	hex	decimal	hex
Unicode	120553 0 0 0	U+1D6E9	120579 0 0 0	U+1D703	120563 0 0 0	U+1D6F3	120599 0 0 0	U+1D717
UTF-8	0 157 155 169 0 0 0	Template:UTF-8/4 9D 9B A9 00 00 00	0 157 156 131 0 0 0	Template:UTF-8/4 9D 9C 83 00 00 00	0 157 155 179 0 0 0	Template:UTF-8/4 9D 9B B3 00 00 00	0 157 156 151 0 0 0	Template:UTF-8/4 9D 9C 97 00 00 00
UTF-16	55349 57065 0 0 0	D835 DEE9 0000 0000 0000	55349 57091 0 0 0	D835 DF03 0000 0000 0000	55349 57075 0 0 0	D835 DEF3 0000 0000 0000	55349 57111 0 0 0	D835 DF17 0000 0000 0000
Numeric character reference	𝛩	𝛩	𝜃	𝜃	𝛳	𝛳	𝜗	𝜗

Character information
Preview	Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar
Unicode name	MATHEMATICAL BOLD ITALIC CAPITAL THETA		MATHEMATICAL BOLD ITALIC SMALL THETA		MATHEMATICAL BOLD ITALIC CAPITAL THETA SYMBOL		MATHEMATICAL BOLD ITALIC CAPITAL THETA SYMBOL
Encodings	decimal	hex	decimal	hex	decimal	hex	decimal	hex
Unicode	120611 0 0 0	U+1D723	120637 0 0 0	U+1D73D	120621 0 0 0	U+1D72D	120657 0 0 0	U+1D751
UTF-8	0 157 156 163 0 0 0	Template:UTF-8/4 9D 9C A3 00 00 00	0 157 156 189 0 0 0	Template:UTF-8/4 9D 9C BD 00 00 00	0 157 156 173 0 0 0	Template:UTF-8/4 9D 9C AD 00 00 00	0 157 157 145 0 0 0	Template:UTF-8/4 9D 9D 91 00 00 00
UTF-16	55349 57123 0 0 0	D835 DF23 0000 0000 0000	55349 57149 0 0 0	D835 DF3D 0000 0000 0000	55349 57133 0 0 0	D835 DF2D 0000 0000 0000	55349 57169 0 0 0	D835 DF51 0000 0000 0000
Numeric character reference	𝜣	𝜣	𝜽	𝜽	𝜭	𝜭	𝝑	𝝑

Character information
Preview	Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar
Unicode name	MATHEMATICAL SANS-SERIF BOLD CAPITAL THETA		MATHEMATICAL SANS-SERIF BOLD SMALL THETA		MATHEMATICAL SANS-SERIF BOLD CAPITAL THETA SYMBOL		MATHEMATICAL SANS-SERIF BOLD THETA SYMBOL
Encodings	decimal	hex	decimal	hex	decimal	hex	decimal	hex
Unicode	120669 0 0 0	U+1D75D	120695 0 0 0	U+1D777	120505 0 0 0	U+1D6B9	120715 0 0 0	U+1D78B
UTF-8	0 157 157 157 0 0 0	Template:UTF-8/4 9D 9D 9D 00 00 00	0 157 157 183 0 0 0	Template:UTF-8/4 9D 9D B7 00 00 00	0 157 154 185 0 0 0	Template:UTF-8/4 9D 9A B9 00 00 00	0 157 158 139 0 0 0	Template:UTF-8/4 9D 9E 8B 00 00 00
UTF-16	55349 57181 0 0 0	D835 DF5D 0000 0000 0000	55349 57207 0 0 0	D835 DF77 0000 0000 0000	55349 57017 0 0 0	D835 DEB9 0000 0000 0000	55349 57227 0 0 0	D835 DF8B 0000 0000 0000
Numeric character reference	𝝝	𝝝	𝝷	𝝷	𝚹	𝚹	𝞋	𝞋

Character information
Preview	Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar		Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar Template:Charmap/showchar
Unicode name	MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL THETA		MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL THETA		MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL THETA SYMBOL		MATHEMATICAL SANS-SERIF BOLD ITALIC THETA SYMBOL
Encodings	decimal	hex	decimal	hex	decimal	hex	decimal	hex
Unicode	120727 0 0 0	U+1D797	120753 0 0 0	U+1D7B1	120621 0 0 0	U+1D72D	120773 0 0 0	U+1D7C5
UTF-8	0 157 158 151 0 0 0	Template:UTF-8/4 9D 9E 97 00 00 00	0 157 158 177 0 0 0	Template:UTF-8/4 9D 9E B1 00 00 00	0 157 156 173 0 0 0	Template:UTF-8/4 9D 9C AD 00 00 00	0 157 159 133 0 0 0	Template:UTF-8/4 9D 9F 85 00 00 00
UTF-16	55349 57239 0 0 0	D835 DF97 0000 0000 0000	55349 57265 0 0 0	D835 DFB1 0000 0000 0000	55349 57133 0 0 0	D835 DF2D 0000 0000 0000	55349 57285 0 0 0	D835 DFC5 0000 0000 0000
Numeric character reference	𝞗	𝞗	𝞱	𝞱	𝜭	𝜭	𝟅	𝟅

These characters are used only as mathematical symbols. Stylized Greek text should be encoded using normal Greek letters, with markup and formatting to indicate text style.

Notes and references

Notes

↑ which resembles digit 0 with a horizontal line.

References

↑ Everson, Michael; Lilley, Chris (2019-05-26). "L2/19-179: Proposal for the addition of four Latin characters for Gaulish". https://www.unicode.org/L2/L2019/19179-n5044-tau-gallicum.pdf.
↑ http://math.stanford.edu/~feferman/papers/id-saga.pdf ^{[bare URL PDF]}
↑ Mednikarova, Iveta (2001). "The Use of Θ in Latin Funerary Inscriptions". Zeitschrift für Papyrologie und Epigraphik 136: 267–276.
↑ 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.
↑ ^5.0 ^5.1 ^5.2 ^5.3 Barry, Kieren (1998), The Greek Qabalah: Alphabetic Mysticism and Numerology in the Ancient World, Samuel Weiser, p. 73, ISBN 1-57863-110-6 .
↑ Kaplan, Robert (2000), The Nothing that Is: A Natural History of Zero, Oxford; New York: Oxford University Press, pp. 66, ISBN 0-19-514237-3, Bibcode: 2000tnti.book.....K .

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Original source: https://en.wikipedia.org/wiki/Theta. Read more

[1] which resembles digit 0 with a horizontal line.

[2] Everson, Michael; Lilley, Chris (2019-05-26). "L2/19-179: Proposal for the addition of four Latin characters for Gaulish". https://www.unicode.org/L2/L2019/19179-n5044-tau-gallicum.pdf.

[3] ttp://math.stanford.edu/~feferman/papers/id-saga.pdf ^{[bare URL PDF]}

[Mednik-4] Mednikarova, Iveta (2001). "The Use of Θ in Latin Funerary Inscriptions". Zeitschrift für Papyrologie und Epigraphik 136: 267–276.

[5] 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.

[Barry_1-6] 5.0 ^5.1 ^5.2 ^5.3 Barry, Kieren (1998), The Greek Qabalah: Alphabetic Mysticism and Numerology in the Ancient World, Samuel Weiser, p. 73, ISBN 1-57863-110-6 .

[7] Kaplan, Robert (2000), The Nothing that Is: A Natural History of Zero, Oxford; New York: Oxford University Press, pp. 66, ISBN 0-19-514237-3, Bibcode: 2000tnti.book.....K .

[note 1]

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