Theta
Greek alphabet  



History  
Use in other languages  
Related topics  


Theta (uppercase Θ or Ө, lowercase θ (which resembles digit 0 with horizontal line) or ϑ; Ancient Greek: θῆτα, thē̂ta, ; Modern: θήτα, thī́ta, ; UK , US ) 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.
Contents
Greek
In Ancient Greek, θ represented the aspirated voiceless dental plosive , but in Modern Greek it represents the voiceless dental fricative .
Forms
In its archaic form, θ was written as a cross within a circle ( or ), and later, as a line or point within a circle ( or ).
The form ϑ was retained by Unicode as U+03D1 ϑ "GREEK THETA SYMBOL" ("=script theta"), separate from U+03B8 θ "GREEK SMALL LETTER THETA". For the purpose of writing Greek text, the two can be font variants of a single character, but θ and ϑ are also used as distinct symbols in technical and mathematical contexts.
Latin
In the Latin script used for the Gaulish language, theta developed into the tau gallicum, conventionally transliterated as Ð, although the bar extends across the centre of the letter. The phonetic value of the tau gallicum is thought to have been .
Cyrillic
The early Cyrillic letter fita (Ѳ, ѳ) developed from θ.
International Phonetic Alphabet
In the International Phonetic Alphabet, represents the voiceless dental fricative, as in thick or thin. It does not represent the consonant in the, which is the voiced dental fricative.
Mathematics and science
Lower case
The lowercase letter θ is used as a symbol for:
 A plane angle in geometry.
 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 parameter frequently used in writing the likelihood function (Bayes theorem).
 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 GGLL schedules are a tool 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^{[1]}
Upper case
The uppercase letter Θ is used as a symbol for:
 Symbol (in italics) for quantity or temperature, by SI standard
 Dimensionless temperature in transport phenomena.
 Big O notation. Denoting an asymptotically tight bound in analysis of algorithms.
 Θ (set theory), a certain ordinal number.
 Representing pentaquarks, exotic baryons in particle physics.
 Brain Signal Frequency (Beta, Alpha, Theta, Delta) ranging from 4–8 Hz.
 One of the variables known as "Greeks" in finance, representing the lostvalue rate of an option over time.
 As a variable indicating Temperature difference in Heat Transfer
 The upper case symbol can be used as the "subzero" the Brooklynbased band Type O Negative used as their logo.
In its archaic form
 In its archaic form () theta is used as a symbol for Earth.
Greek mathematics
The common usage of theta in mathematical problems began with the Greeks. They logically chose this Greek symbol since it was the next in their alphabet not yet used and was easily legible when recreating for multiple uses.
Archaic crossed forms of theta are seen in the wheel letters of Linear A, Linear B, and Egyptian hieroglyphics, the mathematical tensor product, exclusive disjunction, and direct sum operators, the identification symbol for the Earth (as already mentioned), and the Celtic cross. The circumpunct, or circled dot, is seen in a wide range of places.
Symbolism
 In ancient times, Tau was used as a symbol for life and/or resurrection, whereas the eighth letter of the Greek alphabet, theta, was considered the symbol of death.
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).^{[2]}
The Egyptians also used the symbol of a point within a circle (, the sun disc) to represent the sun, which might be a possible origin of its use as the Sun's astrological glyph. It is worthwhile to note that θῆτα (theta) has the same numerical value in isopsephy as Ηλιος (Helios): 318.
Abbreviation
In classical Athens, it was used as an abbreviation for the Greek θάνατος (thanatos, “death”) and as it vaguely resembles a human skull, theta was used as a warning symbol of death, in the same way that skull and crossbones are used in modern times. It survives on potsherds used by Athenians when voting for the death penalty.^{[2]} 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.^{[3]} For this reason, use of the number theta 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.
Character Encodings
 Greek Theta
Character  Θ  θ  ϑ  ϴ  ᶿ  

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  U+0398  952  U+03B8  977  U+03D1  1012  U+03F4  7615  U+1DBF 
UTF8  206 152  CE 98  206 184  CE B8  207 145  CF 91  207 180  CF B4  225 182 191  E1 B6 BF 
Numeric character reference  Θ  Θ  θ  θ  ϑ  ϑ  ϴ  ϴ  ᶿ  ᶿ 
Named character reference  Θ  θ  ϑ  
DOS Greek  135  87  159  9F  
DOS Greek2  172  AC  226  E2  
Windows 1253  200  C8  232  E8  
TeX  \Theta  \theta  \vartheta 
 Coptic Thethe
Character  Ⲑ  ⲑ  

Unicode name  COPTIC CAPITAL LETTER THETHE  COPTIC SMALL LETTER THETHE  
Encodings  decimal  hex  decimal  hex 
Unicode  11408  U+2C90  11409  U+2C91 
UTF8  226 178 144  E2 B2 90  226 178 145  E2 B2 91 
Numeric character reference  Ⲑ  Ⲑ  ⲑ  ⲑ 
 Cyrillic Fita
Character  Ѳ  ѳ  

Unicode name  CYRILLIC CAPITAL LETTER FITA  CYRILLIC SMALL LETTER FITA  
Encodings  decimal  hex  decimal  hex 
Unicode  1138  U+0472  1139  U+0473 
UTF8  209 178  D1 B2  209 179  D1 B3 
Numeric character reference  Ѳ  Ѳ  ѳ  ѳ 
 Mathematical Theta
Character  𝚯  𝛉  𝚹  𝛝  

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  U+1D6AF  120521  U+1D6C9  120505  U+1D6B9  120541  U+1D6DD 
UTF8  240 157 154 175  F0 9D 9A AF  240 157 155 137  F0 9D 9B 89  240 157 154 185  F0 9D 9A B9  240 157 155 157  F0 9D 9B 9D 
UTF16  55349 57007  D835 DEAF  55349 57033  D835 DEC9  55349 57017  D835 DEB9  55349 57053  D835 DEDD 
Numeric character reference  𝚯  𝚯  𝛉  𝛉  𝚹  𝚹  𝛝  𝛝 
Character  𝛩  𝜃  𝛳  𝜗  

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  U+1D6E9  120579  U+1D703  120563  U+1D6F3  120599  U+1D717 
UTF8  240 157 155 169  F0 9D 9B A9  240 157 156 131  F0 9D 9C 83  240 157 155 179  F0 9D 9B B3  240 157 156 151  F0 9D 9C 97 
UTF16  55349 57065  D835 DEE9  55349 57091  D835 DF03  55349 57075  D835 DEF3  55349 57111  D835 DF17 
Numeric character reference  𝛩  𝛩  𝜃  𝜃  𝛳  𝛳  𝜗  𝜗 
Character  𝜣  𝜽  𝜭  𝝑  

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  U+1D723  120637  U+1D73D  120621  U+1D72D  120657  U+1D751 
UTF8  240 157 156 163  F0 9D 9C A3  240 157 156 189  F0 9D 9C BD  240 157 156 173  F0 9D 9C AD  240 157 157 145  F0 9D 9D 91 
UTF16  55349 57123  D835 DF23  55349 57149  D835 DF3D  55349 57133  D835 DF2D  55349 57169  D835 DF51 
Numeric character reference  𝜣  𝜣  𝜽  𝜽  𝜭  𝜭  𝝑  𝝑 
Character  𝝝  𝝷  𝝧  𝞋  

Unicode name  MATHEMATICAL SANSSERIF BOLD CAPITAL THETA 
MATHEMATICAL SANSSERIF BOLD SMALL THETA 
MATHEMATICAL SANSSERIF BOLD CAPITAL THETA SYMBOL 
MATHEMATICAL SANSSERIF BOLD THETA SYMBOL 

Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120669  U+1D75D  120695  U+1D777  120679  U+1D767  120715  U+1D78B 
UTF8  240 157 157 157  F0 9D 9D 9D  240 157 157 183  F0 9D 9D B7  240 157 157 167  F0 9D 9D A7  240 157 158 139  F0 9D 9E 8B 
UTF16  55349 57181  D835 DF5D  55349 57207  D835 DF77  55349 57191  D835 DF67  55349 57227  D835 DF8B 
Numeric character reference  𝝝  𝝝  𝝷  𝝷  𝝧  𝝧  𝞋  𝞋 
Character  𝞗  𝞱  𝞡  𝟅  

Unicode name  MATHEMATICAL SANSSERIF BOLD ITALIC CAPITAL THETA 
MATHEMATICAL SANSSERIF BOLD ITALIC SMALL THETA 
MATHEMATICAL SANSSERIF BOLD ITALIC CAPITAL THETA SYMBOL 
MATHEMATICAL SANSSERIF BOLD ITALIC THETA SYMBOL 

Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120727  U+1D797  120753  U+1D7B1  120737  U+1D7A1  120773  U+1D7C5 
UTF8  240 157 158 151  F0 9D 9E 97  240 157 158 177  F0 9D 9E B1  240 157 158 161  F0 9D 9E A1  240 157 159 133  F0 9D 9F 85 
UTF16  55349 57239  D835 DF97  55349 57265  D835 DFB1  55349 57249  D835 DFA1  55349 57285  D835 DFC5 
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 the normal Greek letters, with markup and formatting to indicate text style.
See also
 Ѳ, ѳ  Fita, a letter of the early Cyrillic alphabet derived from the Greek theta
 ʘ  Bilabial click
 Voiceless dental fricative
Notes
 ^ http://math.stanford.edu/~feferman/papers/idsaga.pdf
 ^ ^{a} ^{b} Barry, Kieren (1999), The Greek Qabalah: Alphabetic Mysticism and Numerology in the Ancient World, Samuel Weiser, p. 73, ISBN 1578631106 [AmazonUS  AmazonUK].
 ^ 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 0195142373 [AmazonUS  AmazonUK].