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**Theta** (UK: /ˈθiːtə/, US: /ˈθeɪtə/; uppercase **Θ** or **ϴ**, lowercase **θ**^{[note 1]} or **ϑ**; Ancient Greek: 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 the value 9.

## Greek

In Ancient Greek, θ represented the aspirated voiceless dental plosive /t̪ʰ/, but in Modern Greek it represents the voiceless dental fricative /θ/.

### Forms

In its archaic form, θ was written as a cross within a circle (as in the Etruscan or ), and later, as a line or point in circle ( or ). Archaic crossed forms of theta are seen in the wheel letters of Linear A and Linear B.

The cursive 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 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]}

## 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

*. It does not represent the consonant in*

**th**in*, which is the voiced dental fricative. A similar-looking symbol, [ɵ], which is described as a lowercase barred o, indicates in the IPA a close-mid central rounded vowel.*

**th**e## 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

- 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.

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*).^{[3]}

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,^{[citation needed]} 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.^{[3]} 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.^{[4]} 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.

**Greek Life**

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

## Character encodings

- Greek Theta

Preview | 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 |

UTF-8 | 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, ϑ, ϑ | |||||||

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

Preview | Ⲑ | ⲑ | ||
---|---|---|---|---|

Unicode name |
COPTIC CAPITAL LETTER THETHE | COPTIC SMALL LETTER THETHE | ||

Encodings | decimal | hex | decimal | hex |

Unicode | 11408 | U+2C90 | 11409 | U+2C91 |

UTF-8 | 226 178 144 | E2 B2 90 | 226 178 145 | E2 B2 91 |

Numeric character reference | Ⲑ |
Ⲑ |
ⲑ |
ⲑ |

- Cyrillic Fita

Preview | Ѳ | ѳ | ||
---|---|---|---|---|

Unicode name |
CYRILLIC CAPITAL LETTER FITA | CYRILLIC SMALL LETTER FITA | ||

Encodings | decimal | hex | decimal | hex |

Unicode | 1138 | U+0472 | 1139 | U+0473 |

UTF-8 | 209 178 | D1 B2 | 209 179 | D1 B3 |

Numeric character reference | Ѳ |
Ѳ |
ѳ |
ѳ |

- Mathematical Theta

Preview | 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 |

UTF-8 | 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 |

UTF-16 | 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 |

Preview | 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 |

UTF-8 | 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 |

UTF-16 | 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 |

Preview | 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 |

UTF-8 | 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 |

UTF-16 | 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 |

Preview | 𝝝 | 𝝷 | 𝚹 | 𝞋 | ||||
---|---|---|---|---|---|---|---|---|

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 | U+1D75D | 120695 | U+1D777 | 120505 | U+1D6B9 | 120715 | U+1D78B |

UTF-8 | 240 157 157 157 | F0 9D 9D 9D | 240 157 157 183 | F0 9D 9D B7 | 240 157 154 185 | F0 9D 9A B9 | 240 157 158 139 | F0 9D 9E 8B |

UTF-16 | 55349 57181 | D835 DF5D | 55349 57207 | D835 DF77 | 55349 57017 | D835 DEB9 | 55349 57227 | D835 DF8B |

Numeric character reference | 𝝝 |
𝝝 |
𝝷 |
𝝷 |
𝚹 |
𝚹 |
𝞋 |
𝞋 |

Preview | 𝞗 | 𝞱 | 𝜭 | 𝟅 | ||||
---|---|---|---|---|---|---|---|---|

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 | U+1D797 | 120753 | U+1D7B1 | 120621 | U+1D72D | 120773 | U+1D7C5 |

UTF-8 | 240 157 158 151 | F0 9D 9E 97 | 240 157 158 177 | F0 9D 9E B1 | 240 157 156 173 | F0 9D 9C AD | 240 157 159 133 | F0 9D 9F 85 |

UTF-16 | 55349 57239 | D835 DF97 | 55349 57265 | D835 DFB1 | 55349 57133 | D835 DF2D | 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

Look up or Θ in Wiktionary, the free dictionary.θ |

- Ѳ, ѳ—Fita, a letter of the early Cyrillic alphabet derived from the Greek theta
- ʘ—Bilabial click
- Voiceless dental fricative
- Theta nigrum

## Notes and references

### Notes

### References

**^**Everson, Michael; Lilley, Chris (2019-05-26). "L2/19-179: Proposal for the addition of four Latin characters for Gaulish" (PDF).**^**http://math.stanford.edu/~feferman/papers/id-saga.pdf- ^
^{a}^{b}Barry, Kieren (1999),*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, p. 66, Bibcode:2000tnti.book.....K, ISBN 0-19-514237-3.