Theta

Greek alphabet
Αα Alpha	Νν Nu
Ββ Beta	Ξξ Xi
Γγ Gamma	Οο Omicron
Δδ Delta	Ππ Pi
Εε Epsilon	Ρρ Rho
Ζζ Zeta	Σσς Sigma
Ηη Eta	Ττ Tau
Θθ Theta	Υυ Upsilon
Ιι Iota	Φφ Phi
Κκ Kappa	Χχ Chi
Λλ Lambda	Ψψ Psi
Μμ Mu	Ωω Omega
Obsolete letters
Digamma	Qoppa
San	Sampi
Other characters
Stigma	Sho
Heta
Greek diacritics

Theta (uppercase Θ, lowercase θ or ϑ; Greek: Θήτα) 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. In Classical Greek θ represented an aspirated voiceless dental plosive (/t̪ʰ/), but in Koiné and later dialects it became a voiceless dental fricative /θ/. In American English the name of the letter is commonly pronounced /ˈθeɪtʌ/. In British English, the name is pronounced /ˈθiːtə/.

Letters such as the early Cyrillic letter fita (Ѳ, ѳ) developed from θ.

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 ).

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).^[1]

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.

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.^[1] 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.^[2]

Symbol

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

• A plane angle in geometry.
• A special function of several complex variables.
• The voiceless dental fricative in the International Phonetic Alphabet, such as in the words thick or thin (but not as in the, which is the voiced dental fricative).
• 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.
• Theta has also gained a new significance in the north-eastern region of the United States as a symbol for affection, in a similar capacity to the “heart” symbol.
• The parameter frequently used in writing the likelihood function.

The upper-case letter Θ is used as a symbol for:

• 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.
• Earth Day.
• Brain Signal Frequency (Beta, Alpha, Theta, Delta) ranging from 4–8 Hz.
• One of the variables known as "Greeks" in finance, representing the lost-value rate of an option over time.

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 astrological symbol for the Earth (as already mentioned), and the Celtic cross. The circumpunct, or circled dot, is seen in a wide range of places.

Usage in names

• Kappa Alpha Theta is a sorority whose members are designated “Thetas”.
• Theta refers to a member of Sigma Phi Theta, a local fraternity at Texas Lutheran University.
• Theta is also the name of a melodic death metal band based in Plattsburgh, New York.
• Theta is the name of a biological weapon and boss featured in the Atari video game Area 51.
• Thetamen is a nickname also used by the fraternity Iota Phi Theta.
• Theta Phi Alpha is a sorority.
• Theta Chi is a Fraternity.
• Theta refers to a member of the Alpha Pi Theta Brotherhood of Emerson College.
• In generative grammar, theta roles are representations of a constituent's syntactic and semantic contributions to a sentence.
• In Scientology, the word "theta" is often used as an adjective to express or convey a sense of spirituality or uplifting feeling. See also thetan, the Scientology term for "spirit".

References