Theta

From Textus Receptus

Theta (uppercase Θ, lowercase θ or ϑ;^[] Ancient Greek θῆτα tʰɛ̂ːta; Modern Greek θήτα ˈθita; ˈθiːtə, ˈθeɪtə) 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 1 Greek 1.1 Forms 2 Cyrillic 3 International Phonetic Alphabet 4 Math and science 4.1 Lower case 4.2 Upper case 4.3 Greek mathematics 5 Symbolism 5.1 Abbreviation 6 Culture 7 Notes 8 See also

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 (Image:Earth symbol.svg or Image:Cross within circle 2.png)

• and later, as a line or point within a circle (16px|The symbol of a line within a circle or Image:Sun symbol.png).

Cyrillic

The early Cyrillic letter fita (Ѳ, ѳ) developed from θ.

International Phonetic Alphabet

In the International Phonetic Alphabet, [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.

Math and science

Lower case

The lower-case 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).
• Along with μ (Mu), population parameters in the Normal/Gaussian/Bell curve distribution, usually designated N(μ,θ).
• The Watterson estimator for the population mutation rate in population genetics.

Upper case

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.
• As a variable indicating Temperature difference in Heat Transfer

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

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).^[]

The Egyptians also used the symbol of a point within a circle (Image:Sun symbol.svg, 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 (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.^[] 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.^[] 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.

Culture

In the science fiction TV series Doctor Who, the character of the Doctor was once known as Theta Sigma whilst he lived on Gallifrey.

Notes

See also

• Ѳ, ѳ - Fita, a letter of the early Cyrillic alphabet derived from the Greek theta
• ʘ - Bilabial click