Theta

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.

The lowercase letter θ is used as a symbol for:

• A plane angle in geometry
• An unknown variable in trigonometry
• 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

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

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.[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.