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a plane angle in geometry; the angle to the x axis in the xy-plane in spherical or cylindrical coordinates (mathematics) the angle to the z axis in spherical coordinates (physics) the potential temperature in thermodynamics; theta functions; the angle of a scattered photon during a Compton scattering interaction
Historically, upper-case letters were used for representing points in geometry, and lower-case letters were used for variables and constants. Letters are used for representing many other types of mathematical object. As the number of these types has increased, the Greek alphabet and some Hebrew letters have also come to be used.
There are several closely related functions called Jacobi theta functions, and many different and incompatible systems of notation for them. One Jacobi theta function (named after Carl Gustav Jacob Jacobi) is a function defined for two complex variables z and τ, where z can be any complex number and τ is the half-period ratio, confined to the upper half-plane, which means it has a positive ...
Theta (UK: / ˈ θ iː t ə /, US: / ˈ θ eɪ t ə /) uppercase Θ or ϴ; lowercase θ [note 1] or ϑ; Ancient Greek: θῆτα thē̂ta [tʰɛ̂ːta]; Modern: θήτα thī́ta) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth 𐤈.
In mathematics, a theta characteristic of a non-singular algebraic curve C is a divisor class Θ such that 2Θ is the canonical class. In terms of holomorphic line bundles L on a connected compact Riemann surface , it is therefore L such that L 2 is the canonical bundle , here also equivalently the holomorphic cotangent bundle .
The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject.
This geometric argument relies on definitions of arc length and area, which act as assumptions, so it is rather a condition imposed in construction of trigonometric functions than a provable property. [2] For the sine function, we can handle other values. If θ > π /2, then θ > 1. But sin θ ≤ 1 (because of the Pythagorean identity), so sin ...
The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.