Mathematics and statistics

Archimedean spiral

The Archimedean spiral, also called the arithmetic spiral, is a plane curve, written r = a + bθ, whose turns stay a constant distance apart.

Arcsine laws for Brownian motion

The Lévy arcsine laws, found by Paul Lévy in 1939, state that Brownian motion's occupation time, last zero, and time of maximum share one arcsine distribution.

The arcsine transformation, usually applied as arcsine of the square root of a proportion, is a variance-stabilizing transformation for binomial data, introduced in the 1930s and 1940s and still used in ecology, agriculture, and meta-analysis.

ARDL bounds test

The ARDL bounds test, or bounds testing, is an econometric cointegration test for long-run relationships that works without knowing whether regressors are stationary or first-difference stationary.

Area of a circle

The area of a circle is the measure of the flat region enclosed by its circumference, given by the formula A = πr², where r is the radius.

Area sampling

Area sampling is a survey sampling method in which geographic areas are selected as intermediate units before sampling the households, farms, or land plots that are the actual survey targets.

Argument (complex analysis)

The argument of a complex number, also called the phase, is the angle it makes with the positive real axis, defined only up to multiples of 2π.

Argument from ignorance

Argument from ignorance (Latin argumentum ad ignorantiam), or appeal to ignorance, is an informal fallacy inferring that a claim is true or false because it has not been proven otherwise.

Argumentum ad populum

Argumentum ad populum, also called the bandwagon fallacy, is an informal logical fallacy in which a claim is treated as true simply because many people believe it.

Arithmetic

Arithmetic is the branch of mathematics that studies numbers and their operations, chiefly addition, subtraction, multiplication, and division, with roots going back to ancient Egypt.

Arithmetic coding

Arithmetic coding is a lossless data compression method that represents an entire message as a subinterval between 0 and 1, achieving better compression than Huffman coding at higher computational cost.

Arithmetic combinatorics

Arithmetic combinatorics, also called additive combinatorics, is a branch of mathematics at the intersection of combinatorics and number theory that studies sets under addition and multiplication.

Arithmetic dynamics

Arithmetic dynamics is a branch of mathematics, established around 2000 by Joseph H. Silverman, that reformulates number theory problems as questions about iterated rational maps.

Arithmetic group

An arithmetic group is a group of integer matrices arising as the integer points of a linear algebraic group over the rationals, with SL(n, Z) the prototype.

Arithmetic logic unit

An arithmetic logic unit (ALU) is a digital circuit within a CPU or GPU's execution unit that performs arithmetic and bitwise logical operations on binary data.

Arithmetic mean

The arithmetic mean, the usual average, is the sum of a set of numbers divided by how many numbers there are, a central measure in statistics.

Arithmetic of abelian varieties

The arithmetic of abelian varieties is the branch of arithmetic geometry studying rational points, torsion, and L-functions of abelian varieties, centered on the Mordell–Weil finiteness theorem.

Arithmetic optimization algorithm

The arithmetic optimization algorithm (AOA) is a population-based, derivative-free metaheuristic introduced by Laith Abualigah and colleagues in 2021 that searches for global optima using arithmetic operators as search operators.

Arithmetic progression

An arithmetic progression, also called an arithmetic sequence, is a sequence of numbers in which consecutive terms differ by a constant, the common difference; its nth term is a + (n − 1)d.

Arithmetic topology

Arithmetic topology is a branch of mathematics studying the analogy that knots are like prime numbers and 3-manifolds are like number rings, named in the mid-1990s.

Arithmetic-geometric mean

The arithmetic-geometric mean is the common limit reached by repeatedly taking the arithmetic and geometric means of two numbers, converging quadratically and underlying the fastest known algorithms for computing π.

Arithmetical hierarchy

The arithmetical hierarchy, also called the Kleene or Kleene–Mostowski hierarchy, classifies sets of natural numbers into levels Σₙ and Πₙ by quantifier alternations, developed by Kleene and Mostowski in the 1940s.

Arithmetical set

An arithmetical set is a set of natural numbers definable by a first-order formula over addition and multiplication, belonging to some level of the arithmetical hierarchy introduced by Kleene in 1943.

Arity

Arity, also called adicity, is the number of arguments that a function or predicate takes, chiefly in mathematical logic and programming; standard names include unary, binary, ternary, and n-ary.

Arrangement of lines

An arrangement of lines is the partition of the plane induced by a finite set of straight lines into vertices, edges, and faces, fundamental to computational geometry.

Ars Magna (Cardano)

Ars Magna, the Great Art, is a book on algebra by Girolamo Cardano published at Nuremberg in 1545, containing the first printed solutions of the cubic and quartic equations.

Artificial hummingbird algorithm

The artificial hummingbird algorithm is a nature-inspired metaheuristic that finds global optima of numerical functions by mimicking hummingbird foraging, introduced by Zhao, Wang, and Mirjalili in 2022 and applied in engineering design.

Artificial rabbits optimization

Artificial rabbits optimization (ARO) is a population-based, nature-inspired metaheuristic introduced in 2022 that mimics rabbit detour foraging and random hiding to solve numerical and engineering optimization problems.

Artin group

An Artin group is a group given by generators and braid relations from a Coxeter matrix; adding relations a_i^2 = 1 yields its Coxeter group.