Quadratic growth


Quadratic growth

In mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position, in the limit as the argument or sequence position goes to infinity. That is, in big Theta notation, f(x)=Theta(x^2).

Examples of quadratic growth include

*Any quadratic polynomial.

*Certain integer sequences such as the triangular numbers. The "n"th triangular number has value "n"("n"+1)/2, approximately "n"2/2.

*The amount of time taken in the worst case by certain algorithms, such as insertion sort, as a function of the input length.

*The numbers of live cells in space-filling cellular automaton patterns such as the Breeder (CA), as a function of the number of time steps for which the pattern is simulated.

See also

* Exponential growth


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Quadratic — In mathematics, the term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree, or equations or formulas that involve such terms. Quadratus is Latin for square . Mathematics Algebra… …   Wikipedia

  • List of mathematics articles (Q) — NOTOC Q Q analog Q analysis Q derivative Q difference polynomial Q exponential Q factor Q Pochhammer symbol Q Q plot Q statistic Q systems Q test Q theta function Q Vandermonde identity Q.E.D. QED project QR algorithm QR decomposition Quadratic… …   Wikipedia

  • Conway's Game of Life — Conway game , which redirects to here, can also refer to games as defined by surreal numbers, which John Conway also developed …   Wikipedia

  • Metcalfe's law — Two telephones can make only one connection, five can make 10 connections, and twelve can make 66 connections. Metcalfe s law states that the value of a telecommunications network is proportional to the square of the number of connected …   Wikipedia

  • Rake (cellular automaton) — A rake in a cellular automaton is a puffer that, instead of leaving behind a trail of debris, emits a stream of spaceships. [ [http://www.argentum.freeserve.co.uk/lex r.htm#rake Rake, Life lexicon] .… …   Wikipedia

  • Dehn function — In the mathematical subject of geometric group theory, a Dehn function, named after Max Dehn, is an optimal function associated to a finite group presentation which bounds the area of a relation in that group (that is a freely reduced word in the …   Wikipedia

  • mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

  • Riemann hypothesis — The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011 …   Wikipedia

  • Number theory — A Lehmer sieve an analog computer once used for finding primes and solving simple diophantine equations. Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers (the… …   Wikipedia

  • List of important publications in mathematics — One of the oldest surviving fragments of Euclid s Elements, found at Oxyrhynchus and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.[1] This is a list of important publications in mathematics, organized by field. Some… …   Wikipedia