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algebraic number

complex number that is a root of a non-zero polynomial in one variable with rational coefficients

AI overview

An algebraic number is a type of number that solves a polynomial equation—like x² - 2 = 0—where the equation is built from whole numbers or fractions. These numbers matter because they form a fundamental building block in mathematics, helping us understand the structure of number systems and solve important problems in algebra and number theory.

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Wikidata facts

Image: Algebraic number in the complex plane.png

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topic's main category: Category:Algebraic numbers
Commons category: Algebraic numbers
set cardinality: aleph null
opposite of: transcendental number
different from: algebraic integer
studied by: number theory
maintained by WikiProject: WikiProject Mathematics
topic has template: Template:Algebraic numbers

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Encyclopedic overview

The square root of 2 is an algebraic number equal to the length of the hypotenuse of a right triangle with legs of length 1.

In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio

Excerpted from Wikipedia’s “algebraic number” article, available under the CC BY-SA 4.0 licence.

algebraic number

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