# irrational number

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Related to irrational number: imaginary number

## irrational number

n.
A real number that cannot be expressed as a ratio between two integers.

## irrational number

n
(Mathematics) any real number that cannot be expressed as the ratio of two integers, such as π

## irra′tional num′ber

n.
a number that cannot be exactly expressed as a ratio of two integers.
[1545–55]

## ir·ra·tion·al number

(ĭ-răsh′ə-nəl)
A real number that cannot be expressed as a ratio between two integers. If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition. Pi and the square root of 2 (√2) are irrational numbers.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 irrational number - a real number that cannot be expressed as a rational numberirrationalreal, real number - any rational or irrational numbertranscendental number - an irrational number that is not algebraicalgebraic number - root of an algebraic equation with rational coefficients
Translations
irrationaaliluku
iracionalni broj
óræð tala
References in periodicals archive ?
Pi, the ratio of a circle's circumference to its diameter, is an irrational number that extends to trillions of digits beyond the decimal point.
In particular, an irrational number is a Liouville number if and only if it is not Diophantine.
They realised that [empty set] was an irrational number and embodied it in the pentagram, which they used as their secret sign.
March 14 has become an unofficial holiday dedicated to the irrational number that can be calculated to over a trillion digits beyond its decimal point.
Pi is what mathematicians call an irrational number, so that not even the most powerful computers could ever calculate its exact value.
It is an irrational number that cannot be represented exactly by a fraction and this was first proved in the 18th century.
The square root of 2, the hypotenuse of the subsequent triangle (the diagonal of that ill-behaved square) thereby became the first irrational number, a number uncontainable, that spun off magnitude from the divinity of number, and produced a decimal that wouldn't repeat and wouldn't ever, ever, ever, end.
The figure is a nod to pi, an irrational number that has intrigued mathematicians for thousands of years.
Blais said, that is fun and held dear by some of his mathematician friends at WPI is 3-14-15 - the first five numbers of pi, an irrational number that is the ratio of a circle's circumference to its diameter.
So at the beginning of one school year, young Patel (Ayush Tandon) undertook the herculean task of instructing his teachers and schoolmates that, henceforward, he would be called "Pi," after the Greek letter that designates what may be mathematics' best-known irrational number.
Infinite continued fraction gives the worst approximation for irrational number [alpha] the smaller is its k + 1 component.
The irrationality of [pi] was not proved until 1761 by Johann Lambert (1728-77), then in 1882 Ferdinand Lindemann (1852-1939) proved that [pi] was a non-algebraic irrational number, a transcendental number (one which is not a solution of an algebraic equation, of any degree, with rational coefficients).

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