Difference between revisions of "Quadratic irrationality"
From Encyclopedia of Mathematics
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| + | A root of a quadratic trinomial with rational coefficients which is irreducible over the field of rational numbers. A quadratic irrationality is representable in the form $a+b\sqrt{d}$, where $a$ and $b$ are rational numbers, $b\ne 0$, and $d$ is an integer which is not a perfect square. A real number $\alpha$ is a quadratic irrationality if and only if it has an infinite periodic [[Continued fraction|continued fraction]] expansion. | ||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> A.Ya. Khinchin, "Continued fractions" , Phoenix Sci. Press (1964) pp. Chapt. II, §10 (Translated from Russian)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> A.Ya. Khinchin, "Continued fractions" , Phoenix Sci. Press (1964) pp. Chapt. II, §10 (Translated from Russian)</TD></TR></table> | ||
Revision as of 09:04, 22 January 2013
A root of a quadratic trinomial with rational coefficients which is irreducible over the field of rational numbers. A quadratic irrationality is representable in the form $a+b\sqrt{d}$, where $a$ and $b$ are rational numbers, $b\ne 0$, and $d$ is an integer which is not a perfect square. A real number $\alpha$ is a quadratic irrationality if and only if it has an infinite periodic continued fraction expansion.
References
| [a1] | A.Ya. Khinchin, "Continued fractions" , Phoenix Sci. Press (1964) pp. Chapt. II, §10 (Translated from Russian) |
How to Cite This Entry:
Quadratic irrationality. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quadratic_irrationality&oldid=29336
Quadratic irrationality. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quadratic_irrationality&oldid=29336
This article was adapted from an original article by A.I. Galochkin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article