Namespaces
Variants
Actions

Difference between revisions of "Quadratic irrationality"

From Encyclopedia of Mathematics
Jump to: navigation, search
m (TeX encoding is done)
m (→‎References: expand bibliodata)
 
Line 4: Line 4:
  
 
====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) {{ZBL|0117.28601}}</TD></TR>
 +
</table>

Latest revision as of 20:31, 1 October 2016


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) Zbl 0117.28601
How to Cite This Entry:
Quadratic irrationality. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quadratic_irrationality&oldid=39350
This article was adapted from an original article by A.I. Galochkin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article