Mediant
From Encyclopedia of Mathematics
of two fractions 
and 
with positive denominators
The fraction 
. The mediant of two fractions is positioned between them, i.e. if 
, 
, then
 |
A finite sequence of fractions in which each intermediary term is the mediant of its two adjacent fractions is called a Farey series. The mediant of two adjacent convergent fractions of the continued-fraction expansion of a real number 
is positioned between 
and the convergent fraction of lower order (cf. also Continued fraction). Thus, if 
and 
are convergent fractions of orders 
and 
in the continued-fraction expansion of 
, then
 |
References
| [1] | A.Ya. Khinchin, "Continued fractions" , Univ. Chicago Press (1964) (Translated from Russian) |
Comments
References
| [a1] | G.H. Hardy, E.M. Wright, "An introduction to the theory of numbers" , Oxford Univ. Press (1979) |
How to Cite This Entry:
Mediant. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Mediant&oldid=33226
Mediant. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Mediant&oldid=33226
This article was adapted from an original article by V.I. Nechaev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article