Location of approximations of a Markoff theorem

Abstract

Relative to the first two theorems of the well known Markoff Chain (J.W.S. Cassels, “An introduction to diophantine approximation” approximations are well located. Literature is silent on the question of location of approximations in reference to the other theorems of the Chain. Here we settle it for the third theorem of the Chain.

Keywords

• continued fractions
• rational approximation.