  How to find "best rational approximations" of maximal commutative subgroups
of GL(n,R)? In this paper we pose and make first steps in the study of this
problem. It contains both classical problems of Diophantine and simultaneous
approximations as a particular subcases but in general is much wider. We prove
estimates for n=2 for both totaly real and complex cases and write the
algorithm to construct best approximations of a fixed size. In addition we
introduce a relation between best approximations and sails of cones and
interpret the result for totally real subgroups in geometric terms of sails.
