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We will establish several arithmetic and geometric properties regarding thebi-sequences of approximation coefficients (BAC) associated with the twoone-parameter families of piecewise-continuous Mobius transformationsintroduced by Haas and Molnar. The Gauss and Renyi maps, which lead to theexpansions of irrational numbers on the interval as regular and backwardscontinued fractions, are realized as special cases. The results are naturalgeneralizations of theorems from Diophantine approximation.

The bisequence of approximation coefficients for Gauss-like and Renyi-like maps on the interval