Find rational approximation to given real number. Based on the theory of continued fractions if x = a1 + 1/(a2 + 1/(a3 + 1/(a4 + ...))) then best approximation is found by truncating this series (with some adjustments in the last term). Note the fraction can be recovered as the first column of the matrix ( a1 1 ) ( a2 1 ) ( a3 1 ) ... ( 1 0 ) ( 1 0 ) ( 1 0 ) Instead of keeping the sequence of continued fraction terms, we just keep the last partial product of these matrices.