Abstract: According to the definition of Chebyshev polynomial and its properties,this paper presents the best approximation in algebraic expression for a polynomial function.Using these results,the author has solved the problem of the best approximation about a set of formula,frequently used for geodetic calculations.Working on an electronic computer,the efficiency with these approximate expressions deduced from Chebyshev polynomial,for example,for the calculation of the meridian length and the reverse problem is five to tens times higher than that with the traditional corresponding formulae.