Exact and "exact" formulae in the theory of composites

The effective properties of composites and review literature on the methods of Rayleigh, Natanzon--Filshtinsky, functional equations and asymptotic approaches are outlined. In connection with the above methods and new recent publications devoted to composites, we discuss the terms "analytical formula, approximate solution, closed form solution, asymptotic formula" etc... frequently used in applied mathematics and engineering in various contexts. Though mathematicians give rigorous definitions of exact form solution the term "exact solution" continues to be used too loosely and its attributes are lost. In the present paper, we give examples of misleading usage of such a term.