Abstract: Optimum seeking methods are those that in practice seek to obtain approximate optimal alternatives through trials for problems with one optimum value. Approximate golden section methods, which use Fibonacci sequence or golden section number, constitute a class of methods that are most important and most often used. This paper gives the relationships of the first trial point and the maximal number of the optimality of symmetry trials of approximate golden section methods. With these relationships, the maximal number of the optimality of symmetry trials can be determined for any approximate golden section method.