Exact expressions of the fine-structure constant

The purpose of many sciences is to find the most accurate mathematical formula that can be found in the experimental value of fine-structure constant. Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time. However,no numerological explanation has ever been accepted by the physics community. In this paper we will present the exact expressions for the fine-structure constant. A simple and absolutely accurate expression for the fine-structure constant in terms of the Archimedes constant. The equivalent expressions for the fine-structure constant from the madelung constant. Also a exact expression for the fine-structure constant in terms of the golden angle,the relativity factor and the fifth power of the golden mean. Also other expressions for the fine-structure constant. Finally we will present the continued fractions for the fine-structure constant.