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This book focuses on introducing approximate formulas for various mathematical constants that are widely used in natural sciences and engineering, including mathematics, and comparing their accuracy. We combined and analyzed the results of previous studies and tried to obtain better approximate formulas for mathematical constants using special mathematical techniques and methods, and obtained relatively good results. In almost all fields of mathematics and engineering, important mathematical constants and special functions are used. Mathematical constants including the circumferential, Napier constants, Euler constants have a variety of applications in various fields of engineering as well as in natural sciences, including Mathematical Analysis, Probabilistic, Special functional theory, Application statistics, and Number theory. This book reflects our results. It consists of the following: First, approximate formulas with respect to mathematical constants are described. Second, the comparison tables between formulas are presented. Third, we display interesting graphs that can intuitively show the accuracy of approximation formulas.