Abstract—The authors of this paper propose the new formula to describe the rational relationship between  and e , where the constant  is the linear combination of the Euler constant  and the new constant，namely . Two advantages can be revealed from the rational relationship. One is that the constants in the new formula can be computed, the other is that the constants such as π and e,  and  in the formula can be converted to each other. There exists two methods to compute the constants using computers in this paper. The significance of conversion between π and e lies in the fact that the use of θ e2 to substitute 2π can simplify the formulas’ computation in probability and statistics.

Index Terms—The ratio of the circumference of a circle to its diameter, the logarithm of the natural constant, the Euler’s constant, the new constant, the new formula.

Wenwei Chen is with College of Information Systems and Management, NUDT, Changsha, China, 410073 (email: zxmdi@163.com).
Xia Zhao is with Department of Mathematics and Systems Science, College of Science, NUDT, Changsha, China, 410073.

Cite: Wenwei Chen, Xia Zhao, "Research on the Imaginary Relationship and Rational Relationship between π and e," International Journal of Applied Physics and Mathematics vol. 7, no. 1, pp. 33-41, 2017.