College of Arts and Sciences

Department of Mathematics

Euler's equation relates the five most important mathematical constants: the base of the natural logarithm (e), the square root of negative 1 (i), the ratio of the circumference of a circle to its diameter (pi), the multiplicative identity (1), and the additive identity (0). It is a direct consequence of four formulas: the Taylor series of e, sin, and cos, and the complex number relation: