During our school days, we learn many formulae such as trigonometric functions, area and volume. Among them there is the most impressive formula, which is Euler's formula, e^ix=cos(x) + i sin(x). This symmetrical and beautiful formula specifies the relationship between the trigonometric functions and the complex exponential function. By substituting x=pi, simple integer, -1 is derived. It makes us feel like watching the strange magic using three different elements, e, pi and i. Also Einstein formula, E=mc² is a beautiful formula, in which the three different concepts, energy, mass and speed of light are simply and clearly connected. One last thing, there is another beautiful formula called Euler product, in which the product with all the prime numbers equals to the zeta function. The prime numbers might be seen as number playing but they seem to form a deep and mysterious mathematical world. Let us hope that more young people will be touched with the beauty of formula and will aim at becoming a scientist.

Related calculator

[1] Exponential function [2] Zeta function