I like math, but might not know as much about it as some real math nuts. I was reading the web comic XKCD, which has a lot of math jokes. I read this comic titled e to the pi times i (language warning) which says if you take *e* to the power of *?* times *i* or e^(?*i)* *gives you negative one. That seemed really odd to me. First thing I did was put the formula into Google and see if it gave the same answer, and it did. The math really bends my mind, so I wanted to share it with everyone else.

So lets look at the constants in the formula:

**?**: Most people are familiar with ?*(or pi)*, which is the ratio to a circle to its diameter. It allows you to move between the diameter of a circle and its circumference. It is an irrational number, meaning it cannot be represented completely in decimal notation. It is approximately 3.14159265. . . .:Is the imaginary result of the square root of negative one, or**i***i*^2 = -1. Since a negative number multiplied by a negative number results in a positive number, without imaginary numbers, this would impossible.*e*: The one less people are familiar with is is Euler’s number or*e*. It is the base of the natural logarithm. It is also irrational with the approximate value of 2.71828 18284 59045 23536. . .

Mathematically speaking ?, e and i are considered some of the most important constants along with 0 and 1. Pretty exciting eh?

So it turns out this formula is called Euler’s identity. I still don’t understand how it works though. According to Carl Friedrich Gauss, since this formula is not immediately apparent to to me (as a student), I will never be a first-class mathematician. That is OK. I just enjoy math as a hobby right now.

I also was perplexed at first with this beautiful identity. To understand it first you have to understand the Euler first derived e^(xi)= cos(x) isin(x).

He arrived at this by using the accepted taylor polynomial for e^x= 1 x x^(2)/(2!) x^(3)/3! x^(4)/4 and so on. So, being as confident in his abilities as he was, Euler simply let x = xi. Then, as you probably noticed now, he let x = pi and got the extraordinary definition.

I wasn’t familiar with that equation either, and I have a BS in math! But there are a ton of topics in math, and I only was exposed to some of them. Since Euler’s Identity is part of algebra, and I never took non-abstract algebra in college, it never came up. Looks cool – thanks!