Euler’s Identity
The Most Beautiful Mathematical Formula
Euler’s equation has it all to be the most beautiful mathematical formula to date. Its simple, elegant, it gathers some of the most important mathematical constants, and it has curious mathematical and physical interpretations.
Lets examine it closely.
The Formula
Euler’s Identify formula is the one displayed at the heading of this article. Lets take a look at it here again:
This three-term formula has amazed mathematicians all over the world since it was coined because the amazing connection it establishes between the different elements involved in it and its different interpretations.
In this post, we will try to remove the magic veil from Euler’s identity, and expose its wonders.
Before that, let's see where this formula comes from.
The History of Euler’s Identity
In the year 1714 British physicist and mathematician Roger Cotes established in one formula the relationship between logarithms, trigonometrical functions and imaginary numbers.
Twenty years later, Leonhard Euler reached the same formula but using exponential functions instead of logarithms. Both formulas, and how to go from one to…
