Five years ago today I posted, *Beautiful Math*, which is about **Euler’s Identity**. In the first part of that post I explored why the Identity is so exquisitely beautiful (to mathematicians, anyway). In the second part, I showed that the Identity is a special case of **Euler’s Formula**, which relates trigonometry to the complex plane.

Since then I’ve learned how naive that post was! It wasn’t wrong, but the relationship expressed in Euler’s Formula is fundamental and ubiquitous in science and engineering. It’s particularly important in quantum physics with regard to the infamous Schrödinger equation, but it shows up in many wave-based contexts.

It all hinges on the **complex unit circle** and the * exp(i×π×a)* function.