Nice article. Euler is one of the greatest mathematicians of all ages, I have a big admiration for him. His formula is indeed beautiful. However, keep in mind that *it is not a theorem*. You are using different words for it: Euler’s theorem, identity and formula are spread through the text. From these, only formula or identity is correct. If you use “theorem” you show that you don’t understand what are you talking about. The difference is huge. For example, Euler’s formula cannot be proved — a common action for theorems.
So please do not use the term Euler’s theorem for this formula.