Euler's Identity and the 3D unit helix
Sine and cosine are the 2D projections of the unit helix.
When I first saw the concept of the unit helix some years ago, trigonometric functions made so much sense.
Unfortunately, I never heard of any of it in school. Trigonometry was taught as a very unintuitive thing, as something one could not have a connection towards, as something not really 'integratable' into one's own mind. There were no elaborations about 'why' equations are the way they are, nor how the methods are used in relation to the "why", and what these methods are in concrete - in a manner which can be plotted in one's own imagination.
The abstraction appeared alienated from the own thinking process. No inner comprehension was really possible.
Yet, seeing only this concept with no further words added, it was an "Eureka-moment" for me.
In my opinion, Euler's Identity deserves the status of the most elegant and beautiful equation.