Easy math proofs or visual examples to make high school students enthusiastic about math I'm a teacher in mathematics at a high school. Math has fascinated me for almost my entire life, so I would like to bring that enthusiasm to my students with beautiful yet easy to understand proofs or demonstrations. It's meant for students who are in their last grade of high school and will be going to university next year.
So what are simple proofs or visual examples that made you love math? The more examples the better! Answers with pictures would be even better!
Thanks in advance!
P.S. Things that I did already teach my students the basics of are: complex numbers, probability theorem, prime numbers, vectors, functions of more variables, a little bit about group theory, set theory. These are all things that I tried to mix with the things they should actually know for their exams. It's meant to give them an idea of what math is really about, not just repeating formulas.

One mathematical fun fact that has left a strong impression on me when I was in middle school was the fact that you could state rules about random phenomena. 
I remember I wasn't familiar with limits, but a teacher had decided to show us funny things about random walks on Excel (yep Excel... :)). 
He basically made random walks on $\mathbb{R}^2$ with step size $1$, and showed us that the average squared distance after $n$ steps when we took a lot of walks was close to $n$.
I liked the fact that it felt like nothing could be said about the walks just by looking at them, but as soon as we computed the right quantity, order emerged.
Visual things are always nice. Plotting walks on the plane with colors, and showing how it looks so chaotic compared to the numbers/figures/functions we knew at the time did the trick I think.
