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.

If they have not learned it in high school, I would recommend showing them how to derive the quadratic formula.  Since the proof only involves basic algebra, the students should be able to solve it on their own.  Showing them that they already have enough math knowledge to prove a helpful mathematical formula may allow them to share in your enthusiasm.  
If they have already learned that, I would recommend showing them iterative series as shown in dynamical systems and the Mandelbrot and Julia fractal sets.  I always found this intriguing since the images were created with only mathematics.  If you need images, there are quite a variety online.  
