TITLE: Easy math proofs or visual examples to make high school students enthusiastic about math
QUESTION [89 upvotes]: 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.

REPLY [4 votes]: "Proofs without words: Exercises in Visual Thinking" is a book dedicated to visual proofs. The book has proofs about Geometry, Trigonometry, Calculus and also Sequences and Series. In case you run out of proofs for the class there is also a sequel of this book "Proofs without words II: More Exercises in Visual Thinking". Since, these are "exercises" no explanations are given for the proofs, and this is probably the fun part with this book.