[Math filter] What fascinatingly cool mathematical topics do you wish you knew about in high school?
I'm giving a talk to a group of students (grades 10, 11, 12) at the end of April, who are attending a Math Camp at my University. The talk is called "What I Wish I Knew About Math In High School" and I'd like to discuss things that I've discovered about math that I think are really cool, but you would never have been encouraged to learn about while you were in high school. The current high school curriculum focuses on algebra, trig, and (in the later years) pre-calculus, which is an amazingly small portion of what math has to offer.
I'm interested in hearing what type of things the hive mind finds fascinating about math. These topics should be relatively easy for anyone to understand (after a brief explanation), and have some sort of "wow" factor to them. Bonus points if you can apply it somehow to "real" life.
An example could be the Golden Ratio
, since it has roots which are purely mathematical, but is debated to be found in nature, art, and music.