[Feature photo above by Michael Cory via Flickr (CC BY 2.0).]
I hear so many people say they hated geometry because of the proofs, but I’ve always loved a challenging puzzle. I found the following puzzle at a blog carnival during my first year of blogging. Don’t worry about the arbitrary two-column format you learned in high school — just think about what is true and how you know it must be so.
I hope you enjoy this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:
One of the great unsolved problems of antiquity was to trisect any angle using only the basic tools of Euclidean geometry: an unmarked straight-edge and a compass. Like the alchemist’s dream of turning lead into gold, this proved to be an impossible task. If you want to trisect an angle, you have to “cheat.” A straight-edge and compass can’t do it. You have to use some sort of crutch, just as an alchemist would have to use a particle accelerator or something.
One “cheat” that works is to fold your paper. I will show you how it works, and your job is to show why …