Trisect and Angle by Folding

trisected angle

You might have heard that you can't trisect an angle using the traditional construction methods with a compass and straight-edge. However, you can fold an angle trisection.
I am always amazed at how recently some of these great things were discovered. Hisashi Abe invented this in 1980. It makes you think that there must be some cool mathematical thing that you can discover, too.