Back in the days of the ancient Greeks, Euclid studied geometry in the plane by drawing straight lines and circles. Meanwhile, the art of folding paper flourished in Japan as a decorative art. Origami may now be used to understand the geometry first codified by Euclid. By folding a piece of paper, we create a line. The additional moves allowed in origami improve on Euclid’s constructions by straightedge-and-compass. Your geometry teachers may have told you that it’s impossible to trisect an angle, but with origami moves this becomes possible!

Some familiarity with straightedge-and-compass constructions will be helpful, but is not required.