An undergraduate seminar during the spring of 2021.
Origami/折り紙 is the art of paper folding. With just a square piece of paper and straight folds, one can construct an amazing variety of shapes and figures.
Beyond the visual art, origami is a wellspring for mathematics. For example, viewing just the crease patterns left on a piece of paper, origami gives a system of planar geometry that is reminiscent to straightedge and compass geometry of the Greeks. Something that is rather amazing already is that the geometry of origami is, in a precise sense, more expressive than the geometry known to Euclid: one can double the cube, trisect an angle, and construct regular heptagons.
I hope this seminar serves as a mathematical shinrinyoku/森林浴, a pleasant excursion out to experience some beautiful mathematics and art during this peculiar time.
Curiousity and excitement are basically the only requirements for this seminar; mathematical notions will be discussed as they come up. The goal of this seminar is to learn some beautiful mathematics, and to have fun doing so. Bonus for finding new friends and pets along the way.
Beyond the mathematical content, I hope that the seminar will convey a sense of how mathematical research is conducted via play and experimentation, and also a feeling for how mathematics is communicated. I hope that the seminar will be very interactive, with lots of participation from both speaker and audience.
Some books that have a wealth of technical information are
Thomas C. Hull (2020), Origametry: Mathematical Methods in Paper Folding,
Joseph O’Rourke (2011), How to Fold it: The Mathematics of Linkages, Origami, and Polyhedra,
Robert J. Lang (2018), Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami.
For the computationally minded, the following also looks like a lot of fun
Another text that would be interesting to look at might be this classic
We meet two hours a week, time soon to be determined based on availability of the participants. Talks will typically be for one hour each.