Origami

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.

Prerequisites, Format, Expectations, etc.

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.

References

Some books that have a wealth of technical information are

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

Schedule

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.

01/14
Organization.
01/22
Raymond Cheng
Overview of Seminar. Angle Trisection and Regular Heptagon
01/29
Lizka Vaintrob
Basic Origami Operations, and an orizuru/折鶴
01/29
Audrey Shu
Field of Origami Numbers
02/05
Lori Leu
Folding Conic Sections
02/05
Leopold Aschenbrenner
Fold and One-Cut
02/12
JuHyung Jeong
Engineering Applications of Origami
02/12
Mohit Medini Singh
Shopping Bag Theorem
02/19
Destine Lee
Curvature Methods in Origami
02/19
Claire Kang
Origami in Architecture
02/26
No Seminar
03/05
No Seminar
Enjoy Spring Break
03/12
Clara Simmons
Textiles, Fibonacci, Origami
03/12
Benjamin Sherwin
Lill's Method and the Tron Turtle
03/19
Lizka Vaintrob
Hyperbolic and Spherical Origami
03/19
Audrey Shu
Geometric Folding Exercises
03/26
Mohit Singh
Paper Silhouettes
03/26
Claire Kang
Polygon Folding Methods Using Paper Tapes
04/02
Lori Leu
Twists
04/02
Luis Lesmes
Applications to Marine Biology
04/09
Leopold Aschenbrenner
Polyhedral Nets
04/09
Destine Lee
Putting the Fold in Manifold