# PME Conference Details

### April 14-15, 2023 Schedule

#### Origami: Doing Math and Science without Scissors or Glue

###### Abstract:

Origami, the art of paper folding, has been practiced in Japan and all over the world for centuries. However, the past decade has witnessed a surge of interest in using origami for science. Applications in robotics, airbag design, deployment of space structures, and even medicine are appearing in the popular science press. Videos of origami robots folding themselves up and walking away or performing tasks have gone viral. What's more, the National Science Foundation has found origami valuable enough to fund millions of dollars towards studying engineering and science applications of origami art. But if the art of paper folding is so old, why has there been an increase in origami applications now? One answer is because of math. Advances in our understanding of how folding works has arisen due to success in modeling origami mathematically. In this presentation we will explore why origami lends itself to mathematical study and see how origami-math has inspired science applications as well as influenced origami as an artistic medium.

#### Rigid Origami and No-hands Folding

###### Abstract:

As mentioned in the first talk, origami has enjoyed increased attention in math and science over the past 10 years. One aspect that has especially blossomed is rigid origami, where we insist that the origami model can be smoothly folded and unfolded with the faces of paper between the creases remaining flat (or rigid, as if they were made of metal or wood). Engineers especially like rigid origami as a way to design interesting mechanisms that work at large scales (think solar panel arrays) and tiny scales (think folded capsules and stents in the human body).

To actuate a rigid origami mechanism without the aid of human hands, we apply driving forces to the crease lines, such as with springs. We say these driving forces make the origami model self-fold. In doing this we often confront a problem where it is not possible to predict the way the springs will make the model fold from the unfolded state. In this talk we will develop a mathematical model of self-folding and describe how to design a driving force such that a given crease pattern will uniquely self-fold to a desired mode without getting caught in a bifurcation. We'll use linear algebra to find necessary conditions for self-foldability and see how it works on actual examples. This is joint work with Tomohiro Tachi (University of Tokyo), my students at Western New England University, and was partially supported by NSF grants EFRI-1240441 and DMS-1906202.

##### College of Saint Benedict Saint John’s University

Bret Benesh
Chair, Mathematics Department
CSB Main 207
320-363-5790

[email protected]