Other Geometries ? (Origami)

As I prepare for the upcoming school year, I have been thinking about students exposure to geometry.  Prior to adopting our current textbook, my students would explore hyperbolic, spherical, and Euclidean geometries. (I didn't use a textbook.)  With our current textbook, students explore only Euclidean Geometry.

This posting are my thoughts about introducing my students to origami. I am planning to write a weekly posting about other big ideas for next school year.

Anytime I ask students about origami, they talk about folding a crane or a frog.  I would like students to understand the changes that have occurred with the use of origami in the last few decades. "BETWEEN THE FOLDS (a movie) chronicles 10 stories of several fine artists and theoretical scientists that are abandoning more conventional career paths to forge lives as modern-day paper folders. Featuring interviews with and insights into the practice of these intrepid paper folders. Through origami, these offbeat and provocative minds are reshaping ideas of creativity and revealing the relationship between art and science."

I still believe students should experience the act of paper folding. It is fun and allows us to explore (or extend) ideas in a traditional geometry course.  But I would like my students to learn about these paper folders and how science has been impacted by their work. Of the 10 stories chronicled in Between The Folds, I really enjoyed Robert Lang and Erik Demaine. 

The video is a Ted Talks presentation by Robert Lang. The presentation is called Flapping Birds and Space Telescopes.He discusses how origami has changed because of mathematics.

Erik Demaine is the youngest MIT professor to be hired, at 20 years of age. In this video and the Between the Folds segment, Erik discusses how mathematics and origami are being used to study folding materials (such as a table) and how folding proteins impact our health.

Erik got me thinking about folding proteins being used to predict possible diseases that may impact my health or the health of a family member or a friend.  So I spent some time searching for other resources.  And there are many.  Here are some examples of other work being done:

McGill University
Stanford University
Science Daily

Also Erik talked about sheets of special material that might be used to fold different items for your house.  You simply download a program so the sheet of materials fold into a table, chair, or bed. Here are some examples of other work being done:

Purdue University
Science Daily

The University of Texas has developed an origami test strip to cheaply test a person for malaria and the HIV virus.  At a cost of ten cents per test strip,  people will eventually have the means to test for these diseases.

(Other than ideas, I don't have student materials to share. I am writing a digital document using  Joomag for my students.)