After attending a brilliant MoMath talk on Mathematical Origami given by Erik Demaine, I have been folding, cutting, and taping more than I ever thought I would.  Here are a few of the ways I have been inspired.  In addition, I have also posted some folding photos on my facebook page.

Intoduction:  Some Basic Mathematical Folding

Basic Folds  Simple demonstrations of the basic folds:  a line through two points; midpoint of a segment; perpendicular bisector of a segment; angle bisector of an angle.

Incenter of a Triangle  Use basic folds to find the incenter of a triangle!

Circumcenter of a Triangle Use basic folds to find the circumcenter of a triangle!

Centroid of a Triangle  Use basic folds to find the centroid of a triangle!

Introduction:  The One-Cut Challenge

One-Cut Challenge:  Triangles  Start investigating the one-cut problem by playing around with triangles.

One-Cut Challenge:  Quadrilaterals  Investigate the one-cut problem with squares, rectangles, and other quadrilaterals.

Fun with One Cut:  Exploring some fractal folding and cutting.

Time 2000 — Fun With One Cut:  My workshop on mathematical folding at the 2013 TIME 2000 conference.

Miscellaneous Folding

Paper Pyramids:  Turning triangles into solids!

Foam Pyramids:  Trying out a new medium.

Foam Tables:  Folding inspired by the American Invitational Mathematics Exam (AIME)!

Fractal Origami:  Turn A1 paper into Pythagoras’s Tree!

Math Art!

Math Art:  Paper Cut-Outs:  A lovely student-created cut-out; accidental art in math exploration.

Math Art:  Smashing Cones:  Pretty soon we were cutting, taping, and smashing cones!

Math Photo:  A Peck of Paper Pyramids

Applications of Mathematical Origami

Real Life Transformers:  An amazing application of origami; truly revolutionary thinking!

Folding Steel:  Another innovative application of mathematical origami.

Automatic Origami:  Check out this origami that unfolds itself!

Other Resources

“How to Fold It“, a book and website by Joseph O’Rourke, Smith College.