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.

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: 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.