Origami is the art of paper folding. It can also be described mathematically with a set of seven axioms, which are complete. In this talk, we will see the following.
1. The fold-and-cut theorem: If you draw a number of disjoint polygons (not necessarily convex) on a sheet of paper, it is always possible to fold the sheet of paper in such a way that just a single straight line cut with a pair of scissors will separate out each polygon individually.
2. Angle trisection: Using Origami, it is possible to find the real roots of any degree 3 real polynomial, which can be used to solve problems that are unsolvable using a straightedge and compass (like trisecting an angle). This proof can also be extended to degree n polynomials.
If time permits, we will also discuss geometric folding, and several other open problems in computational Origami.