Folding equilateral triangles in a square -- Dividing a length into equal nths: Fujimoto approximation -- Dividing a length into equal Nths exactly -- Folding a parabola -- Can origami trisect an angle? -- Solving cubic equations -- Folding strips into knots -- Haga's "origamics" -- Folding a butterfly bomb -- Business card modulars -- Five intersecting tetrahedra -- Making origami buckyballs -- Making origami tori -- Modular menger sponge -- Folding and coloring a crane -- Exploring flat vertex folds -- Impossible crease patterns -- Folding a square twist -- Matrix model of flat vertex folds -- Matrix model of 3D vertex folds -- Rigid folds 1: Gaussian curvature -- Rigid folds 2: Spherical trigonometry -- Appendix: Which activities go with which courses?.