Orthogonal Fold & Cut
arXiv:2202.01293
Abstract
We characterize the cut patterns that can be produced by "orthogonal fold & cut": folding an axis-aligned rectangular sheet of paper along horizontal and vertical creases, and then making a single straight cut (at any angle). Along the way, we solve a handful of related problems: orthogonal fold & punch, 1D fold & cut, signed 1D fold & cut, and 1D interval fold & cut.
10 pages, 7 figures. Improved text and figures. Presented at 23rd Thailand-Japan Conference on Discrete and Computational Geometry, Graphs, and Games. To appear in Thai Journal of Mathematics