I'll be trying to make as complete a list of my papers here as I can. (i.e., as much as the publishers will let me!)  All are in PDF format.  I apologize if any of the graphics in these files look yucky.
 

• On the Mathematics of Flat Origamis, Congressus Numerantium, Vol 100 (1994), 215-224.
  I wrote this one while in grad school. Please ignore my attempts to define "origami" rigorously, as it is flawed. The other proofs and such are fine though.
  
• Unit Origami as Graph Theory, in COET95: Proceedings of the 2nd International Conference on Origami in Education and Therapy, V'Ann Cornelius, ed., Origami USA, New York (1995), 39-47.
  This was another grad school paper where I tried to describe some of the connections between (and the usefulness of) modular origami and graph theory. A shorter version of this paper appeared as "Planar Graphs and Modular Origami" in Origami Science and Art: the 2OSM Proceedings, which was published in 1997.
• A Note on "Impossible" Paper Folding, The American Mathematical Monthly, Vol. 103, No. 3 (1996), 242-243.
  I also wrote this one while in grad school, so please forgive the rather flippant tone. Nonetheless, this is probably my most cited paper.
  
• Defective List Colorings of Planar Graphs, with N. Eaton, Bulletin of the Institute of Combinatorics and its Applications, Vol. 25 (1999), 79-87.
  
• In Search of a Practical Map Fold, Math Horizons, February (2002), 22-24.
  
• Classifying Frieze Patterns Without Using Groups with s.-m. belcastro, The College Mathematics Journal, Vol. 33, No. 2, (2002), 93-94.
  
• Modeling the Folding of Paper into Three Dimensions using Affine Transformations, with s.-m. belcastro, Linear Algebra and its Applications, Vol. 348 (2002), 273-282.
  
• Counting Mountain-Valley Assignments for Flat Folds, Ars Combinatoria, Vol. 67 (2003), 175-188.
  
• The Combinatorics of Flat Folds: a Survey, in Origami³: Proceedings of the Third International Meeting of Origami Science, Mathematics, and Education, A.K. Peters, Ltd., Natick, MA (2002).
  
• Origami Quiz, in The Mathematical Intelligencer, Vol. 26, No. 4 (Fall 2004), 38-39, 61-63.
  
• Constructing pi via origami, preprint (2007).
  This is more of a philisophical musing on what the consequences would be for origami geometric constructions if we allowed curved creases. It turns out that if we allow them, constructing pi becomes fairly easy. Hmmm...

Presentation Slides

• Counting and 3-Edge Coloring Spherical Buckyballs, presented at the Joint Meetings of the AMS and the MAA, San Antonio, TX, Jan. 12-15, 2006.
• Origami and Constructible Numbers talk, which I've given versions of at number of places, including Erik Demaine's Computational Origami class at MIT, some regional MAA Section meetings, and the 2008 Joint Meetings in San Diego. It talks about Margherita Beloch's proof that origami can solve cubic equations and Lill's method for finding real roots of polynomials.

Unpublished Things

• Review of the book Beyond Measure.
  I was asked to review this book (written by Jay Kappraff, published by World Scientific, 2002) by the Mathematical Intelligencier a number of years ago. My review was kind of harsh because, well, I didn't like the book. The review editor of the Intelligencier liked my review, but it seems they never printed it. I can understand that -- why print a review of a bad book when there are so many good books out there to promote? Therefore, I'm posting my review here in hopes of warning people away form this book. Yeah.