Thomas Hull


BA Mathematics, 1991, Hampshire College
MS Mathematics, 1993, University of Rhode Island
Ph.D. Mathematics, 1997, University of Rhode Island


Tom Hull is a leading expert on the mathematics of origami (paper folding) and has given talks on this topic all over the world.  His research uses graph theory, combinatorics, geometry, and other areas of math, with applications in engineering, materials science, art, and education.  He is the faculty advisor of the Math Club,  he enjoys having students be involved in his research, and he teaches regularly in our graduate Masters in Mathematics for Teachers (MAMT) program.  He also likes playing Ultimate Frisbee and reading supernatural horror.

Some of my publications can be found on the arXiv.


Mathematics of Origami

Using math to understand the laws behind paper folding.  This has applications in engineering, materials science, art, and education, as well as being an interesting math subject in its own right.

Graph Theory

Studying properties of graphs (networks of points and lines), in particular graph colorings.


Euclidean, non-Euclidean, projective, and fractal geometry, especially as they apply to origami.

Courses Taught

Undergraduate Courses: Calculus I, I, III, Linear Algebra, Modern Aspects of Geometry, Creative Problem Solving, Graph Theory, Combinatorics, Introduction to Modern Algebra, Real Analysis I, II, Complex Analysis

Graduate Courses (MAMT): Calculus Revisited, Creative Problem Solving, Discrete Mathematics, Geometry Revisited, Analysis, Algebraic Structures, Origami in Mathematics and Education, Topology and Fractals

Scholarly Works


Thomas C. Hull (2020). Origametry: Mathematical Methods in Paper Folding . NY: Cambridge University Press.

Thomas C. Hull (2012). Project Origami: activities for exploring mathematics, 2nd Edition . MA: AK Peters/CRC Press.

Thomas C. Hull (2002). Origami^3: Third International Meeting of Origami Science, Math, and Education . MA: AK Peters/CRC Press.

Book Chapters

Thomas C. Hull (2009). Folding regular heptagons . In E. Pegg, A. Schoen, T. Rogers (Eds.), Homage to a Pied Puzzler (pp. 181-191) Natick, MA : A K Peters.

Journal Articles

T. Tachi and T. C. Hull (2017 ). Self-foldability of rigid origami . ASME Journal of Mechanisms & Robotics ,9 , 021008-021017.

Z. Abel, J. Cantarella, E. Demaine, D. Eppstein, T. Hull, J. Ku, R. Lang, T. Tachi (2016 ). Rigid origami vertices: conditions and forcing sets . Journal of Computational Geometry ,7 , 171-184.

H. Akitaya, K. Cheung, E. Demaine, T. Horiyama, T. Hull, J. Ku, T. Tachi, R. Uehara (2016 ). Box pleating is hard . Discrete and Computational Geometry and Graphs. JCDCGG 2015. Lecture Notes in Computer Science, ,9943 , 167-179.

J.-H. Na, A. A. Evans, J. Bae, M. C. Chiappelli, C. D. Santangelo, R. J. Lang, T. C. Hull, and R. C. Hayward (2015 , January ). Programming reversibly self-folding origami with micro-patterned photo-crosslinkable polymer trilayers . Advanced Materials ,27 , 79-85.

B. Ballinger, M. Damian, D. Eppstein, R. Flatland, J. Ginepro, T. Hull (2015 ). Minimum forcing sets for Miura folding patterns . ACM-SIAM Symposium on Discrete Algorithms (SODA15) , 136-147.

T. Hull (2015 ). Coloring connections with counting mountain-valley assignments . Origami 6: Proceedings of the 6th International Meeting on Origami Science, Mathematics, and Education , 3-10.

Jessica Ginepro and Thomas C. Hull (2014 , November ). Counting Miura-ori Foldings . Journal of Integer Sequences ,17 , Article 14.10.8.

J. L. Silverberg, A. A. Evans, Lauren McLeod, Ryan Hayward, Thomas Hull, Christian D. Santangelo, I. Cohen (2014 , August ). Using origami design principles to fold reprogrammable mechanical metamaterials . Science ,345 , 647-650.

Thomas C. Hull (2011 , April ). Solving cubics with creases: the work of Beloch and Lill . The American Mathematical Monthly ,118 , 307-315.

Thomas C. Hull and Eric Chang (2011 ). The flat vertex fold sequences . Origami^5: Fifth International Meeting of Origami Sceince, Mathematics, and Education , 599-607.

Thomas C. Hull (2009 ). Configuration spaces for flat vertex folds . Origami^4: Fourth International Meeting of Origami Science, Mathematics, and Education , 361-370.

Thomas C. Hull (2006 , February ). H.P. Lovecraft: a horror in higher dimensions . Math Horizons , 10-12.

Thomas C. Hull (2003 ). Counting mountain-valley assignments for flat folds . Ars Combinatorica ,67 , 175-188.

sarah-marie belcastro and Thomas Hull (2002 ). Classifying frieze patterns without using groups . The College Mathematics Journal ,33 , 93-98.

sarah-marie belcastro and Thomas Hull (2002 ). Modelling the folding of paper into three dimensions using affine transformations . Linear Algebra and its Applications ,348 , 273-282.

Nancy Eaton and Thomas C. Hull (1997 ). Defective list colorings of planar graphs . Bulletin of the Institute of Combinatorics and its Applications ,25 , 79-87.

Thomas C. Hull (1996 ). A note on "impossible" paper folding . American Mathematical Monthly ,103 , 242-243.

Thomas C. Hull (1994 ). On the mathematics of flat origamis . Congressus Numerantium ,100 , 215-224.

Conference Proceedings

E. Demaine, M. Demaine, D. Huffman, T. Hull, D. Koschutz, T. Tachi (2016 , September ). Zero-area reciprocal diagram of origami . IASS Annual Symposium 2016 “Spatial Structures in the 21st Century” Tokyo, Japan