Associate Professor of Applied Mathematics, Franklin & Marshall College, Lancaster, PA
August 2023-present Courses taught
Calculus I (Active Calculus text; used derivative gateway exams, regular in-class group work, group homework, writing assignments)
Linear Algebra and Differential Equations (Andrilli & Hecker and Blanchard, Devaney, & Hall texts; Mathematica labs)
Associate Professor, Western New England University, Department of Mathematical Sciences
September 2008-May 2023 Undergraduate courses taught
Calculus I, II, III (Hughes-Hallett and Active Calculus texts; used derivative and integration gateway exams, regular in-class group work, group homework, graphing calculators, and Mathematica/Sage labs)
Linear Algebra (Andrilli & Hecker text; taught in computer classroom in discovery-based manner with emphasis on learning proof-writing; take-home exams; Mathematica used extensively)
Modern Aspects of Geometry (Stillwell text; Euclidean, spherical, hyperbolic, and projective geometries covered; GeoGebra, Spherical Easel and other software used extensively in-class and for hw; required individual projects with written and presentation assessments)
Creative Problem Solving (Zeitz text; focus on different tactics and tools for problem-solving and for communicating solutions; regular in-class presentations; take-home exams)
Graph Theory (Chartrand & Zhang and Trudeau texts; required readings, with class time spent on problems and proofs)
Combinatorics (Mazur text; required readings, with class time spend on group work; problem presentations by everyone at the start of every class)
Real Analysis (Schumacher text and Marsden-Hoffman text; inquiry-based class with required readings and assigned proof presentations; take-home exams)
Real Analysis II (Marsden-Hoffman and Wilcox-Myers texts; inquiry-based class with required readings and assigned problem presentations, covered Lesbegue measure and integration)
Topology (taught seminar-style using Morris' open text Topology Without Tears)
Senior Research Projects (advised year-long projects, major paper drafting, conference presentations)
Aubrey Babcock, The Mathematics of Rubik's Cube, 2009-2010
John Liberti, Angle Trisection, 2009-2010
Amy Lindquist, The Mathematics of Sudoku, 2010-2011
Mikaela Berthiaume, Finding the Optimal Strut Width of Five Intersecting Tetrahedra, 2011-2012
Jillian Sawyer, Fractals and Origami, 2012-2013
Jessica Ginepro, A Combinatorial Exploration of the Miura Map Fold, 2013-2014
Krista Kelly, Origami and Abstract Algebra, 2013-2014
Alyssa Gehm, Exploring and Counting Polyhedral Nets, 2014-2015
Sarah Vogel, The Structure of Spherical Buckyballs, 2014-2015
Kristen Kenny, An Upper Bound for Valid Mountain-Valley Assignments of the Snake Tessellation, 2015-2016
Noah Moreau, Chaotic Properties in Exchange Rates, 2017-2018
Lindsay Williams, The Rubik's Cube: Mathematics and Applications, 2017-2018
Alyssa Stefanelli, Fractals and Image Compression, 2019-2020
Aubrey Rumbolt, A Mathematical Study of M. C. Escher's "Up and Down,"" 2019-2020
Johnna Farnham, The Mandelbrot Set, 2020-2021
Xin Yan, The Lebesgue Integral, 2020-2021
Master of Arts for Mathematics Teachers courses taught
All courses emphasized proof-writing and incorporated in-class group work and regular presentation of solutions.
Discrete Mathematics (Ensley & Crawley and belcastro text; inquiry-based learning class; readings and presentations required)
Creative Problem Solving (Polya and Zeitz texts; daily problem activities to emphasize problem-solving strategies and communication of solutions; final paper and presentation required)
Calculus Revisited (Marsden and Tromba text; extensive group projects on textbooks from the calculus reform movement)
Geometry Revisited (Stillwell text with supplements on hyperbolic geometry from Apostle; GeoGebra, Spherical Easel, and other software used extensively)
Analysis (Marsden-Hoffman text with supplements on Lebesgue integral; student-presentation intensive)
Algebraic Structures (Judson text; covered groups, rings, fields, and some Galois Theory; weekly assigned problem presentations)
Fractals and Topology (Barnsley's Superfractals text; taught in computer classroom with extensive use of Mathematica)
Origami in Mathematics and Education (Hull text; activity-driven class with emphasis on conjecture and proof-building; final projects to design activities for use in their own classes)
Director, MathILy-EST REU
Summer 2019
NSF-funded REU held at Bryn Mawr College, 8-week program supervising research with six undergraduates.
Lead Instructor, MathILy, Bryn Mawr College
Summers, 2013-18, 20-21
MathILy (which stands for serious Mathematics Infused with Levity) is a 5-week summer enrichment program for talented high-school students. I have taught intensive courses on linear algebra, proof techniques, generating functions, projective geometry, finite difference calculus, complex analysis, dynamical systems, and origami mathematics for this program.
Assistant & Associate Professor, Merrimack College, Department of Mathematics
September 1997-May 2008
Courses taught: Discrete Mathematics, Calculus for Business, Precalculus, Calculus I, II, III, Topics in Geometry, Combinatorics, Abstract Algebra, Combinatorial Geometry, Introduction to Real Analysis, Directed Studies: Topology, Chaos and Fractals, Advanced Origami Geometry
Staff, Hampshire College Summer Studies in Mathematics (HCSSiM) Summers, 1991-1994, 1998-2009
HCSSiM is a six-week enrichment program for talented high-school students. Throughout the years I have taught a wide range of subjects there, including proof techniques, graph theory, group theory, generating functions, fractal geometry, projective geometry, discrete dynamical systems, set theory, automata theory, Markov chains, and origami mathematics.
Visiting Assistant Professor, University of Cincinnati, Department of Mathematical Sciences
2002-2003
On leave from Merrimack College. Courses taught: Honors Calculus I, II, and III, Calculus III Mathematica Lab, Finite Math Calculus.
Mathematics Instructor, The Math Circle, Harvard and Northeastern University Fall 2000
Research Papers
I am interested in the modeling of folding processes (origami), combinatorics, graph theory, and discrete geometry.
See my Origami Research Corner for details.
Face flips in origami tessellations, with Hugo Akitaya, Vida Dujmovic, David Eppstein, Kshitji Jain, and Anna Lubiw, Journal of Computational Geometry, Vol. 11, No. 1 (2020), 397-417.
Rigid foldability is NP-hard, with Hugo Akitaya, Erik D. Demaine, Takashi Horiyama, Jason Ku, and Tomohiro Tachi, Journal of Computational Geometry, Vol. 11, No. 1 (2020), 93-124.
Rigid foldability of the augmented square twist, with Michael Urbanski*, Origami^{7}: Proc. of the 7th International Meeting on Origami Science, Mathematics, and Education, Tarquin (2018), 533-543.
Box Pleating is Hard, with Hugo Akitaya, Kenny Cheung, Erik D. Demaine, Takashi Horiyama, Jason Ku, Tomohiro Tachi, Ryuhei Uehara, in Akiyama et al. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2015. Lecture Notes in Computer Science, Vol. 9943, Springer (2016), 167-179.
Rigid origami vertices: conditions and forcing sets, with Zachary Abel, Jason Cantarella, Erik D. Demaine, David Eppstein, Jason Ku, Robert Lang, and Tomohiro Tachi, Journal of Computational Geometry, Vol. 7, No. 1 (2016), 171-184.
Locked rigid origami with multiple degrees of freedom, with Zachary Abel and Tomohiro Tachi, in Miura et al. (eds.), Origami^{6}: Proc. of the 6th International Meeting on Origami Science, Mathematics, and Education, AMS (2015), 131-138.
Rigid flattening of polyhedra with slits, with Zachary Abel, Robert Connelly, Erik D. Demaine, Martin L. Demaine, Anna Lubiw, and Tomohiro Tachi, in Miura et al. (eds.), Origami^{6}: Proc. 6th Int. Meeting on Origami Science, Mathematics, and Education, AMS (2015), 109-117.
Symmetric colorings of polypolyhedra, with sarah-marie belcastro, Origami^{6}: Proc. of the 6th International Meeting on Origami Science, Mathematics, and Education, AMS (2015), 21-31.
Minimum forcing sets for Miura folding patterns, with Brad Ballinger, Mirella Damian, David Eppstein, Robin Flatland, and Jessica Ginepro*, ACM-SIAM Symposium on Discrete Algorithms (SODA15), ACM (2015), 136-147.
Counting Miura-ori foldings, with Jessica Ginepro*, Journal of Integer Sequences, Vol. 17 (2014), Article 14.10.8.
The flat vertex fold sequences, with Erik Chang, Origami^{5}: Fifth International Meeting of Origami in Science, Mathematics, and Education, Lang et al. ed., A K Peters (2011), 599-607.
Configuration spaces for flat vertex folds, in Origami^{4}: Fourth International Meeting of Origami Science, Mathematics, and Education, Lang ed., AK Peters, (2009), 361-370.
Folding regular heptagons, in Homage to a Pied Puzzler, Pegg et al., ed., AK Peters (2009), 181-191.
The combinatorics of flat folds: a survey, in Origami^{3}: Third International Meeting of Origami Science, Mathematics, and Education, Hull ed., A K Peters (2002), 29-38.
Folding points to a point and lines to a line, with Hugo Akitaya, Brad Ballinger, Erik Demaine, and Christiane Schmidt, in He, Sheehy eds., Proceedings of the 33rd Canadian Conference on Computational Geometry (CCCG 2021), 271-278.
Double-line rigid origami, with Tomohiro Tachi, Proceedings of the 11th Asian Forum on Graphic Science, August 6-10, 2017, Tokyo, Japan, H. Suzuki (ed.)
Zero-area reciprocal diagram of origami, with Erik D. Demaine, Martin Demaine, David Huffman, Duks Koschitz, Tomohiro Tachi, Proceedings of the IASS Annual Symposium 2016 "Spatial Structures in the 21st Century", September 26-30, 2016, Tokyo, Japan, K. Kawaguchi, M. Ohsaki, T. Takeuchi (eds.)
Project Origami: Activities for Exploring Mathematics, 2nd edition, CRC Press/AK Peters, Wellesley, MA (2012).
Translated into Japanese under the title ドクター・ハルの折り紙数学教室 by Nippon Hyoronsha, Tokyo (2015) and in Chinese under 數學摺紙計畫 by Shimao Publishing, New Taipei City, Taiwan (2018).
"Origami: Art, Geometry, and Robots,” for the National Night of the Classical High School, Italy (invited speaker, over Zoom, May 5, 2023).
"Origami: Where Art, Math, and Science Meet,” Deerfield Gallery Art Association Fiddleheads Gallery, Northfield, MA (invited speaker, April 21, 2023).
"Origami: Doing Math and Science without Scissors or Glue” and "Rigid Origami and No-hands Folding,” Pi Mu Epsilon Conference, University of Saint Benedict and Saint John's College, Collegeville, MN (invited speaker, April 14-15, 2023).
"Flexible 3D structures arising from a non-Euclidean rigid origami vertex duality," AMS Special Session on Mathematics and Art, Joint Mathematics Meetings, Boston, MA, (invited speaker, Jan. 4-7, 2023).
"Rigid origami applications in engineering: configuration spaces and self-folding," AMS Special Section on Real World Applications of Mathematics, Joint Mathematics Meetings, (invited speaker, online conference, April 6-9, 2022)
"Mathematical Origami and its Myriad Applications,"" Spring 2022 Section Meeting of the Eastern Pennsylvania-Deleware MAA Section (invited speaker, online conference, April 2, 2022)
"Face Flips in Flat Origami and the Origami Flip Graph," Art, mathematics and engineering based on the science of origami symposium, Advanced Mathematical Science Institute, Meiji University, Tokyo, Japan (keynote speaker, given via Zoom, Dec. 2, 2021)
"Folding Points to a Point and Lines to a Line," 33rd Canadian Conference on Computational Geometry, CCCG, (online conference, August 12, 2021)
"Origami and Math: Paper, Polymers, and Robots" for STEM World: Free Virtual STEM Convention, hosted by STEMEY (invited speaker, given via Zoom, August 15, 2020)
"Origami-Mathematics: How to fold paper, polymers, and robots," Pi Mu Epsilon Student Mathematics Conference, Moravian College, PA (keynote address, February 22, 2020)
"The Persistent Usefulness of Origami Mathematics in Engineering : Some New Results to Consider," The Third International Workshop on Origami Engineering (IWOE 2020), Melbourne, Australia (invited lecture given remotely, via Zoom, January 21, 2020)
"Folding Compact Manifolds and Modern Origami," Mathematics Colloquium, University of Essex, Colchester, UK (invited speaker, Sept. 3, 2018)
"Rigid Foldability of the Augmented Square Twist," 7th International Meeting of Origami Science, Mathematics, and Education, Oxford University, Oxford, UK (Sept., 2018)
"Self-foldability of Monohedral Quadrilateral Origami Tessellations," 7th International Meeting of Origami Science, Mathematics, and Education, Oxford University, Oxford, UK (Sept., 2018)
"Folding Paper, Polymers, and Robots: Origami & Math," Common Hour Talk, Franklin & Marshall College, Lancaster, PA (invited speaker, Feb. 15, 2018) https://tinyurl.com/yad652vo
"Combinatorial Geometry in Origami: the Kawasaki-Maekawa Connection," Joint Meetings of the AMS/MAA, San Diego, CA (Jan., 2018)
"The Central Role of Combinatorics in Origami," Origami-based Geometric Modeling and Analysis Symposium, Meiji University, Tokyo, Japan, (keynote speaker, Aug. 2017)
"Double-Line Rigid Origami," 11th Asian Forum on Graphic Science, The University of Tokyo, Komaba Campus, Japan (Aug. 2017)
"Self-foldability and Rigid Origami," MEAM Seminar, University of Pennsylvania (invited speaker, June 2017)
"Origami: How to Do Math and Science Without Scissors or Glue," National Academy of Sciences Distinctive Voices Lecture Series, Irving, CA (Dec. 2016) http://www.nasonline.org/programs/distinctive-voices/
"Origami-Mathematics and Applications" Yokohama National University, Yokohama, Japan (invited speaker, Nov. 2015) International Christian University, Mitaka, Japan (invited speaker, Dec. 2015)
"Folding a New Tomorrow: Origami Meets Math and Science," Distinguished Lecture Series, MAA Carriage House, Washington D.C. (invited speaker, Nov. 2015) https://www.youtube.com/watch?v=c3SJ7W6OWfM
"Folding Compact Manifolds Without Boundary: An Origami Perspective," Mathematics Colloquium, Worcester Polytechnic University, Worcester, MA (invited speaker, Sept. 2015)
"Modern Origami Theory," 14th Japanese-American Frontiers of Science (JAFoS) Symposium, National Academy of Sciences/Japan Society for the Promotion of Science, Tokyo, Japan (invited speaker, Dec. 2014)
"Mathematical Methods in Origami, Self-Folding, and Meta-Materials," ASME Conference on Smart Materials, Adaptive Structures, and Intelligent Systems, Newport, RI (invited speaker, Sept. 2014)
• "Counting Miura-ori Phantom Folds," 6th International Meeting of Origami Science, Mathematics, and Education, University of Tokyo, Tokyo, Japan (August, 2014)
• "Forcing Sets in Self-folding Origami," SIAM Conference on Discrete Mathematics, Minn., MN (June 2014)
"Origami Tessellations, their Symmetry, and Applications," St. Louis University Department of Mathematics and Computer Science Colloquium, St. Louis, MO (invited speaker, April 2011)
"Counting Foldings: Origami Via Combinatorics," Lafayette College REU, Easton, PA (invited speaker, July 2010)
(and an additional 23 talks given since 2010)
Grants
NSF, PI, standard research grant: RUI: Configuration Spaces of Rigid Origami (DMS-1906202)
Awarded July 2019, $220,000, 3-year grant to study configuration spaces of rigidly-foldable origami mechanisms. Supports undergraduate research and outreach through Western New England University's MAMT program.
Japan Society for the Promotion of Science (JSPS) Grant
Funded 2-week research visit at the Univ. of Tokyo, Japan to work with Dr. Tomohiro Tachi, Aug. 6-19, 2017.
NSF, Co-PI, NSF Emerging Frontiers in Research and Innovation ODISSEI grant: Meta-Materials from Self-Folding Polymer Sheets (EFRI-1240441)
PI: Christian Santangelo (UMass), Co-PIs: Itai Cohen (Cornell), Ryan Hayward (UMass), Thomas Hull, awarded August 2012. $2 million, 5-year grant to develop theory and mechanics of a self-folding polymer technology. Supported undergraduate research and outreach through the MAMT program at Western New England University.
MAA/NSF, PI, Regional Undergraduate Mathematics Conference (RUMC) grant
Awarded June 2011, $5000 grant to help host the Hudson River Undergraduate Mathematics Conference at WNE in April 2012.
Awards
Western New England University’s 2018 Arts and Sciences Faculty Research Award, May 2018
Murray Fellowship Award, Merrimack College, 2004–2005
$10,000 grant to pursue research work and book-writing projects in origami-mathematics.
Yoshino Award, Japanese Origami Academic Society, 2004
Funded invitation to the 2004 convention of the JOAS, where I gave a presentation at Toyo University on the uses of paper folding in education.
Project NExT Fellow, 1998–1999 (silver dot)
Competitive MAA Fellowship for new Ph.D.s. Helped organize panel discussions for Project NExT fellows at the 1999 AMS/MAA Joint Meetings.
Best Practices in K-12 STEM Research Workshop (invited participant), Green Bank Observatory, WV (April 10-12, 2022)
NSF Panel reviewer (Fall 2019)
Program Committee member for 7OSME (the 7th International Meeting of Origami in Science, Mathematics, and Education), Oxford University (Sept. 5–7, 2018)
External Examiner for a math Ph.D. defense on origami mathematics, University of Essex, UK, (Sept 4, 2018)
Kavli Japanese-American Frontiers of Science, Program Group Member (2014–2016, co-chair 2016)
Organized AMS Special Session on Origami Methods and Applications with E. Demaine and R. Lang, Joint Mathematics Meetings (Seattle 2016)
Hudson River Undergraduate Mathematics Conference, Steering Committee Chair (2012) Managed planning and local organization of the 2012 HRUMC, held at Western New England University
Arnold Ross Lecture Committee, AMS (2008–2011, chair 2010–2011)
Organized MAA Invited Paper Session on The Mathematics of Origami with T. Veenstra Joint Mathematics Meetings (San Francisco 2010)
Project NExT Consultant (2009–2010, 2016–2017)
Board of Directors: Origami USA (a national non-profit cultural and educational arts organization) (1995–2008)
MAA minicourse “Using Origami in Undergraduate Mathematics Classes” Joint Mathematics Meetings (New Orleans 2007, Atlanta 2005, Phoenix 2004)
Panel Discussion: Getting your first book published, Joint Mathematics Meetings (Jan. 2007)
3rd International Meeting of Origami Science, Math, and Education, Program Chair, Asilomar Conference Center, Monterey, CA (March 2001)
Organized AMS Special Session on Mathematical Methods in Paper Folding with R. Lang, Joint Mathematics Meetings, Baltimore, MD (Jan. 1998)
Referee for numerous journals, 6-8 papers per year, including The American Mathematical Monthly, Mathematics Magazine, The College Mathematics Journal, SoCG, MathSciNet, Discrete and Computational Geometry, Journal of Computational Geometry, Science, Nature, Physics Review Letters, and ASME journals.