Mathematical Models of Origami and Origami Design
These articles deal exclusively with making a mathematical model of
origami (usually topological or combinatorial) in hopes of gaining a
better understanding of the paperfolding process.
- Azuma, Hideki, Some mathematical observations on flat foldings
(abstract), Abstracts for the Second International Meeting of Origami
Science and Scientific Origami, Otsu, Japan (1994), 45-46.
- Bern, Marshall and Barry Hayes, The complexity of flat origamis,
Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete
Algorithms (1996) 175-183.
- Davis, Chandler, The set of non-linearity of a convex
piecewise-linear function, Scripta Mathematica, Vol. 24 (1959),
219-228.
- Di Francesco, P., Folding and coloring problems in mathematics and
physics, Bulletin of the American Mathematical Society, Vol. 37, No. 3
(July 2000), 251-307.
- Duncan, J.P., Duncan, J.L., Folded developables, Proceedings of
the Royal Society of London, Series A, Vol. 383 (1982), 191-205.
- Fuchs, D., Tabachnikov, S., More on paperfolding, The American
Mathematical Monthly, Vol. 106, No. 1 (Jan. 1999), 27-35.
- Huffman, David A., Curvature and creases: a primer on paper,
IEEE Transactions on Computers, Vol. C-25, No. 10 (Oct. 1976),
1010-1019.
- Hull, Thomas, On the mathematics of flat origamis, Congressus
Numerantium, Vol. 100 (1994), 215-224.
- Hull, Thomas, Origami math, parts 1, 2, 3 and 4, Newsletter for
Origami USA, No. 49-52 (Fall 1994 - Fall 1995).
- Justin, Jacques, Mathematics of origami, part 9, British
Origami, (June 1986), 28-30.
- Justin, Jacques, Aspects mathematiques du pliage de papier (in
French), Proceedings of the First International Meeting of Origami Science
and
Technology, H. Huzita ed. (1989), 263-277.
- Justin, Jacques, Mathematical remarks about origami bases,
Symmetry: Culture and Science, Vol. 5, No. 2 (1994), 153-165.
- Justin, Jacques, Towards a mathematical theory of origami,
Origami Science and Art, K. Miura ed., Otsu, Japan (1997), 15-30.
- Kawahata, Fumiaki, The technique to fold free angles of
formative art "origami", Origami Science and Art,
K. Miura ed., Otsu, Japan (1997), 63-72.
- Kawasaki, Toshikazu, On high dimensional flat origamis,
Proceedings of the First International Meeting of Origami Science and
Technology, H. Huzita ed. (1989), 131-141.
- Kawasaki, Toshikazu, On solid crystallographic origamis [in
Japanese], Sasebo College of Technology Report, Vol. 24 (1987),
101-109.
- Kawasaki, Toshikazu, On the relation between mountain-creases and
valley-creases of a flat origami [abridged, English translation],
Proceedings of the First International Meeting of Origami Science and
Technology, H. Huzita ed. (1989), 229-237.
- Kawasaki, Toshikazu, On the relation between mountain-creases and
valley-creases of a flat origami [unabridged, in Japanese], Sasebo
College of Technology Report, Vol. 27 (1990), 55-80.
- Kawasaki, Toshikazu, R(gamma)=1, Origami Science and Art,
K. Miura ed., Otsu, Japan (1997), 31-40.
- Kawasaki, Toshikazu and Masaaki Yoshida, Crystallographic flat
origamis, Memoirs of the Faculty of Science, Kyushu University, Series
A, Vol. 42, No. 2 (1988), 153-157.
- Koehler, J., Folding a strip of stamps, Journal of
Combinatorial Theory, Vol. 5 (1968), 135-152.
- Lang, Robert J., A computational algorithm for origami design,
Proceedings of the 12th Annual Symposium on Computational Geometry
(1996), 98-105.
- Lang, Robert J., Mathematical algorithms for origami design,
Symmetry: Culture and Science, Vol. 5, No. 2 (1994), 115-152.
- Lang, Robert J., The tree method of origami design,
Origami Science and Art, K. Miura ed., Otsu, Japan (1997), 73-82.
- Lunnon, W.F., A map-folding problem, Mathematics of
Computation, Vol. 22, No. 101 (1968), 193-199.
- Lunnon, W.F., Multi-dimensional map folding, The Computer
Journal, Vol. 14, No. 1 (1971), 75-80.
- Maekawa, Jun, Evolution of origami organisms, Symmetry: Culture
and Science, Vol. 5, No. 2 (1994), 167-177.
- Maekawa, Jun, Similarity in origami (abstract), Abstracts for
the Second International Meeting of Origami Science and Scientific
Origami, Otsu, Japan (1994), 65-66.
- Miura, Koryo, A note on intrinsic geometry of origami,
Proceedings of the First International Meeting of Origami Science and
Technology, H. Huzita ed. (1989), 239-249.
- Miura, Koryo, Folds - the basis of origami, Symmetry: Culture
and Science, Vol. 5, No. 1 (1994), 13-22.
- Miura, Koryo, Fold - its physical and mathematical principles,
Origami Science and Art, K. Miura ed., Otsu, Japan (1997), 41-50.
- Suzuki, Kunio, Creative origami "snowflakes": some new approaches
to geometric origami (abstract), Abstracts for the Second
International Meeting of Origami Science and Scientific Origami,
Otsu, Japan (1994), 37-38.
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