Origami 3 Third International Meeting of Origami Science, by Thomas Hull

By Thomas Hull

The e-book comprises papers from the court cases of the third overseas assembly of Origami technological know-how, Math, and schooling, backed by means of OrigamiUSA. They conceal themes starting from the math of origami utilizing polygon buildings and geometric projections, functions, and technological know-how of origami, and using origami in schooling.

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Extra info for Origami 3 Third International Meeting of Origami Science, Mathematics, and Education

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The cover and back cover of the pamphlet are glued to their adjacent pages, so that a quadrilateral thickens two old flaps and adds two new flaps. We continue gluing pamphlets between flaps of the growing book as we 3 Kawasaki’s Theorem for flat origami [4, 12] states that at any vertex interior to the paper, the sum of alternate angles must be dM(H .  0 %HUQ HW DO M V )LJXUH  Taping together a cut leading to a leaf of xg amounts to joining two “armpits” in the book of flaps. go down the tree.

The number of creases used by our algorithm is not really excessive, linear $ 'LVN3DFNLQJ $OJRULWKP IRU DQ 2ULJDPL 0DJLF 7ULFN  in the number of disks in the initial disk-packing. The number of disks, in turn, depends upon a fairly natural complexity measure of the polygon. Define the Local Feature Size, N37 w€D, at a point € on an edge of h to be the distance to the closest edge that is not adjacent to [16]. The local feature size is small at narrow necks of the polygon. $It is not hard to see that the number of disks around the boundary of h is 5w (h dbMN37 w€DMD, where the integral is over the boundary of h .

Hull, “Modelling the folding of paper into three dimensions using affine transformations”, Linear Algebra and Its Applications, to appear. [2] M. Bern, B. Hayes, “The complexity of flat origamis”, Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, (1996) 175-183. [3] D. Fuchs, S. Tabachnikov, “More on paperfolding”, American Mathathematical Monthly, Vol. 106, No. 1, (1999) 27-35. [4] T. Hull, “On the mathematics of flat origamis”, Congressus Numerantium, Vol. 100, (1994) 215-224.

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