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
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 wD, at a point on an edge of h to be the distance to the closest edge that is not adjacent to . 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 wDMD, 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.  M. Bern, B. Hayes, “The complexity of flat origamis”, Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, (1996) 175-183.  D. Fuchs, S. Tabachnikov, “More on paperfolding”, American Mathathematical Monthly, Vol. 106, No. 1, (1999) 27-35.  T. Hull, “On the mathematics of flat origamis”, Congressus Numerantium, Vol. 100, (1994) 215-224.