By Thomas Hull

The e-book includes papers from the complaints of the third overseas assembly of Origami technological know-how, Math, and schooling, backed via OrigamiUSA. They hide subject matters starting from the math of origami utilizing polygon structures and geometric projections, purposes, and technology of origami, and using origami in schooling.

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

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Let t be the planar graph obtained from the decomposition by removing all angle bisector edges and all edges along the boundary of h . We would like to find a set of edges - —a matching—such that each vertex of t lying in the interior of p is incident to exactly one edge of - . By reversing the orientations of the edges of -, we ensure that each vertex satisfies Maekawa’s $ 'LVN3DFNLQJ $OJRULWKP IRU DQ 2ULJDPL 0DJLF 7ULFN  )LJXUH  (a) Cutting out a tree xg (shaded) spanning interior corners leaves a tree of molecules x- .

Houdini. In Paper Magic, E. P. Dutton & Company, 1922, 176–177. [12] T. Hull. On the mathematics of flat origamis. Congressus Numerantium 100 (1994) 215–224. [13] R. Lang. A computational algorithm for origami design. Proc. 12th ACM Symp. Comp. Geometry, 1996, 98–105. [14] E. Lodi, L. Pagli, and N. Santoro, eds. Fun with Algorithms, Carleton Scientific, 1999. [15] National Standards and Emblems. Harper’s New Monthly Magazine 47 (1873) 171–181. [16] J. Ruppert. A new and simple algorithm for quality 2-dimensional mesh generation.

If an MV assignment is given as well, can we tell whether it is valid? These are also the focus of this survey. We will not discuss the special cases of flat origami tessellations, origami model design, or other science applications.  &ODVVLF 6LQJOH 9HUWH[ 5HVXOWV We start with the simplest case for flat origami folds. We define a single vertex fold to be a crease pattern (no MV assignment) with only one vertex in the interior of the paper and all crease lines incident to it. Intersections of creases on the boundary of the paper clearly follow different rules, and nothing of interest has been found to say about them thus far (except in origami design; see [14], [15]).

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