Mathematicians like to claim that math is in everything. I won’t start a discussion about if this is true. However, what I can tell you is that math is in origami. I am sure you all know the art of folding paper in creative shapes. Also it is an ancient Japanese art, it is a quite “young” hobby for the rest of the world. “Modern origami, in the sense of what one finds when looking at a typical origami instruction book, only dates back to the 1940s and 1950s.” Since then, a lot of progress has been made in this field. While in the 1970s the people thought, "It is impossible to make a grasshopper using one sheet of square paper”, we know know: it is possible. And we know: origami is not only free creative art, it also follows some certain rules. This is were the mathematicians entered the field. With increasing complexity of the origami figures, finding a way to fold them became more and more complicated. In the 1990s, “Fumiaki Kawahata, Toshiyuki Meguro, and Jun Maekawa in Japan and Robert Lang in the United States independently discovered a connection between origami design and circle-packing.” Every “peak” in a origami figure,… a leg/antenna/tooth/… needs to be made from a circle on the square paper. These circles can be on the border of the squared paper or in the middle of it. I can not explain why it has to be a circle. Let us believe that. Then I can tell you, that this way of thinking of “figure extensions” as circles is the base of the popular tree algorithm for designing folding schemes for origami figures. Every part of the planned figure becomes a point in a network scheme with lines (edges) between the points which correspond to the size relation of the later formed body part. This map is then projected to the squared paper by drawing for every point a circle with a radius corresponding to the edge length. The problem is to find a way to “arrange the circles, making them reasonably large and, for convenience, positioning them along axes of symmetry of the square, if possible.” The rest is “quite” easy: “connect some of the centers of neighboring circles with creases to begin an outline of the crease pattern.“ Of course there are now conputer programs for this (http://www.langorigami.com/article/treemaker please look here also for pictures as a visual support for my description). But fact is, this algorithm, based on mathematical rules, helps forming new origami figures and this is why math is in origami (as claimed in the beginning of this text). "Origami design secrets: mathematical methods for an ancient art."
Robert J. Lang and Thomas C. Hull The Mathematical Intelligencer 27.2 (2005): 92-95.
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IdeaI love to increase my general science knowledge by reading papers from different fields of science. Here I share some of them. Archiv
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