Origamics : mathematical explorations through paper folding /

In this unique and original book, origami is an object of mathematical exploration. The activities in this book differ from ordinary origami in that no figures of objects result. Rather, they lead the reader to study the effects of the folding and seek patterns. The experimental approach that charac...

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Bibliographic Details
Main Author: Haga, Kazuo, 1934-
Other Authors: Fonacier, Josefina., Isoda, Masami.
Format: eBook
Published: Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2008.
Online Access:CONNECT
Table of Contents:
  • 1. A point opens the door to origamics. 1.1. Simple questions about origami. 1.2. Constructing a pythagorean triangle. 1.3. Dividing a line segment into three equal parts using no tools. 1.4. Extending toward a generalization
  • 2. New folds bring out new theorems. 2.1. Trisecting a line segment using Haga's second theorem field. 2.2. The position of point F is interesting. 2.3. Some findings related to Haga's third theorem fold
  • 3. Extension of the Haga's theorems to silver ratio rectangles. 3.1. Mathematical adventure by folding a copy paper. 3.2. Mysteries revealed from horizontal folding of copy paper. 3.3. Using standard copy paper with Haga's third theorem.
  • 4. X-lines with lots of surprises. 4.1. We begin with an arbitrary point. 4.2. Revelations concerning the points of intersection. 4.3. The center of the circumcircle! 4.4. How does the vertical position of the point of intersection vary? 4.5. Wonders still continue. 4.6. Solving the riddle of "[symbol]". 4.7. Another wonder
  • 5. "Intrasquares" and "extrasquares". 5.1. Do not fold exactly into halves. 5.2. What kind of polygons can you get? 5.3. How do you get a triangle or a quadrilateral? 5.4. Now to making a map. 5.5. This is the "scientific method". 5.6. Completing the map. 5.7. We must also make the map of the outer subdivision. 5.8. Let us calculate areas.
  • 6. A petal pattern from hexagons. 6.1. The origamics logo. 6.2. Folding a piece of paper by concentrating the four vertices at one point. 6.3. Remarks on polygonal figures of type n. 6.4. An approach to the problem using group study. 6.5. Reducing the work of paper folding; one eighth of the square will do. 6.6. Why does the petal pattern appear? 6.7. What are the areas of the regions?
  • 7. Heptagon regions exist? 7.1. Review of the folding procedure. 7.2. A heptagon appears! 7.3. Experimenting with rectangles with different ratios of sides. 7.4. Try a rhombus
  • 8. A wonder of eleven stars. 8.1. Experimenting with paper folding. 8.2. Discovering. 8.3. Proof. 8.4. Morer revelations regarding the intersections of the extensions of the creases. 8.5. Proof of the observation on the intersection points of extended edge-to-line creases. 8.6. The joy of discovering and the excitement of further searching.
  • 10. Inspiration from rectangular paper. 10.1. A scenario: the stern king of Origami Land. 10.2. Begin with a simpler problem: how to divide the rectangle horizontally and vertically into 3 equal parts. 10.3. A 5-parts division point; the pendulum idea helps. 10.4. A method for finding a 7-parts division point. 10.5. The investigation continues: try the pendulum idea on the 7-parts division method. 10.6. The search for 11-parts and 13-parts division point. 10.7. Another method for finding 11-parts and 13-parts division points. 10.8. Continue the trend of thought: 15-parts and 17-parts division points. 10.9. Some ideas related to the ratios for equal-parts division based on similar triangles. 10.10. Towards more division parts. 10.11. Generalizing to all rectangles.