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# Origami and Math: Simple to Complex

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Paperfolders at every level of expertise will appreciate this original compilation of models inspired by mathematical principles. Origami master John Montroll presents 39 projects, each made from a single square sheet of paper. Models range from the simplicity of a triangle to highly complex cubicles and other geometric shapes.
Montroll, who is noted for meticulously developed folding sequences that result in better models with fewer steps, provides detailed instructions and diagrams. He also discusses techniques for dividing paper into fractions, folding to any location on the edge of the square, and using mathematics to attain precision in folding animal models, including camels and elephants. Other models include a collection of polygons, 2-D and 3-D models that employ pentagonal symmetry, and eight chessboards of increasing complexity.

Dover Original.

5 Questions with John Montroll: An Exclusive Dover Interview

We sat down with Mr. Montroll to discuss his influences, the impact of math on origami, and what he sees for the future of the artform.

How did you first get interested in origami and what were your influences?
I was four when a Japanese neighbor taught me origami. At six, I had some books, showing the Japanese style.

Where do you find the inspiration for your original models?
The models in the books were made by folding, cutting, using multiple sheets, and sometimes from non-square paper. I wanted to make origami where each model could be folded from a single uncut square so I had to make them up. Since I started as a child, "creating" was natural. Whatever I wanted to fold, I would make up. There was nothing great about my models, but I enjoyed exploring and found there was no end. In time, my work evolved as I discovered more techniques, and also philosophies, in the quality of origami. Now I can say that developing new, theme-related ideas and writing books gives me inspiration.

Do you think that there is a strong relationship between origami and mathematics?
Yes. There is much math — geometry, algebra, trigonometry, etc. — in the structure of folding which can be used to develop and control the folding methods and designs. Math is especially used in my Dover books Origami and Math and Classic Polyhedra Origami. Still, math is not essential and there are many aspects of origami that do not use math. Even if math was used in the design of a model, the folder need not understand it.

As a teacher, do you integrate origami into your lesson plans?
As a math teacher, I can say students love doing origami! Sometimes, if my students finish their class work early, I let them fold from my books. Or we have some days, such as before vacations, where we do origami. But I will admit that I do not use origami as part of the math lesson!

What new directions do you think the art of origami will be taking in the future?
In the past few decades, origami has made huge developments in many directions. More people are involved, more ideas have been explored, all with more styles and techniques. The future will reveal newer directions for more people to explore and find their particular interest.

Bonus Question!
Do you have a favorite Dover book?
I actually have two favorites, both by Beethoven: Complete Piano Sonatas, Volume I and Complete Piano Sonatas, Volume. II. I enjoy playing his work and these books are well tattered!

 Availability Usually ships in 24 to 48 hours ISBN 10 0486488861 ISBN 13 9780486488868 Author/Editor John Montroll Grade level 7 and Up (ages 12 and up) Page Count 120 Dimensions 8 1/2 x 11

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