E-grāmata: Origamics: Mathematical Explorations Through Paper Folding [World Scientific e-book]

While most people are familiar with origami, those animals and other shapes made by folding paper, few of us have thought of paper-folding as anything but an art or craft. For biologist Haga, however, the results of paper folding can shed light on the relationship between mathematics and the physical world. In this first of his books to be translated into English, readers are taken through a series of exercises in which origami creations illustrate common theorems in high school-level math. Exercises range from the simple (creating a Pythagorean triangle) to complex (dividing a line into as many as 17 equal segments). Sadly, a somewhat pedantic English translation sometimes gets in the way of the subject matter. While the book is aimed at teachers, readers who are mathematically inclined should also find much of interest in its pages. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)

The art of origami, or paper folding, is carried out using a square piece of paper to obtain attractive figures of animals, flowers or other familiar figures. It is easy to see that origami has links with geometry. Creases and edges represent lines, intersecting creases and edges make angles, while the intersections themselves represent points. Because of its manipulative and experiential nature, origami could become an effective context for the learning and teaching of geometry.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 characterizes much of science activity can be recognized throughout the book, as the manipulative nature of origami allows much experimenting, comparing, visualizing, discovering and conjecturing. The reader is encouraged to fill in all the proofs, for his/her own satisfaction and for the sake of mathematical completeness. Thus, this book provides a useful, alternative approach for reinforcing and applying the theorems of high school mathematics.