Amazing Origami
A real treat! This is a super book. From the moment I opened the cover I was excited. Not only is it a book on origami (of which I have many), it is a book about maths and origami.
There are three chapters, the first is called Dividing Areas and incorporates a lovely proof. You have the physical evidence that the area of the triangle is 1, but as you fold the triangles into smaller and smaller similar triangles you reach a limit with the parts not quite adding up to 1. It certainly grabbed the attention of my students. They easily accepted that if we went on folding an infinite number of times we would reach 1 as the limit of the sum. They were confident with the answer 1 because of the use of origami. The origami proof was easily accessible and very visible.
Next you are shown how to divide a piece of paper into any odd number of parts by iteration. You can then go on to make shooting stars. Theoretical exactness and errors are discussed as you are shown how to fold a three-dimensional drawing template for a regular pentagon.
The second chapter entitled ‘Fun with Geometry’ shows how the impossible becomes possible! You cannot construct 7, 9, or 11-sided polygons by just using a pair of compasses and a ruler (Euclidean construction). However, just by folding a strip of paper you can! I was eager to try and began, as invited, with a pentagon. A strip, which for the pentagon was a quarter of a square, is used. The folding was very straightforward and rhythmic and once I was brave enough to almost pull it apart to join the two ends, I had rather a neat pentagon. You can then progress to larger sided polygon by folding a square into the required number of sections (again using the iterative technique) and doing some rather nifty folding to find exactly the right place to cut the strip before folding up the polygon. As you might be able to tell, I am hooked and intend to incorporate whatever I can into my teaching of polygons to my Year 8 class in a few weeks time.
Before closing Chapter 2, I must tell you about more proofs and some work on tangrams. There is a lovely proof of Pythagoras' Theorem along with three different folding proofs for the sum of the angles on a straight line. The tangram work is inspiring and reveals twenty different ways in which you can fold a square in half and then challenges you to use the pieces to make the four given puzzles. What is more you can use the seven pieces of the original Chinese tangram to make each of the twenty shapes, proving once again that all the pieces are equal in area.
Chapter 3 looks at three-dimensional objects starting with nesting boxes (in two different ways), and then looking at variations on the cube, where different corners are inverted or different colour combinations are used. The rest of the platonic solids and various variations of them are then offered before a final challenge to the reader to take these solids and really observe them and explore their relationships with each other.
This book has so much to offer being rich in mathematics and origami and by using the ideas in the classroom will certainly enrich your students' mathematical experience. This is a fascinating and wonderful book, buy it, enjoy it and let your students enjoy it too.
Review by: Julie Gibbon
Amazing Origami
Kunihiko Kasahara
Sterling Publishing
ISBN 0806958219
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