We haven’t finished this yet, but we still wanted to tell you about it. It’s Kazuo Haga’s new book, Origamics: Mathematical Explorations Through Paper Folding (ISBN-13: 978-9812834898).
We’re no math head — anything above the most primitive forms of trig causes us anxiety and vague spiritual discomfort. That isn’t because we don’t enjoy the underlying principles of mathematics; it’s because mathematicians, ever since the late Renaissance, have insisted on divorcing number from distance and stacking abstraction upon abstraction until Hell won’t have it. We’re sure it’s all very interesting, if you can master the syntax — but that’s where we get off. We like geometry, not this airy-fairy chop-logic they teach in the schools.
So this books hits me where I live — I already knew the three Haga theorems from Kasahara’s books, Origami³ and the article on the Tanteidan site, but useful as they are, I can’t say I ever really understood where they came from or how they worked. The first few chapters work you through the reasoning behind the theorems and then delightfully extend them to silver rectangles — you know, A4 and its ilk. Nice, slow presentation, with a very personable narrator and the math remains within the world of the real. A very pleasant read.
Example: in the midst of discussing his third theorem, Haga comments:
I thought of this folding more than 10 years after the publication of Haga’s second theorem. My profession is biology, and for a while I concentrated on a new phenomenon in my field, and so I did not have time to play with those paper squares. I used to do paper folding while riding on the bus or train. I thought of this new way of folding while I was on a bus going from Tokyo station to Tsukuba Center. I did not notice I was talking to myself at that time, until some of the other passengers started staring at me. Suddenly, I felt embarrassed. Nevertheless, I was excited by my discovery and continued to look for relations as the bus proceeded.
I suppose we all like to read ourselves into any novel that comes to hand — as an inveterate bus folder, I found this little confession just delightful.
The middle of the book delves into distribution maps and this, of course, goes right by me. Maybe I’ll get it the next time I read through. Tend to doubt it, though.
The last section is a wonderful fairytale about the King of Origami Land, who throws a wandering stranger into the dungeon for daring to fold rectangles instead of squares. The stranger is sentenced to starve in jail, unless he can fold his A4 into 17 equal sections. Won’t tell you how it ends, but it’s a rattling good story and not a bad reflection on the hegemony of the square-headed over today’s Origami Land.
The world needs more such math books.