Folding from circular paper

It's a long time ago now, but some subscribers to origami - L may remember the early books in English by Isao Honda which were published in the West from 1957. The models appeared to be derived from those of Akira Yoshizawa, but were inferior and often used cuts. However, the books were most cheerful and colourful. They all had actual folded models stuck to the pages. There were many of these books, the first ones not issued under Honda's own name, but under name of the Toto Origami Club, or the Asahi Origami Club. Later ones were published under Honda's own name. Undoubtedly the most delightful of these colourful books was a hardback titled "How to Make Origami" (1961). It was one of the books which inspired my own love of origami and I have often heard people mention this book and how it introduced them to the pastime.

Now I mention these books, not because they were themselves anything to do with circular origami: in fact, they were not, but they were part of a Japanese tradition of colourful books illustrated with actual folded models. The books of Tatsuo Miyawaki, published from 1964 onwards were of this kind and very cheerful happy books they are too, even if the standard of paperfolding was rather elementary. The books by Tatsuo Miyawaki were variously titled "Happy Origami", (four titles), "Pop-up Origami" (two titles) and Jolly Origami (two titles).

Then in 1966, a new series in much the same format by a new writer, Keinichi Fukuda began to appear. Like the books by Honda, they were colourful books illustrated with actual folded models But they were different in that they introduced the idea of circular origami and went appropriately under the generic name of "Sunny Origami". There were ten of these books altogether, the first being "Angel Book", published in 1966 and the last ones, "Frog Book", "Cat Book" and "Little Red Riding Hood", all published in 1972. The most interesting of the books were those "The Life of Buddha", "The Life of Jesus Christ" and "The Life of Shinran Shonin" which related in outline the lives of the respective religious leaders.

It seems to me that the packets of circular origami paper bought by Tim Heil and Steve Woodmansee were probably marketed in connection with this series of books. Each book was supplied with a packet of circles of paper of various sizes, but, of course, one packet would not go very far, and no doubt the publishers ensured that further packets could be bought from the shops.

It must be frankly stated that the standard of folding of these Sunny Origami Books is very elementary in the extreme. There is little folding in our sense of the word: just a few simple book folds. The books are illustrated with actual models, but they are more like collages than origami models. In fact, for a long time I listed these books in my library , not under "Paperfolding", but under "Other Paper-crafts"! But if they are accepted for what they are, these are very jolly, cheerful, colourful books. I think they answer Tim's and Steve's questions about what you did with the packets of circular paper. Whatever it was, it was not origami in our sense of the word!

This brings me to the deeper question folding circular paper. Is it possible to use it for creating models in the ordinary sense of origami? I think not.

Let us start by book-folding a circular piece of paper. We immediately get a straight line. Fold again and there is another straight line.. Before we have gone very far, we find that we have the same familiar crease patterns as when we fold square paper. The same basic folds appear and the only difference is that we find irrelevant segments of paper sticking our from the fold we have made. It may be possible to use these segments of paper creatively in the model, but the scope seems to be very limited. What about a rocking chair?

Another possibility may be the folding or a serial of radial pleats from the centre. We can fold an umbrella that way, but probably not much else. Perhaps we might just arrive at a peacock.

The most interesting use for folding a circle is so fold the paper in mountains and valleys from the centre, the creases being made not in straight lines, but in an increasing spiral from the centre, The paper can then be wound up to form a tight cylinder of paper around the axis passing vertically through the centre. This has seriously been suggested as a way of folding solar panels for space craft .

Fred Rohm was one of the most creative and original paperfolders of all time. He was self-taught and refused to read origami books in case they prejudiced his original approach to paperfolding. If anyone could have made anything of folding circular paper, he would have been that person. He discussed the problem in "Folder's Fodder", his column in "The Origamian" Vol. 6, No 2, for Summer 1966, where he wrote:

"Suffice to say that the thought of the use of a circle as a spring-board to new folds generally occurs to all creative folders at one time or another and I am no exception. The idea seems an intriguing one at first glance, for is it not true that the circle has no straight edges for use as guide lines? How can one 'book' fold something which is not rectangular or how does one fold a diagonal without corners from which to start? Why, the whole concept of folding could be changed with the circle replacing the square!

"But alas, one soon finds that the very first crease produces a straight line which, in spite of what we may wish, may be used as a 'diagonal or an edge. One soon finds that after the second or third creases the paper handling must be done just as though a square had been used in the first place. I also found that I became annoyed with the segments of the circle sticking out like sore thumbs! The net result was that, try as I might, my folds made from a circle were no more novel than those made from a square. Neither did my efforts produce any new folds. And a paper cutter can't cut a circle! So instead of starting a new folding trend, I just succeeded in spending a lot of valuable time in scissor-cutting circles, a practice which, if carried to extremes is not too far away from cutting paper dolls!"

I suggested earlier in this note that a folder might make use of the surplus curved segments to create a rocking chair. Fred Rohm r4eally did fold a rocking chair and it appears in Sam Randlett's "Best of Origami", published in 1963. The fold is of an old woman in a rocking chair and he gave it the title "Whistler's Mother" after the famous painting by Whistler. But no, Fred Rohm makes no attempt to fold from a circle. His fold is from a square, using a stretched bird base. It is, in fact, a clear demonstration that circular paper is not necessary even for models with curves.

The only other questions to be asked are: Why does paper always crease in a straight line? And complementary to this first question, two more: Are there any origami models which have curved lines? And: Can paper really be folded in a curved line?

I think I'll leave those questions for another time.

In response to my lack of enthusiasm for folding from circular paper, Robert Lang points out that many of the twist folds of Jeremy Shafer and Chris Palmer are "rather well" adapted to folding from circles.

Yes YES! I had overlooked the rotational qualties of twist folding. The nearest I got was the "spiral folding" proposed for satellite solar panels, but in that catagory, the folding of curved spiral lines presents practical difficulties for he folder. I really should have remembered the kind of folding developed with so much interest by Jeremy and Chris. I would like to point out, however, that their work springs from that of Shuzo Fujimoto. Yet Yoshihide Momotani invented the "twist" some years before Fujimoto. He used it to effect in some of his flowers, but never exploited it further. Possibly it had been invented before that, but I haven't yet consciously come across an earlier instance.

There are problably other approaches to folding which involve patterns rotated about a centre. Indeed, pentagonal, hexagonal and octagonal (et al.) folding is often, although not always, of this kind. The work of Philip Shen comes to mind, althouh he usually starts from a square. Here indeed is a fallow field to be tilled by someone who can release him/herself from the blinkers of folding from the traditional square and rectilinear creasing.

But modern origami "tesselations" are not limited to finite circles of origami paper of small size. The patterns develoed by Shuzo Fujimoto, Jeremy Shafer and Chris Palmer do not confine themseves to the bounds of the paper they are using, As they work outwards, so the actual shape of the paper they are using becomes irrelevant, and as far as the ultimate pattern they are folding is concerned, it doesn'f matter whether they are folding from square or circular paper or paper of any other shape. The GEOMETRY of folding is independent of the shape of the paper. (and, of course, the geometry is still made up of straight lines, whether they rotate or not.)

Now it may be possible to develop origami tessellations to the extent that the shape of the paper does becomes relevant, just as the number of carbon atoms in pure carbon, irrelevant in the open structures of diamond or graphite, does become relevant in the closed stucture of Carbon-60. Let's hope it does, because it will indicate that closed structures have been developed in origami tessellations, (I'm not particularly thinking of spheroid objects here - don't take my Buckyball analogy too far.) All I mean is that the tessellation would, from its inherent geometry, necessarily fit the shape of the paper in which the folding was started, whether circular or any other particular shape. That would be yet another leap forward in our understanding of the universe of paperfolding and how it works.

In the meantime I will continue to stuff all these new ideas into my file marked "Circular Origami". I hope that soon it will be thick and fat.