




Date: Fri, 6 Dec 1996 11:30:09 -0400 (AST)
From: DLister891@aol.com
Subject: Radomes and Soccer Balls: an Origami Sighting.

Regular and semi-regular polyhedra have long interested paperfolders - they
have a fascination which appeals to the "Origami Mind". This fascination has
increased for paperfolders with the development of modular folding as many
folders, from beginners to creative giants have struggled to fit their chosen
modules of folded paper together to construct ever larger and more complex
species of polyhedra.

The connection between modular folding and  ordinary origami has always
seemed to me somewhat tenuous, because the only aspect of real paperfolding
involved is the folding of countless identical modules of minimal
paperfolding interest and, as even enthusiastic modular folders admit, it
very boring. (It can, too, have a transcendental effect for those who are
prepared to explore techniques of meditation.) The real interest has been the
fitting of the modules together, and that is something quite different from
paperfolding. Nevertheless I, too, have been fascinated and I have followed
the work of Tomoko Fuse devotedly as she has produced book after book crammed
with unexpected ideas for modular origami. My own interests, outside
paperfolding, have extended to the geodesic domes designed by or invented by
or conceived by or discovered by the American architect Richard Buckminster
Fuller. There is a great fascination in the radomes which litter the world's
landscape and in the larger geodesic domes such as the one built  for Expo 67
at Montreal.

My bedtime reading this week is "The Most Beautiful Molecule" by Hugh
Aldersey-Williams about the discovery of the third molecular form of carbon
after graphite and diamond, (which have themselves intrigued mankind ever
since we began to take an interest in the world about us). The discovery by
Rick Smalley of the United States and Harry Kroto of Great Britain and their
assistants, among them Bob Curl, was so unexpected that it has captured the
imaginations of millions who were never remotely interested in chemistry and
has helped to rescue chemistry from the eclipse it had suffered in the shadow
of the great discoveries during this century, of nuclear physics and
astronomy. The research started in September, 1985 when Harry Kroto, of the
University of Sussex near Brighton on the south coast of England paid a visit
to Rice University in Houston Texas. There, a complicated piece of apparatus
had been developed, which Kroto though could help him in his research into
the formation of carbon molecules he had found to exist in space. Research
quickly led to a wholly unexpected result, a new form of carbon, which had
not only not been known before, but which had not existed even in the wildest
imaginations of speculative scientists.

The new form of carbon appeared to be a molecule of sixty atoms, and once
this was realised the conundrum was how a model should be constructed to give
a picture of the structure and chemical bonding of the molecule. Graphite is
in the form of flat "nets" of carbon atoms and It was thought that the
 "nets"  might wrap round and link up  to form spheres of sixty atoms. What
geometry would they take? A pattern of hexagons was suggested, but hexagons
could not in any way be curved to make a sphere It was thought that geodesic
domes might be an analogy and someone seemed to recall that they also
contained pentagons. Different members of the team experimented with cocktail
sticks and jelly sweets to build models. Rick Smalley went home and cut out
first cardboard hexagons, which would not work. He then cut out some
pentagons and found that by surrounding a pentagon with hexagons, he could
make a curved dish. He persisted and before long, he could see how he could
make a quasi-sphere using twenty hexagons separated by twelve pentagons. Then
the startling revelation came to him that it would have exactly sixty apexes
or  points! The apexes must be where the sixty carbon atoms lay in
relationship to each other. The puzzle was solved.

When the team met the next day, it was quickly discovered that this model
with sixty apexes was the simplest of Buckminster Fuller's geodesic domes
from which all the more complex domes were derived. In his larger, more
complex domes, Fuller merely divided the hexagons and pentagons into
triangles, and then subdivided the triangles into smaller triangles, to
created the thousands of facets of a large geodesic dome. Look carefully
among the subdivided hexagons of a geodesic dome  and you will always find
 just twelve pentagons (allowing for  the theoretical ones which are obscured
by the base of the dome). The researchers also discovered that  their
 quasi-sphere had a name and that it was officially known as a Truncated
Icosahedron. More prosaically, it was found to be in the form of a common
soccer ball, very familiar to most of the children on the Earth and some of
their fathers, too!

And my origami sighting? It comes on page 75 of "The Most Beautiful
Molecule":

"The group duly assembled in Rick's office. Rick came in and tossed his paper
model onto the table. They had all felt the solution, whatever it was would
be novel. But this was beyond their wildest expectations.

"Bob [Curl] kept his cool. He inspected the model. Then he said that he would
only believe it if the bonds worked out in the conventional fashion of other
aromatic molecules....... Rick had called it a day in the early hours without
going this final distance. He had done enough origami for one night. In the
event, it was readily shown with more sticky tape that the double and single
bonds went round the sphere in alternating pattern. It passed the Curl Test.
It really was special."

The new form of carbon was cumbersomely named "Buckminsterfullerene" in
honour of the inventor of the geodesic dome, or "buckyballs" for short. (I
cannot help thinking, however, that simply "Fullerene" would have been more
manageable and elegant.)

Since then the chemists of the world have been busily engaged in working out
related forms of carbon having the shapes of other  polyhedra with different
numbers of atoms or constructed as  long unclosed tubes. What practical use
will all be? We have to admit that we do not yet know for certain. Many
exciting ideas have been put forward;  an immense amount of research is being
carried out in numerous laboratories throughout the world, and it will
remarkable if nothing comes of this wholly  unexpected extension of organic
chemistry, the chemistry of life itself.

Despite Rick Smalley's weariness with "origami", it would be stretching the
point and completely unrealistic to claim that origami had much to do with
the discovery of Carbon 60. Yet the incident reminds us that the most
fundamental and important discoveries come from very simple concepts. Modular
paperfolders have long been familiar with the structures of polyhedra of
every kind. Mainstream origami, too, has its own peculiar geometry. Perhaps
one day, that geometry itself will throw light on a scientific problem of the
greatest importance and value for mankind, which at present nobody has ever
dreamed about.

Later Rick Smally and Harry Kroto compared notes and found that in 1967  they
had both made private visits with their wives to EXPO 67 at Montreal and had
both been fascinated by the huge geodesic dome that formed the United States
pavillion. They  had not then the slightest inkling that one day the most
elementary of geodesic domes would lead them to a fundamental discovery of
incalculable importance  Now they are united again. The two of them together
with  Bob Curl, have jointly been awarded the Nobel Prize for Chemistry. It
is to be presented to them in Stockholm next Tuesday, 10th December.

David Lister

Grimsby, England.

DLister891@AOL.com





Date: Fri, 6 Dec 1996 17:29:06 -0400 (AST)
From: DLister891@aol.com
Subject: Folding from Circlular paper.  [Long]

I feel very flattered by the favourable comments on my contributions made by
Tim Neil (29.11.96), Cathy Palmer-Lister (4.12.96) and Patricia Gallo
(4.12.96).

I will bear in mind the suggestions that I should write a book, but I must
point out that writing books isn't easy, and getting them published is even
harder. We'll see. At present I'm very much behind with my correspondence and
I apologise to everyone to whom I owe a letter. Time is the enemy. Not only
that, when it comes to writing an article, there must be something to spark
off the outflow of words.

It so happens that  Tim Hill has kindled the first sparks of an idea by
mentioning circular origami paper, followed by Steve Woodmansee, who was no
less baffled as to what to do with the stuff. I have also been reminded of
circular folding by a private communication telling me that a bookseller in
the United States has for sale a copy of  "Happy Origami". I thought a short
piece about circular origami might not come amiss. So here it is:

------------------------------------------------------------------------------
---

                                                    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.

David  Lister

Grimsby, England.





Date: Fri, 6 Dec 1996 22:19:05 -0400 (AST)
From: Valerie Vann <75070.304@compuserve.com>
Subject: Re: Radomes Soccer Balls Geodesic Modulars

David Lister, indefatigable origami historian
and master of origami trivia (in the best sense
of the word) writes:

<< The connection between modular folding and
<< ordinary origami has always
<< seemed to me somewhat tenuous, because the
<< only aspect of real paperfolding
<< involved is the folding of countless
<< identical modules of minimal
<< paperfolding interest

At the risk of raising the old argument that modular origami
is not really origami :-) I would comment that it seems to me
that the connection between folding modules and "ordinary
origami" is no more tenuous than folding "ordinary origami"
from materials which are so far removed from
paper that they lack the properties of paper,
have properties lacking in paper that are essential to
the design, or are used to circumvent what may be regarded
as the "shortcomings" of paper in the case of
the particular design. I refer to, for example, foil,
foil backed tissue, plastic or mylar "paper substitutes", etc.

The majority of modular folds, including traditional ones,
(kusudama) are of PAPER, plain and simple, and the form
and success of the module depends usually on exploiting or
working with the specific properties of folded paper, rather
than avoiding, ignoring or defeating those properties. In the
case of Business Card Origami (which again, some seem to
think is not origami), the specific properties of a specific
size, shape, and weight of heavy PAPER determine the
success of the resulting model. The same is true of
currency folds: many of these are no where as successful
when made of ordinary letter paper as they are when made
of the wonderfully strong malleable paper that is used for
USA currency.

<< The real interest has been the
<< fitting of the modules together, and
<< that is something quite different from
<< paperfolding

Again, I don't think it much different, if at all.
In my opinion, the best modular origami requires
engineering an assembly method that is feasible,
designing folds that stay folded, and usually,
a "locking method" that exploits both folds and
the properties of folded paper. The same can be said
of well-designed "ordinary origami", and especially
of those designs that can be best made, or at least
successfully made from "ordinary" paper. A Robert
Lang Lion comes to mind (no foil backed paper needed.)

Re: the "connection" between Fullerenes/"Bucky Balls"
(recently discovered carbon molecules with 60 atoms)
and origami:

First, while it is of course possible to model
a fullerene structure in origami, the actual paper model of
the fullerene "soccerball" polyhedral structure was not
origami in any sense usually attributed to origami.
It was made of hexagons and pentagons cut out of paper
and crudely joined on the edges with tape. (There was
a fascinating PBS television show - Nova series, I
think - about the Bucky Ball discoveries.)

I've been working on and off for about a year on a "real"
modular origami "Bucky Ball", i.e. not just a soccerball
polyhedron (20 hexagonal, 12 pentagonal faces, 90 edges),
however. I wanted one with "atoms" joined by "bonds",
so what I cooked up has little balls (polyhedrons) for
each of the apexes of the soccerball, joined by slender
narrow "struts" representing the "bonds". Since each
atom takes 12 modules plus one module per bond, there
are 810 modules involved, and assembly is rather tricky,
so there will probably be 14 more fullerenes discovered
and Tom Hull will get the Nobel in Mathmatics before
it gets finished. :-)

Geodesics:

There is a very "real" connection between modular origami
and geodesic principles: modular origami
often has geodesic properties, i.e. a structure whose
components are in tension and compression. Paper,
interestingly enough has good tensile strength in the
direction of the grain. Folded paper can have good
compressive strength also. (Witness the amazing strength
of the unit Jeannine Mosely is using in her "Mengers
Sponge fractal project.)

Like Buckminster Fuller geodesic domes, modular origami
polyhedral forms often are held in shape by interesting
combinations of tension and compression. Often the
method of approximating angles by folding, and/or
errors introduced by the thickness of the folded paper
cause the structure to tend to fly apart, while this
tendency is countered by a locking mechanism, so that
the units are in tension. Locking mechanisms are typically
dependent on exploiting a fold or crease, i.e. the paper
is "hooked" around a corner/edge. In other cases, the
"lock" is a product of the friction between adjacent
paper surfaces.

Also similar to geodesic dome construction, modular
origami designs sometimes depend on the ability of
the angle between the planes on the two sides of a
paper crease to widen or close in response to the forces
of the structure. In other words, the "connections" of the
structure (e.g. at the apexes of a polyhedral model)
can be "self-adjusting", so that the precise angle of
the joints doesn't have to be calculated, it will result
from the structural forces. This feature occurs in a
number of my "strut" unit models. This would be impossible
in a steel structure, for example, while in a folded
paper structure it is a major property of both the material
and the assembly method. All of which is
accomplished by using paper for the former, and "folding
paper" for the latter. (If that ain't origami, what is it?)

In some other designs, an open sink can be exploited as
a self-adjusting joint or apex that compensates for
angular approximation errors. My favorite example of this
is a unit designed by David Petty used to construct what
is geometrically an icosidodecahedron. Petty's module has
an open sink at the apex/intersection of each set of four
edges. The faces are convex, with planes sloping into the
center of the structure. However, the planes intersect at
a slightly too large angle (the "real angle" would be
difficult or impossible to fold accurately), so that in
Petty's original design, the sinks are under great
tensile forces and tend to split. By adding a second sink
in the opposite direction, the sink can be turned into
a four-way self-adjusting "hinge", relieving the destructive
tension. (This Petty unit is one of my all time favorites,
even in its original form; wonderfully elegant and
ingenious.)

In conclusion:

A number of origami practioners ("artists") have constructed
geodesic origami structures, myself included. Most recently
here on the list there was mention of an article:

> Ian Harrison in _Mathematics Teaching_ #153
> Dec 95 called "Origami Spheres".
> It consists of "strut modules" for
> building skeletal polyhedra.

R.A.Kennedy has described these "spheres" to me earlier as
being geodesic spheres, i.e. geodesified polyhedron models.

(A geodesified polyhedron typically has the non-triangular
faces filled in with triangles. The resulting polyhedron
has more edges, but is no longer "regular", since the length
of the additional edges vary in a calculated way that assures
that all the apexes of the polyhedron are equidistant from
the center of the polyhedron. Since the variation in the
"edge" length is typically small, there will be the appearance
of 6 equilateral triangles meeting at a single apex, which
is impossible in the geometry we all learned and loved
in school. :-)

Last summer I constructed a geodesified snub dodecahedron
using 210 of a very slender version of my basic "strut" unit.
The resulting sphere is very strong and rigid as a result of
the geodesic tensile forces and the "V" cross section of
the struts. I had discovered that all the struts (two
different lengths were required) could be made of identically
sized paper, since a simple variation in the folding
produced a shorter strut of the length required, within
less than 1% of the calculated edge length. (Dr. Robert
Lang was kind enough to verify my old fashioned calculations
using a computer program called Mathmatica.)

3 postscripts:

My thanks to David Lister, whose thoughtful contributions to
the origami-l sometimes singlehandedly uphold its status
as an "origami discussion group".

A Web search on "fullerenes" will turn up a wealth of
"Bucky Ball" sites, some with greath graphics. There are
some long helical DNA-looking forms of fullerenes. I'd
be tempted to build one, but it would take more modules
than Jeannine Mosely's Biz Card Fractal...

And for the technical diehards:
A soccerball polyhedron is a truncated icosahedron.

Valerie Vann
75070.304@compuserve.com
http://users.aol.com/valerivann/index.html





Date: Fri, 6 Dec 1996 22:27:15 -0400 (AST)
From: Rjlang@aol.com
Subject: Re: Folding from circular paper

I'd like to add a few comments on David Lister's commentary on folding from
circles, the general gist of which was that folding from a circle was
something of a force-fit to origami. I should point out that many of the
twist folds of Jeremy Shafer and Chris Palmer have both a centroid and
rotational and/or spiral symmetry about the centroid and are, in fact, rather
well adapted to folding from circles. One thing a circle offers that a square
does not is that it can be used for crease patterns that have arbitrary
N-fold rotation symmetry, while a square is a force fit for N not equal to a
power of 2. So, for example, Chris Palmer's hexagonal patterns fit a circle
better than a square, and I would bet that a decagonal tesselation based on
Penrose tiles would fit better as well.

I think the reason there aren't many origami models from circles is not that
circles are inherently less suitable than squares for origami. It's that
folks haven't really tried to exploit the unique attributes of the circle;
instead, they've tried to use the same techniques that they used on squares.
And as any good mathematician will tell you, squaring the circle doesn't work
very well!

Even among more convention origami, there are some models that work better
from a circle than from a square. For example, in _Origami Sea Life_, there's
a sea urchin based on a square tesselation that is one of a family of sea
urchins with 4, 16, 25, 36, etc., spines. There's another family of sea
urchins based on a hexagonal tesselation with 7, 19, 37, etc., spines; and
the hexagonal pattern fits more neatly into a circle than it does into a
square.

Finally, to answer some of David's closing questions:

> Why does paper always crease in a straight line?

Because the locus of points in a plane equidistant from two fixed points is a
straight line, is one way of putting it.

> Are there any origami models which have curved lines? And: Can paper really
be folded in a curved line?

There are oodles; many 3-D models have curved lines and curved creases. But
since David is well acquainted with the curved 3D works of Dave Brill and Max
Hulme, among others, I assume these questions were purely rhetorical!

Robert J. Lang





Date: Fri, 6 Dec 1996 22:40:59 -0400 (AST)
From: J Armstrong <jcanada@clark.net>
Subject: Re: Sightings

Another sighting: I was at the Bank of Montreal in Peterborough this
summer and there was a poster ad for the bank's services that included
fold marks to make some kind of plane.  the idea being that the bank was
as fast as a jet or some such garbage.





Date: Fri, 6 Dec 1996 22:56:42 -0400 (AST)
From: jdharris@post.cis.smu.edu (Jerry D. Harris)
Subject: The Forms of Origami

>At the risk of raising the old argument that modular origami
>is not really origami :-)

        I certainly don't want to jump into a form war here, but I'm
curious as to how many different "kinds" (I suppose, as an evolutionary
scientist, I ought to use the word "species"  8-D  ) of origami people
generally accept.  I usually only think of 3 different kinds:

* Single sheet -- obviously, where models are produced from single pieces
of paper (regardless of shape),

* Modular -- where a model is produced from several identical folded pieces
(modules).  Often there is only one kind of module used, but some models
require combinations of 2 or 3 module types, and

* Composite -- where a model is produced from two or more differing pieces.
Examples would be many of the models in Honda's _World of Origami_,
Yoshizawa's _Sosaku Origami_, and Kasahara's _Creative Origami_ where a
quadruped is composed of two pieces of paper:  one for the front end of the
body, and another for the rear; the two pieces require different folding
methods and are not identical (and thus are not "modules").

        Of course, I make no judgement about one being "superior" to any
other form; I simply prefer the first kind (and even then, I'm orthodox in
preferring only squares).  Does anyone else perceive it this way?  More
categories?  Less?

Jerry D. Harris                       (214) 768-2750
Dept. of Geological Sciences          FAX:  768-2701
Southern Methodist University
Box 750395                            jdharris@post.smu.edu
Dallas  TX  75275-0395                (Compuserve:  102354,2222)

                                              .--       ,
                                         ____/_  )_----'_\__
                                 ____----____/ / _--^-_   _ \_
                         ____----_o _----     ( (      ) ( \  \
                       _-_-- \ _/  -          ) '      / )  )  \
"Evolution: It's      _-_/   / /   /          /  '     /_/   /   \
Not For Every-       //   __/ /_) (          / \  \   / /   (_-C  \
Body!"              /(__--    /    '-_     /    \ \  / /    )  (\_)
                   /    o   (        '----'  __/  \_/ (____/   \
  -- Michael       /.. ../   .  .   ..  . .  -<_       ___/   _- \
     Feldman       \_____\.: . :.. _________-----_      -- __---_ \
                    VVVVV---------/VVVVVVVVV      \______--    /  \
                         VVVVVVVVV                   \_/  ___  '^-'___
                                           _________------   --='== . \
                     AAAAAAAAAAAAAAAAAAA--- .      o          -o---'  /





Date: Sat, 7 Dec 1996 00:30:12 -0400 (AST)
From: Marcia Mau <marcia.mau@pressroom.com>
Subject: Origami Sighting

Page B-16 of December 6th's Wall St. Journal newspaper has  an article about
Richard Smalley (who will receive the Nobel Prize for chemistry next
Tuesday) and a photo of his office whose theme is "homage to the buckyball."
The article mentions "A green and orange origami version, sent by an
admiring stranger, adorns his computer."  There is a large (non origami)
model of a buckyball in the photo.

Anyone know who sent the origami model?

David Lister's posting reminded me I had read this article earlier today.
Marcia Mau
Vienna, VA USA
marcia.mau@pressroom.com





Date: Sat, 7 Dec 1996 00:39:49 -0400 (AST)
From: Jean Villemaire <boyer@videotron.ca>
Subject: Re: The Forms of Origami

Jerry D. Harris wrote:
>
> >At the risk of raising the old argument that modular origami
> >is not really origami :-)
>
>         I certainly don't want to jump into a form war here, but I'm
> curious as to how many different "kinds" (I suppose, as an evolutionary
> scientist, I ought to use the word "species"  8-D  ) of origami people
> generally accept.  I usually only think of 3 different kinds:
>
> * Single sheet -- obviously, where models are produced from single pieces
> of paper (regardless of shape),
>
> * Modular -- where a model is produced from several identical folded pieces
> (modules).  Often there is only one kind of module used, but some models
> require combinations of 2 or 3 module types, and
>
> * Composite -- where a model is produced from two or more differing pieces.
> Examples would be many of the models in Honda's _World of Origami_,
> Yoshizawa's _Sosaku Origami_, and Kasahara's _Creative Origami_ where a
> quadruped is composed of two pieces of paper:  one for the front end of the
> body, and another for the rear; the two pieces require different folding
> methods and are not identical (and thus are not "modules").
>
>         Of course, I make no judgement about one being "superior" to any
> other form; I simply prefer the first kind (and even then, I'm orthodox in
> preferring only squares).  Does anyone else perceive it this way?  More
> categories?  Less?

My question would be :  how many ways are there to name categories in
origami?  This is one way : single sheet vs multiple sheets (which may
subdivide in modular and composite or compound).  Or origami on square,
rectangular, triangular, circle paper, papermoney, tickets.  These would be
definition by ways of folding.  We could also include historical approach:
origami pre-sinks vs post-sinks, traditionnal vs modern...  Then, we could
use subjects, maybe a meta-index of models:  figurative vs abstract (which
would include all geometrical, ball origami...), naturalistic, theatrical
(origami scenes), functional (magical, containers, flying, domestic objects
such as wallets...)  And many more.  Maybe even your friendly "shared and
artistic" would come out as kinds.  Or pure, pureland...

We need to get our categories in order.  It depends on what you intend to do
with such definitions of origami.

I suppose Joseph will tell me again I'm wrong.  Well I had fun writing this.

Jean Villemaire
Montreal, Quebec
boyer@videotron.ca





Date: Sat, 7 Dec 1996 07:45:04 -0400 (AST)
From: Steve Woodmansee <stevew@empnet.com>
Subject: Re: Folding from Circlular paper.

David's very interesting response to our thread concerning circular origami
paper prompted some additional thoughts, especially in view of this section
of his post:
>
(in progress)
>...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.
>
So far, I've worked exclusively with square paper.  Anything more or less
seems tainted, even though I know that sounds foolish.  The square offers a
particular symmetry and balance that to me is an integral part of the zen of
folding.

My objection to round paper is the same as that described by David Lister;
almost immediately one must reduce the round paper to straight angles.  To
me, this is at odds with that which is so magical about origami, that
something  so rigid (straight lines, squares) can be made to do so much
without corrupting the source material by cutting or pre-conditioning.
Starting out with round paper seems to miss the point of the exercise.

I'm sure I'll find myself alone in this sentiment, but I feel the same way
(though to a far lesser degree) about rectangular or other non-square paper.
If the paper must be conditioned before being folded, the origami seems
somehow less pure, as if we could not accomplish everything we set out to do
unless we cut some corners (unforgivable pun).

Incidentally, it's been over 20 years since I last saw the round paper - has
anyone seen any lately?

                         ''~``
                        ( o o )
+------------------.oooO--(_)--Oooo.------------------+
|                                                     |
|          "Origami: Welcome to the Fold!"            |
|                Steve Woodmansee                     |
|              Bend, Oregon U.S.A.                    |
|                                                     |
|                    .oooO                            |
|                    (   )   Oooo.                    |





Date: Sat, 7 Dec 1996 07:57:47 -0400 (AST)
From: Steve Woodmansee <stevew@empnet.com>
Subject: Montroll's Prehistoric Origami

I can't remember if I've already posted this, so am doing so again just to
be sure.

In my recent travels I have inadvertently purchased two copies of John
Montroll's Prehistoric Origami (They have two different covers; one is a
photograph of the models, the other is a drawing).

I know that for most people this is not a hard-to-find book, but if anyone
wants it and hasn't been able to obtain it through conventional means I
would be happy to trade or ...?

Please respond by private e-mail if interested.

                         ''~``
                        ( o o )
+------------------.oooO--(_)--Oooo.------------------+
|                                                     |
|          "Origami: Welcome to the Fold!"            |
|                Steve Woodmansee                     |
|              Bend, Oregon U.S.A.                    |
|                                                     |
|                    .oooO                            |
|                    (   )   Oooo.                    |





Date: Sat, 7 Dec 1996 15:06:24 -0400 (AST)
From: Valerie Vann <75070.304@compuserve.com>
Subject: Origami math-ed article

Tom Hull writes:

<<another origami-math related article!  The
<<reference...
<<"Folded Paper, Dynamic Geometry, and Proof: a three-tier approach to the
<<conics" by Daniel Scher, _Mathematics Teacher_, March 1996, Vol 89, No 3,
<<pp. 188-193.
<<This article tell you how to fold parabolas, ellipses and hyperbolas
<<into a sheet of paper.  It's nothing new, but it's darn cool to see this
<<stuff resurface in the math education literature!

For those without ready access to this Math Teacher journal,
try the classic:

Geometric Exercises in Paper Folding
T. Sundara Row
Dover Publications
ISBN 0-486-21594-6

This isn't origami, but it's available from OUSA supply
center or any bookseller. Still in print when last I
looked.

Since the original was written in 1893, published in 1905,
and picked up by Dover in 1966, the current generation
accustomed to lots of pictures and interactive computer
graphics may find it rather tough going, but if you
persist and follow along paper in hand, you might end up
able to design your own origami sea shell.

It covers construction of polygons, tri-sections, and the
Conic Sections (parabola, ellipse, hyperbola, and other
stuff like the limacon and cycloid, all using a sheet
of square paper instead of the usual geometry tools.

[My apologies to Tom for sending him this direct; I forgot
I was using the email program that requires manually setting
the recipient to the origami-l...]

Valerie Vann
75070.304@compuserve.com





Date: Sat, 7 Dec 1996 15:08:23 -0400 (AST)
From: Valerie Vann <75070.304@compuserve.com>
Subject: Rose

I agree the "diagonal" Rose ("Rose II")is more difficult
than the "Rose I" ("square Rose"). It took me 3 tries to
get a satisfactory result. It tears very easily in the
middle sink.

Those attempting the Rose I from the Origami for the
Con. diagrams for the first time should also be aware
that the diagrams in the book are for a "bud" or not
fully-open rose. A slight modification of the outer
petals and closure method are required to get the
fully-blooming rose pictured in the book.

<< Is the Rose square?>>

Actually, both Roses are "Four-Fold" (real roses
are five-fold), and the bottom closure involves
four flaps in both cases.

Rose I can be mounted on a Sonobe Cube made
from the same size square paper as the Rose.

Strong malleable paper that will work into soft
curves with handling helps both Roses, though
I do both with regular 6 inch kami (standard origami
paper.)

--valerie
Valerie Vann
75070.304@compuserve.com





Date: Sat, 7 Dec 1996 16:32:18 -0400 (AST)
From: "Sergei Y. Afonkin" <sergei@origami.nit.spb.su>
Subject: Fingers... only ten fingers! Could you help?

   Dear friends,

   One of our origami-student collects different games and trick  with
human fingers  because she give such lessons for children in a primary
school. Knowing me as subscriber of origami-l she asked  me  to  write
this message.  May be you know some literature written about the item.
It seems to me that I have seen one  by  Eric  Kenneway  in  London...
Small old pocketbook...  In case you know literature of that kind (may
be more modern one), please inform me. I will be very grateful!

Your Sergei Afonkin, the chairman of St.Petersburg Origami Center
                                  ,    ,
sergei@origami.nit.spb.su        ("\''/").___..--''"`-._
                                 `9_ 9  )   `-.  (     ).`-.__.`)
                                 (_Y_.)'  ._   )  `._ `. ``-..-'





Date: Sat, 7 Dec 1996 19:12:47 -0400 (AST)
From: halgall@netverk.com.ar
Subject: Re: Folding from Circlular paper.

David, Steve, and others,

I read the commentaries about folds in circular paper and
seem very interesting.

I works many with circular paper and I have realized many folds
in this paper,  for children. If well, are not folds in 3D, folds are
where the children can use the imagination to believe stories
with the folds.
I believe that the teaching of folds in circular paper in children
of kindergardens is good, firstly because is in agreement with
the first figure geometryic that teach ( in our plans of study ),
second, because help in the teaching of other form.

Many of that are working or worked with children,  we are knowing
that the first drawings that they realize are with  tadpoles form,
and with the time transform it in circle, therefore tell that the circle
 is the first geometryic figure that incorporate the children in their
knowledges.
The folds of Mrs. Dubreton and Mrs.Elyane Felez-Greit, are a sample
of folds in circular paper dedicated to the children.

The circular paper has not the attributes of the paper square ( do not
refer to me to the paper,  if not the manner ), for this, does not wants
to tell that we not could realize lovely folds. I am in agreement,
when tell that in group seem a collage.

IMHO,  the basic pliegues known differ many if we are thinking to
apply to the circular paper, for this case,  must establish new based,
but for folds in circular paper.

Happy Folding!!!

Patricia Gallo





Date: Sat, 7 Dec 1996 23:42:55 -0400 (AST)
From: Steven Casey <scasey@enternet.com.au>
Subject: Re: Fingers... only ten fingers! Could you help?

>   Dear friends,
>
>   One of our origami-student collects different games and trick  with
>human fingers  because she give such lessons for children in a primary
>school. Knowing me as subscriber of origami-l she asked  me  to  write
>this message.  May be you know some literature written about the item.
>It seems to me that I have seen one  by  Eric  Kenneway  in  London...
>Small old pocketbook...  In case you know literature of that kind (may
>be more modern one), please inform me. I will be very grateful!
>
>
>Your Sergei Afonkin, the chairman of St.Petersburg Origami Center
>                                  ,    ,
>sergei@origami.nit.spb.su        ("\''/").___..--''"`-._
>                                 `9_ 9  )   `-.  (     ).`-.__.`)
>                                 (_Y_.)'  ._   )  `._ `. ``-..-'
>                               _..`--'_..-_/  /--'_.' .'
>                              (((.-''  (((.'    (((.-'
>
>

The name of the book by Eric Kenneway is :

Fingers Knuckles and Thumbs - Tricks and games for hands

ISBN 0 600 33659 X

A book about tricks, games and illusions to perform using just your own pair
of hands. Covers things like hand shadows, cats cradle, finger and thumb
pictures, "This is the church, this is the steeple...", Pat a Cake,
Scissors,paper,stone,
finger stretching,thumb snatching, the old magnetic hand trick all the old
school yard tricks and games.

Cheers,

Steven Casey,
scasey@enternet.com.au
Melbourne Australia





Date: Sun, 8 Dec 1996 01:15:13 -0400 (AST)
From: Steven Casey <scasey@enternet.com.au>
Subject: Spiral folds (Formerly: Folding from circular paper)

Re Spiral/ curved folding & Escher, a sighting:

In previous posting David Lister asks:

>> Are there any origami models which have curved lines? And: Can paper really
>be folded in a curved line?

And Robert Lang responded with:

>There are oodles; many 3-D models have curved lines and curved creases. But
>since David is well acquainted with the curved 3D works of Dave Brill and Max
>Hulme, among others, I assume these questions were purely rhetorical!
>
>Robert J. Lang
>

This thread has reminded me of an article in Scientific American in
September 1991 on page 27.

Its a Profile on David A. Huffman subtitled "Encoding the "neatness" of Ones
and Zeroes"

The following is a very condensed version giving a little background on
David A. Huffman.

Part 1 Background:
In 1951, at age 25 David E. Huffman created a data compression scheme some
of you might be familiar with known as Huffman Encoding. Its a system that
is used in VCR's, computer networks, modems, high definition TV and numerous
other devises.

His doctoral thesis was on formal methods for devising asynchronous
sequential switching circuits, an important type of computer logic.

During the 60's he outlined a method for converting one sequence of numbers
into another without loosing any information in the translation, a technique
that obvious applications in cryptography.

Due to family problems in early years he lagged behind other children by two
years in learning to speak. His mother, tried to help by becoming a
mathematics teacher at a school for troubled children. But a series of tests
immediately made clear to his mother and teachers that his reticence had
masked precociousness. At School, Huffman soon leapfrogged his classmates.
He finished a Bachelor's Degree in Electrical Engineering at age 18.

Huffman believes his tumultuous early years fostered a love of mathematics.
"I like things neat" he says. "I like to wrap things up and get definitive
answers, possibly because of the uncertainties of my early life.

Part 2 Escher:
In the early 1970's Huffman became a debunker of optical illusions. What
inspired him were the seemingly incongruous shapes in the work of M.C.
Escher: Triangles containing three right angles for example. Inspecting
Escher's creations, which he admires, led him to devise a set of rules to
determine whether an artists picture or a video image had cheated in
depicting a two- dimensional representation of a three dimensional scene.

Huffman determined a method for showing whether boundaries between
geometrical element in an image- represented as Y, V or T shapes, amongst
others- logically fit into a coherent pattern. He describes his proof as an
image grammar."I wanted to create a sieve so grammatical pictures would go
through and ungrammatical images would be seen as unrealizable," he says.
This contribution to the young field of scene analysis, has been used in
developing machine vision systems for robots.

In the early 80's Huffman published a paper that proved that a digital
computer could be designed that would virtually eliminate one of the staples
of Boolean Algebra. He showed that a hypothetical machine could function
using only one NOT operation.

Part3 The sighting!:

Since that time, Huffman has exchanged paper writing for paperfolding. He
wanted to see how the lines and intersections on the flat surfaces that he
had poured over in his work on scene analysis could be folded into three
dimensional sculptures. Using a stylus to emboss lines into paper or vinyl
sheets, he has concocted *spirals*, *domes* and other shapes. Huffman has
lectured on the theory and practice of paperfolding at M.I.T. and Standford
among other institutions.

The article shows a picture of Huffman with some of his creations. One is a
six sided sheet of paper with curved creases spiraling out from the centre
another is a rectangle with concentric curved creases.

One famous model I know of that employs curved folding is the "Lazy Susan"

Cheers,

Steve Casey
scasey@enternet.com.au
Melbourne Australia





Date: Sun, 8 Dec 1996 04:32:51 -0400 (AST)
From: Tim Heil <teach@ezl.com>
Subject: Re: Folding from Circlular paper.

        Many thanks to David Lister for his comments on circular paper.

        I don't remember clearly but the title "Sunny Origami" sounds
vaguely familiar and may, in fact, have been on the packages of circular
paper my wife brought to me. Perhaps Steve Woodmansee's memory is better
than mine on that account. All of the folds in that package were indeed very
elementary, including the butterfly I mentioned.  Also, that butterfly could
have been just as easily folded from square paper and did not require round
paper at all.

        I believe that Robert Lang and Patricia Gallo are correct in that
circular paper's unique attributes have probably not been fully explored.
However, I also think that Fred Rohm was probably correct in that there is a
very limited range for this exploration.  If radial or rotational symmetry
nor curved raw edges are not involved in a model then I can see little
advantage to using circular paper.  However, I would be happy if someone
could prove that statement wrong and show us some interesting folds from
circular paper.

        Finally, speaking of shapes other than square paper (The new guy's a
heretic!  Stone him! :), in Honda's "The World of Origami" are mentioned
rhombic, pentagonal, hexagonal and octagonal paper, but no models are
diagrammed using any of them.  There are crease patterns shown for some
models, but my origami skills are not yet developed enough for me to figure
them out.  Does anyone know if there were any models from these shapes in
the unabridged edition?  I have only the abridged paperback version.
----------------------------------------------------------------
|| Tim Heil                ||     I wouldn't have seen it     ||
|| (teach@ezl.com)         ||     if I hadn't believed it.    ||





Date: Sun, 8 Dec 1996 04:33:49 -0400 (AST)
From: Tim Heil <teach@ezl.com>
Subject: Re: Fingers... only tenfingers!

        If Sergei means "purse" by "pocketbook", there is a traditional
purse called a "tato" described and diagrammed in "Complete Origami" by Eric
Kenneway, p. 167 in my copy.

        There is also a traditional purse on pp. 38-39 of "Secrets of
Origami" by Robert Harbin.  I have seen this purse and a related hexagonal
purse folded in leather.

        Hope this helps, Sergei.
----------------------------------------------------------------
|| Tim Heil                ||     I wouldn't have seen it     ||
|| (teach@ezl.com)         ||     if I hadn't believed it.    ||





Date: Sun, 8 Dec 1996 05:10:18 -0400 (AST)
From: Steve Woodmansee <stevew@empnet.com>
Subject: Re: Folding from Circlular paper.

At 04:33 AM 12/8/96 -0400, you wrote:
(snip)
>        I don't remember clearly but the title "Sunny Origami" sounds
>vaguely familiar and may, in fact, have been on the packages of circular
>paper my wife brought to me. Perhaps Steve Woodmansee's memory is better
>than mine on that account. All of the folds in that package were indeed very
>elementary, including the butterfly I mentioned.  Also, that butterfly could
>have been just as easily folded from square paper and did not require round
>paper at all.
>
I don't remember the name of the paper kit which contained the round paper
but I do vaguely recall the butterfly Tim mentions.  In the kit I had (kit=a
bunch of round paper and a 1-page folded set of basic diagrams), most of the
models involved small cuts, for example to make the antennae on the
butterfly.  Between the lack of adequate diagrams and the need to cut the
paper to achieve the finished model, all of my origami alarms were being set
off.  Still, I'd be willing to give it another try if there were diagrams
available that followed "origami purist" methods.

I do think it is significant that the topic has sparked some discussion in
this group - I believe we are all intrigued by the possibility that there is
a whole other world of origami possibilities lurking in the shadows of this
obscure paper.

                         ''~``
                        ( o o )
+------------------.oooO--(_)--Oooo.------------------+
|                                                     |
|          "Origami: Welcome to the Fold!"            |
|                Steve Woodmansee                     |
|              Bend, Oregon U.S.A.                    |
|                                                     |
|                    .oooO                            |
|                    (   )   Oooo.                    |





Date: Sun, 8 Dec 1996 05:16:30 -0400 (AST)
From: Steve Woodmansee <stevew@empnet.com>
Subject: Honda's Hardback edition (was Re: Folding from Circlular paper)

At 04:33 AM 12/8/96 -0400, Tim Heil wrote:

..(snip snip) in Honda's "The World of Origami" are mentioned
>rhombic, pentagonal, hexagonal and octagonal paper, but no models are
>diagrammed using any of them.  There are crease patterns shown for some
>models, but my origami skills are not yet developed enough for me to figure
>them out.  Does anyone know if there were any models from these shapes in
>the unabridged edition?  I have only the abridged paperback version.

Many years ago when I first encountered the Honda book, it was in the form
of a hardback edition in my Junior High School library.  I distinctly recall
several models in that edition that are not in the paperback edition I
purchased some years later.  I seem to recall that among them was a piano, a
sambo (?), and several more.  The Sambo (hope I got that right) is pictured
in the paperback edition being carried by two monkeys, but the diagrams are
not given.

I recall these models especially because I was allowed to do an entire
showcase in the school library containing all of my origami models and the
two I mentioned are in several photographs of the exhibit that were taken at
the time.

Surely someone out there has the original hardback?  If so, what models are
unique to the hardcover edition?  Are any of these available in the archives?

                         ''~``
                        ( o o )
+------------------.oooO--(_)--Oooo.------------------+
|                                                     |
|          "Origami: Welcome to the Fold!"            |
|                Steve Woodmansee                     |
|              Bend, Oregon U.S.A.                    |
|                                                     |
|                    .oooO                            |
|                    (   )   Oooo.                    |
