IXIn connection with the above mentioned demonstrations I have to say that not always are
shown all their steps, in some occasions because of its simplicity and in others, on the contrary, due
to its complexity. When this complexity would carry us too far away of origami, I have preferred to
take for granted what is already demonstrated in specialised books of mathematics.
A demonstration is made once and is not repeated anymore. So, it may happen that if the or-
der of a certain themes has been changed as required by book editing, a subject may have its demon-
stration not in its first appearance. Nevertheless I hope that the intended demonstrative rigour is kept
generally throughout the book
I wish to add that I had no intention whatsoever to cover all the exhaustive information
available. My ruling criterion to choose the subjects was, in the first place to show a didactic or re-
search projection, and then to keep an adequate balance between maths and paperfolding.
I mentioned before the use of CAD along this book. All its figures have been drawn with
CAD. There is no special difficulty with 2D figures but that may not be the case with 3D ones:
sometimes I have been forced to develop calculus programs to help the analytical CAD support.
The reader will find a bibliography at the end of the book. Since in origami not always is
easy to assign the name of the author to a given work, I have made this assignment in the text only
in cases when the situation was clear to me. The list of acknowledgements is, besides that, a kind of
fuzzy bibliography.
.
Hereinbefore I said that origami is performed just only with paper used at the same time as
raw material and instrument. But as a matter of fact, I have taken licence to some exceptions that do
not injure its foundation and, at the same time, help the practice. Those exceptions may be such as
marking with a pencil by transparency, using scissors to cut or mark creases, the use of adhesive
paper or glue to fix 3D figures, etc.
I never had the intention to compete with origami process creators that achieve complex
geometrical figures of a great merit: now bodies out of a single paper, now figures made out of
moduli, in both cases perfectly locked up: whenever the risk of loosing the balance between origami
and maths, I always reverted to the licence I mentioned before.
I have to refer also that the reader will find in between some chapters (just to cover blankspaces in the text) the so-called Interlude. What is shown there has nothing to do with maths,
but represents a series of beautiful figures that will break with the possible tiresome mathematical
developments. The crease pattern and complete figure are shown together to graphic scale. I should
recommend the curious reader to try to get the first without looking at it, just fixing his attention in
the finished figure: it ́s an exciting exercise. Many of the complete figures have been taken from, or
merely inspired by Makio Araki and Toshikazu Kawasaki.
A relation of origami symbols is included to help those fond of maths but not familiar with
origami practises. At the end, the only thing left is to ask for patience and comprehension to those
inclined to origami rather than to maths. This is the kindest request of
THE AUTHOR