VIIPREFACE
I must admit my difficulty to explain the title given to this book. As a matter of fact, it has
been an exercise to overcome the sense of amazement exhibited by my co-speakers.
The questions:
¿Can you imagine a hatful of maths within a paper folded hat of those made for us when little chil-
dren?
¿How many maths can be associated to the paper folded aeroplane of our childhood?
Not to mention our beloved pajarita, well known all around but difficult to draw properly by
almost everybody (try it if you are sceptical).
The hereby questions have to do with persons who know at least the relationship between
origami and paper folding, for most people are unaware of it. Learned persons use to mention Una-
muno at this point, and that ́s all. Commonly you may come across questions like this: Explain me
what papiroflexia means (papiroflexia is the Spanish word for origami), because it sounds like the
name of a disease ...
Therefore, if with origami happens what already we know, and mathematics are rather un-
popular, as also is recognised, the resultant of mixing both may be at least quite risky.
Nevertheless, my consciousness of the close affinity between geometry and origami, and my
fondness of geometry made me to endure an special affection towards origami.
Well before I came across origami, I had already published two treatises dealing with ge-
ometry.
The first of them, under the name of Tubes bent in space, was a study based on pure space
geometry to solve certain problems of the automotive industry. The second one was entitled 3D
measuring machines, geometric principles and practical considerations and aimed at the comput-
erisation of a 3D measuring mechanical outfit, through analytical geometry. It consisted basically in
a great deal of combined calculus programs to enable the 3D measurements of any component at the
workshop.
While digging out into the geometrical profile of origami I discovered that the art of folding
paper had many other ways of relationship with the mathematics such as infinitesimal calculus, al-
gebra, topology, projective geometry, etc. Eventually this particularity forced my decision for the
final title of the book.
In spite of that, there remains an important question that should be clarified: ¿Which helps to
which? ¿Origami to mathematics or viceversa?
The answer is not a simple one, for sometimes the paper folder employs mathematics not
been aware of it. For example, if I take a square of paper and fold its lower side over the upper one,
the result is a folding line which is the axis of symmetry that converts one side into the other; but I
do not necessarily need to know that I had played with the geometrical concept of symmetry to pro-
ceed with the rest of my folding.