Jesús de la Peña Hernández
Fig. 5 is the final set as seen from the outside. Fig. 6 represents the sphere with its seat-
ing circle as explained above. Fig. 7 shows the cone with its three generatrices that are the lines
of tangency to the three circles of the sphere: they are, in turn, three sides of the above-
mentioned tetrahedron. Finally, Fig. 8 has in it all the lines required for full representation; as
we can see, there are many of them: that is the reason why it has been decomposed in the pre-
vious figures.20 PAPER FLEXIBILITY
It seems reasonable to touch upon this matter, for it is inseparable from origami. I do
dare say that along this book we only have dealt with paper flexibility, strictly speaking, but in
three occasions: while studying Möbius bands (Point 14.1), and in former Point 19 when con-
structing the cylinder and the cone.
The Spanish word for origami (paperfolding) is papiroflexia but in my opinion it would
be worthwhile coining the Spanish neologism papiroplegia, which is closer to folding than to
flexing. Of course I am aware that the flexia (flexing) is always previous to the plegia (folding),
but at the same time it seems a misuse to take the latter for the former indistinctly.
Note: The English suffix plegia (with a totally different meaning) exists in Spanish spelled as
plejia.
20.1 HOOKE ́S LAW
These preliminary considerations have led me to disclose, elementally though rigor-
ously, the flexibility of a piece of paper. Therefore I have decided to approach the study of its
modulus of elasticity, the Young ́s Modulus E that we find in Hooke ́s law. It is well known
that this law is the fundamental of materials resistance.
The first thing that came to my mind was to support a sheet of paper on the respective
edges of two books to allow it to flex freely as a beam resting on both extremities and subjected
to its own weight. Next, I should apply all the measurable data to the differential equation of
the elastic line in order to get E.
Soon I realised though, how problematic it was that configuration. My research con-
veyed me to the “Handbook of pulp and paper technology” where I could find an improved set-
up of my experiment: instead of having a beam resting on both extremities, the beam was
somehow embedded and left to be freely projected in the cantilever mode; look to Figs. 1 and 2
to see surmounted the difficulties inherent to double resting.