Origami: technique, art, technology | Roberto Gretter | TEDxTrento

Origami is a skill capable of turning a sheet of paper into a work of art. Origami geometry is responsible for all astonishing models that we can fold nowadays, and spreading them out is key to grasp their secrets. Twist and tessellation lay the foundations of many technological applications.

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This is the pangolin of Eric Joisel.
It is an origami,

it is folded by only one esagonal
sheet of paper, without any cut.

Origami's rules are easy:

(Applause)

you take a sheet of paper and fold it,
you don't use any scissors or glue.

Origami is an art - and it takes
a bit of courage to say it -

because almost all
think that origami is simply...

a child's play.

I will try to change your mind.

Today origami is this:

every model has its author,
this is a horse made by Roman Diaz...

who is a veterinary capable to
capture the essence of animals.

Instead Robert Lang
is one of the origami's theorists.

Among other things,
he formulated a theory...

about how to design complex origami,
of which I will just tell you something.

This is a model of mine,
a three-dimensional pram.

Satoshi Kamiya is known for creating
very complex models like this wasp,

while Giang Dinh
made simplicity his magic bullet:

he works with wet cardboard,

he sprinkles it
and he can obtain these plastic figures.

Eric Joisel is an other author,
the pangolin's author too,

and he is a master
in creating also human figures

and using the volume of the paper

to create effects like, for example,
Harlequin's legs.

How have we reached this point?

Let's start from the simpliest thing:
the square base.

It is a paper square. First you fold
the medians, then the diagonals,

close it and you obtain this figure:
it is a square base and it has 4 flaps.

No surprises, it comes from a square:
4 sides, 4 angles, 4 flaps.

Folding a model by John Montroll,

at a certain point,
you get your hands on this stuff,

which seems a square base,
but has 5 flaps instead of 4.

So you ask yourself,

"But how, I started from a square:
where does the fifth flap come from?"

The trick to understand this,

to understand how it works,
is to reopen the sheet.

So you reopen the sheet
and you will see that the author...

didn't do nothing but drawing
a pentagon inside the square...

and hiding all the exceeding paper.

So the message here is,

"If you want to understand
how it works, reopen the model."

This is one of the scorpions
made by Robert Lang...

it has a lot of tips.

To understand how this runs,
it has to know how an umbrella works.

So imagine:
a closed umbrella is the folded end,

an open umbrella is the paper
which is needed to obtain that end.

A bigger umbrella
will give a longer end.

This is the same model,
the same scorpion but reopened.

It has been folded
and then reopened,

marking the position
of its different ends.

Every point is a circle, an umbrella:

that big umbrella, the blue one,
is for the tail,

the red ones are the paws,
the green ones are the claws.

Now we go back to our presentation.

This is the figure you have just seen,

and this map of the folds...

is called technically ‘crease pattern’.

This is the Lang original version,
where you can see all the work folds.

Therefore the problem of projecting
a complex origami turns into...

the mathematic problem of having
the circles on the plane opportunely.

It's not only circles, you can see
that there are also some figures,

they are lightly out of sorts but
they would show some streams...

which divide the points and can give
a topology to the model.

Let's take a step back in time:
there is as such geometry of origami,

made of axioms and theorems.

It is a more powerful geometry
than the ’ruler and compass‘ one,

meaning that all the workable
constructions with ruler and compass...

are also workable with origami,

but origami can do other ones, such
dividing an angle into three equal parts.

A small example of origami geometry:

we start from this square,
we make these folds...

and what we obtain
is this figure here.

They are only three folds,

but you can glimpse a big triangle,
which I state it is equilateral.

It is equilateral because its sides...

are three of the square's sides,
so all they are equals, ok?

And if it is an equilateral triangle
these are exactly 60 degrees,

therefore I can find very easily
60 degrees from a square.

An other example concerns...

the division of a sheet in equal parts.

As you can see,
the points on the diagonal are six...

and so they divide that segment
into five equal parts.

On the other diagonal
the division is in thirds,

therefore, through very few folds,
which are that ones highlighted here,

I can obtain
a division in fifths and thirds.

Why do I need this for,
maybe we will discover it later.

In origami, one of the best moves
is the twist.

The twist is built
on a central polygon

going around and some parallel folds...

which spread out two by two
from the polygon.

It is so called because
when you make this fold,

the central polygon actually
makes a rotation.

What is twist used for?

The twist it is for creating
some roses like this.

This one is built on a pentagonal twist,

it is by Naomiki Sato.

Or it is for creating
tessellations, like these here.

Especially look that in the middle,

which soon you will see in a new light.

Tessellations can also be very complex,

like this made by Alessandro Beber:

this has some twists
with 12, 3, 4 and 6 sides.

Twists are also used in technology:

here the question
is that of a solar panel...

which has to be locked up
in a rocket...

or a shuttle, to be thrown
and, when it is in space,

it has to be opened
with minimum effort and damage.

This is the series of moves to be done.

It is this.

This is how it is thrown, then,

once it is high, it opens.

(Applause)

This is a twist...

and this is a tessellation of a twist,
it is the former beehive.

So, as you can see,
each hexagonal stuff...

can be opened.

Therefore
these are related to each other.

I go mad for motion origami,
which are these I'm showing you.

This is a fractal:

it means that I have
a row made of 12 external petals,

a bit smaller one,

which have the same shape
but different dimension.

And this is a single paper sheet.

(Applause)

The surprising thing
is not only its opening,

but its closing, because paper remembers.

(Applause)

I want to amaze you again
with a pair of motion models:

this is called flexicube,

it is made from a single paper strip...

which composes 8 little hinged cubes,

in order to have this continuous movement.

Instead this is its father:
the double star flexicube,

a model by Dave Brill.

Although it is a flexicube also,
it is the only model not made of...

a single paper sheet,
there are 64 fitted modules.

It can go round also,
but at a certain point I can stop,

I can open the trunk
and pull out the first star.

But it is a double star felxicube,

because there are two stars.

(Applause)

Here I let you imagine
how much geometry is inside here,

but this is half cube and this an other
half cube: they are pulled together.

But also this is half cube:
this is half cube, the star,

and if I turn it,
it will become a box for stars,

that is a box which exactly has
the space to contain a star inside.

(Applause)

Why would anyone make origami?

There are a lot of reasons.

Origami instigates manual skills,
fantasy and creativity,

makes children like Maths.

The reason why I fold origami...

is because it is nice: it is magic,
the magic of transformation really.

The ‘Center for diffusion of origami’
is a no-profit association...

which gathers all Italian origamists
and also organise meetings.

The meetings about origami
are hotbeds of ideas...

where everyone brings his own models,
shows them,

explains them
and makes them fold by others.

In this way there is a fusion of ideas...

that has also brought to meetings
about origami and teaching.

Now we are organizing...

the third meeting for next April.

It will be a great chance,
for teachers and instructors...

who wants to use origami...

for their job, to get in touch
with different opportunities.

I wanted to finish with Zsebe's bear,
showing how it folds,

but I don't know if I still have time...

Yes? Do I still have time?

Claudio Ruatti: Take a minute!

RG: I will take a minute then, here it is!

I have already folded something
because otherwise I could not do it.

Here one can already infer
a little structure:

this will become a bear,
with head and tail.

From the head one can obtain
the ears in some way,

then the great thing
is the way you shape the head.

Now here we need to zoom in
really to this part.

So, first you fold up,
now I have exactly a rhombus.

I fold up its face,
then I squash from the inside...

and I close the top part,
which will become the bear's hump.

It is taking the shape of a bear,
you can see its face,

but now the basic move:
it is an upstream fold here,

followed by a downstream fold
placed right down,

which make the bear's face pop up.

Sorry, it has come off a bit like that.

(Applause)

This is how the model should be.

I have finished my presentation,
more or less.

This is a model created for this occasion:

it is a model which basically has a cut.

What happens is that...

one has a sheet of paper and folds it

- as you can see,
the TED logo has been drawn.

What happens is that if one just cut it,

which you should not do with origami,
but if one makes a single cut here,

he will separate the three letters
and obtain the figure you were seeing.

(Applause)

Thank you.