hi i'm robert j lang i'm a physicist and
origami artist and today i've been
challenged to explain origami in five
levels if you know a little origami you
might think it's nothing more than
simple toys like cranes or cootie
catchers but origami is much more than
that out of the vast cloud of origami
possibilities i've chosen five different
levels that illustrate the diversity of
this art
[Music]
do you know what origami is is that
where you fold you fold paper to make
different animals like those
yes in fact it is have you ever done any
origami before
nope would you like to give it a try
sure okay so we'll do some but i want to
tell you a little bit about origami most
origami follows two i'll call them
customs almost like rules it's usually
from a square
and the other is it's usually folded
with no cuts so these guys are folded
from an uncut square that's awesome so
you ready yep okay we're going to start
with a model that every japanese person
learns in kindergarten it's it's called
a crane traditional origami design it's
over 400 years old so people have been
doing what we're about to do for 400
years wow let's fold it in half from
corner to corner
unfold it
and then we'll fold it in half the other
direction
also corner to corner but we're going to
lift it up and we're going to hold the
fold with both hands
we're going to bring these corners
together making a little pocket and then
this is the trickiest part of this whole
design so you're going to put your
finger underneath the top layer and
we're going to try to make that layer
fold right along the edge now you see
how the sides kind of want to come in as
you're doing that
yeah it's called a petal fold it's a
part of a lot of origami designs but
it's key to the crane now we're ready
for the the magic
we're going to hold it in between thumb
and forefinger reach inside grab the
skinny point that's between the two
layers which are the wings
and i'm going to slide it out so it
pokes out at an angle we'll take the two
wings we spread them out to the side and
you have made your first origami crane
wow
now this is a traditional japanese
design but there are origami designs
that have been around so long we're not
entirely sure where they're originated
we're going to learn how to fold a
cootie catcher so we'll start with the
white side up and we're going to fold it
in half from corner to corner
and we'll unfold and now we're going to
fold all four corners to the crossing
point in the center
we'll fold it in half
like a book
on the folded side we'll take one of the
folded corners i'm going to fold it up
through all layers there's a pocket in
the middle i'm going to spread the
pocket and bring all four corners
together where you have original corners
of the square we're going to just pop
those out
this is one of the most satisfying
moments i think
yeah because it suddenly changes shape i
have
seen these before my friends use these
yeah but there's something else we can
do with this model we set it down push
on the middle
then pop it inside out
so that three flaps come up and one
stays down and then it's called talking
crow because here's a little crow's beak
and mouth wow there's thousands of other
origami designs but these are some of
the first people learn and this was in
fact one of the first origami designs i
learned some 50 years ago wow
so what do you think of that what do you
think of origami i think that the people
that make them are talented
it's hard
seeing the stuff that we've made here
i'd bet that they could do
rocket ships just so much that you can
do with them thanks for coming thanks
for having me
a lot of origami is animals and birds
and things there's also a branch of
origami that is uh
it's more abstract or geometric called
tessellations tessellations
like most origami are folded from a
single sheet of paper but they make
patterns like whether it's woven
patterns or like that or woven patterns
like this if you hold them up to the
light you can you can see patterns the
thing that makes them cool is they're
sort of like tilings it looks like you
could put this together by cutting
little pieces of paper and sliding them
together but there's still one sheet
they weren't cut there's no cuts in
these just folding we can build these up
from smaller building blocks
of folds learn how to fold little pieces
and put them together in the same way
that a that a tiling like this
looks like it's built up of little
pieces can you make a fold that starts
at the dot it doesn't run all the way
across the paper how about like
that
each of these folds is peaked like a
mountain and we call these mountain
folds okay but if i made it the other
way then it's shaped this way and i'll
call it a valley fold in all of origami
there's just mountains and valleys so
all the folds are like reversible so
they're all reversible and it turns out
that
in every origami shape that folds flat
it's going to be either three mountains
in the valley or if we're looking at the
backside
three valleys in a mountain they always
differ by two that's a rule of all flat
origami no matter how many folds come
together at a point and i'm going to
show you a building block of
tessellations it's called a twist
because that center square as i unfold
it
it twists it rotates if i had another
twist
in the same sheet of paper i could make
these folds connect with that and these
ones connect with that and if i had
another one up here i could make all
three and if i had a square array and
all the folds lined up i could make
bigger and bigger arrays like these
because these are just very large twists
in this case it's an octagon rather than
a square but they're arranged in rows
and columns and let's just try going
along
all right
there is our tessellation with squares
and hexagons so you've now designed and
folded your first origami tessellation
and perhaps you can see how just using
this idea of building up
tiles and small building blocks you
could make tessellations as big and
complex as you want that was cool yeah
so what do you think now of origami
tessellations origami i think is the
folding of paper to make anything in
general from 3d things to
like a
flat things and i think origami is about
turning simple things into complex
things and it's all about patterns that
is a great definition
[Music]
so here's a dragonfly and he's got six
legs four wings here's a spider with
eight legs ants with legs and these
just like the crane are folded from a
single uncut square what to figure out
how to do that we need to to learn a
little bit about what makes a point so
let's come back to the crane you can
probably tell that the corners of the
square ended up as points yes right
that's a corner four corners the square
four points how would you make
one point out of this sheet of paper i'm
thinking of like a paper airplane yeah
exactly actually you've discovered
something pretty neat because you made
your point
not from a corner so you've already
discovered one of the key insights any
flap any point leg of the ant takes up
a circular region of paper here's our
boundary
to make your point
from an edge you use that much paper and
the shape it's almost a circle if we
take the crane we'll see if the circles
are visible in the crane pattern
and here's the crane pattern
and here's a boundary of the wing okay
and here's the other wing the crana has
four circles
but actually there's a little bit of a
surprise because what about this
there's a fifth circle
which is like that but it does the crane
have a fifth flap in it let's
refold it and
put the wings up
well yes there is there's another point
and that point is the fifth circle of
our crane okay and to do that we use a
new technique called circle packing in
which all of the long features of the
design are represented by circles so
each leg becomes a circle each wing
becomes a circle and things that can be
big and thick like the head or the
abdomen can be points in the middle now
we have the basic idea
of how to design a pattern we just count
the number of legs we want we want a
spider if it's got let's say eight legs
it's also got an abdomen that's another
point and it's got a hit so maybe that's
10 points if we find an arrangement of
10 circles we should be able to fold
that into the spider so in this book
origami insects 2 is one of my books and
has some patterns and this is one of
them
for flying ladybug and in fact it is
exactly this flying ladybug we've got
the crease pattern here in the circles
and you might now be able to see which
circles end up as which parts knowing
that the largest features like the wings
are going to be the largest circles
smaller points will be smaller circles
so any thoughts which might be well the
legs and the antenna would probably have
to be
these smaller ones in the middle that's
right oh this looks like the back
because it's a bunch of circles all the
way down like here
exactly and then and then the wings
you've got four big wings
which you can see on the ends there and
then i guess my head you got it so you
are ready to design origami awesome
origami artists all around the world now
use ideas like this to design not just
insects but
animals and birds and all sorts of
things
that are
i think unbelievably complex and
realistic but most importantly beautiful
wow that's so impressive i think i
learned how to make one of these paper
creams when i was in third grade but i
guess i never unfolded it to actually
see where it was coming from and so now
that it's all broken up into circles it
makes these super complicated you know
insects and animals and everything seems
so much simpler so that's so cool that's
pretty exciting about it thank you so
much for telling me about this
whenever there's a part of a spacecraft
that is shaped somewhat like paper
meaning it's big and flat we can use
folding mechanisms from origami to make
it smaller telescopes solar arrays they
need to be packed into a rocket go up
but then expand in a very controlled
deterministic way when they get up into
space these are the
the building blocks of
many many origami deployable shapes it's
called a degree 4 vertex it's the number
of lines so in this case we use solid
lines for mountain we use dashed lines
for valley we're going to fold it and
use these two to illustrate some
important properties of origami
mechanisms it's important in the study
of mechanisms to take into account the
rigidity so what we're going to do to
help simulate rigidity is to take these
rectangles and we're going to fold them
over
and over
so that they just become stiff and rigid
okay so this is what's called a single
degree of freedom mechanism you have one
degree of freedom i can choose this form
and then if these are perfectly rigid
every other fold angle is fully
determined one of the key behaviors here
is that with the smaller angles up here
the two folds that are the same parity
and the folds that are of opposite
parity move at about the same rate but
with this as we're getting closer to 90
degrees we find
they move at very different rates and
then at the end of the motion the
opposite happens this one is almost
folded but this one goes through a much
larger motion so the right the relative
speeds differ so when we start sticking
together vertices like this if they're
individually single degree of freedom
then we can make
very large mechanisms that open and
close but with just one degree of
freedom so these are examples of a
pattern called the miura ori when you
stretch them out they're pretty big okay
and they fold flat and a pattern almost
exactly like this
was used for a solar array for a
japanese mission that flew in 1995. so
then you like fly it up
compactly and then once you get up there
there's like some sort of like motorized
mechanism but you only need it on one
fold yeah so typically what the
mechanism will run from corner to corn
two diagonally two opposite corners okay
because then
you can right stretch it out that way
notice some differences between the one
you have and the one i have
and how this one sort of opens out
almost evenly
and but this one opens out more one way
and then the other yeah
what sort of angle would you want so
that they open at the same rate
infinitesimally small
so sadly the only way to get them at
exactly the same rate is when these are
microscopic slivers for sure then that's
not useful and it's exactly the
difference
between the motions of these two
vertices
so
these angles are closer to right angles
and the closer you get to a right angle
the more asymmetry there is between the
two directions right and then the other
difference is how efficiently they pack
so these started at about the same size
but when they're flat
notice that yours is much more compact
so if i were making a solar array i'd
say oh i want that one but if i say well
i want them to open
at the same rate then i want this one
so there's a trade-off there's an
engineering trade-off to get them both
to work and there's another place that
shows up in deployable structures in a
very cool structure this is a folded
tube it sort of pops out like this but
it has this neat property that if you
twist it quickly it changes color
there's a
mars rover application where they they
need a sleeve that protects a drill and
as the drill goes down the sleeve is
going to collapse and they're using a
pattern very much like this
interesting there are many open
mathematical questions
and so room for mathematicians like
yourself to have a big impact on the
world of origami and mechanisms and even
though those
studies are mathematically interesting
they're going to also have real world
applications in space solar arrays
drills telescopes and more any questions
or thoughts about this if you want to
like send something to space it probably
makes sense to do it compactly so if you
have something that you can fold up and
then unfold at just like one of the
folds that's going to be probably the
easiest way to get something up there
and expand it to what it needs to be
[Music]
i'm tom hall i'm a math professor math
magician i've been
doing origami since i was eight years
old and studying the mathematics of
origami ever since grad school at least
the first thing i want to show you is
origami in the real world this is the
origami lamp it comes shipped flat
but
it folds
clip holds it together the lamp has leds
on the inside so when we power it up we
get light we have a lamp shade and we
get the base why does origami lend
itself to say this type of application
origami
applications have in common is that at
some stage
the thing is flat and so whenever you
need to either start from a flat state
and then take it to a 3d state
or conversely for deployables like space
you want to have it in a fully folded
flat state but then take it to a 3d
state or possibly an unfolded flat state
whenever a flat state is involved
origami is a really effective way of
making the transition between those
states another aspect of origami and
origami mechanisms that has lent itself
to many different uses is the fact that
it's scalable when you have an origami
crease pattern like the mirror ori used
in solar panel deployment the type of
motion that you see happening here will
happen whether this is on a piece of
paper that's small like this or on a
larger scale or even on a smaller
smaller smaller smaller scale engineers
in particular robotics engineers are
turning to origami for designing
mechanisms that will either be really
big or really really small this looks
like the most promising way of getting
nano robotics to work this is another
real world application but this
particular implementation is used to
make a wheel for a rover cool so this is
something that can actually get really
really tiny but then get big and fat and
roll new problems arise
when we try to make origami out of
things other than paper yeah but also
new
opportunities an example here which is a
kind of a variant of the miura ori it's
got a three-dimensional structure if i
stretch it one way it expands the other
but because it has these s-bends in the
pattern
if you squeeze it it doesn't go all the
way flat yeah this is a epoxy
impregnated aramid fiber and so if i put
this fold pattern into it
and then compress it
and then put a skin on the top and
bottom this becomes
incredibly lightweight but incredibly
strong yeah another origami challenge
that comes up with
these patterns is we're going to make an
aircraft out of this thing we're going
to need
hundreds of yards of folded origami
we're not going to do it by hand and
this might be the new frontier
in origami engineering
which is the design of machines
that can fold patterns that have
applications so talking about a machine
that is actually
folding it into this not just making the
creases but yeah actually folding it so
what goes in his sheet and what comes
out is this or something this y that's
cool yeah what do you see as kind of
like the next big breakthrough is there
anything out there on the horizon that
you're just like oh wow this is really
exciting it's something we've talked
about a little bit that with all the
richness of behavior of uh origami from
a flat
sheet it seems like there ought to be an
equally rich world of things that don't
start flat but are still made from flat
sheets of paper like a cone
bistable properties and
you can combine them together with the
copies of themselves to make cellular
structures they're astonishingly stiff
and rigid and useful for mechanics the
thing that i think i'm the most excited
about comes from math
mainly when i look at origami when i
look at all these applications or just
all these different origami folds i see
structure math is really about patterns
the patterns that we see in origami are
reflecting some kind of mathematical
structure and we don't quite know yet
what all of that structure is and if we
can tie a mathematical structure that's
already well studied to something we see
happening in origami then we can use the
math tools right away to help solve the
engineering problems and the origami
problems and the fact that there's so
many applications to this is really
making people excited who are working in
the area i'm really excited to see what
happens with that in the next five years
[Music]