Transcript Origami basics

Origami
Jeanine Meyer
Mathematics/Computer Science &
New Media
Origami
• Paper folding
– associated mostly with Japan (origami means paper
folding in Japanese) but concurrent invention in
different parts of the world
• China
• Spain
– hobby, craft, art form
– mathematical aspects
• mathematics is not just numbers, also patterns and shapes
• basic mathematics to current research
Origami
• MANY websites
– use google
– Meyer family origami site:
http://newmedia.purchase.edu/~Jeanine/origami
• some examples used to demonstrate/teach Flash
• look in my office (NS 3003), mostly by Aviva Meyer
• Origami USA has convention in June in NYC
• Local clubs
– Mt. Kisco
Today
• magazine cover box
– rectangle not a square
• business card frog
– rectangle not a square, with spring
• water bomb
– traditional fold, Chinese
• water bomb base ornament
– modular example
• hungry fish
– action figure (need to divide paper into thirds)
Directions available on Meyer Family Origami site
Magazine cover box
• The 'lip' (fold over) is made using the difference
between the width and the height
– ¼ * length – ¼ * width
– .25*length – .25*width
• Final dimensions
– ½*length by ½*width by ¼*width
– .5 * length by .5*width by .25*width
– .50 * length by .50*width by .25*width
Many boxes, most more sturdy!
Business card frog
• Again: rectangle, not a square
• Spring comes from stiffness of paper
RELATIVE to area (weight?)
• Experiment: make a jumping frog from
different sizes of regular paper. If the
paper is small enough, the frog will jump.
• Aside: Why does a Barbie doll have a very
small waist?
Water bomb
• Traditional fold, perhaps from China
• Calculate / imagine the surface area of the
final model.
• Try: color outside surfaces of model and
then unfold.
Water bomb ornament
• Picking 3 sets of 2 of same color helps
final assembly in 3 dimensions
• Modulars typically have 'pockets' and
'pokes'
Hungry fish
• Dividing into thirds: why the 's' method
works. It is more than trial-and-error!
– Say first guess is wrong by an error e.
– Folding over to that point has the effect of
halving the error. Folding over again halves
the error. The error gets reduced each time, to
arrive at a estimate that is fairly accurate.
http://www.ushistory.org/betsy/flagstar.html
Research
• Generalize Betsy Ross method's for 5
pointed star
• Given any polygon, is it possible to fold a
square into a flat shape, make one cut,
and produce the polygon
– Answer: yes, done by Eric Demaine
Research
• Under investigation: various questions:
given a set of lines representing folded
lines, is it possible how produce it? How
long (how many steps) would it take?
• Origami for industry: how to build a
telescope to be unfolded in space, how to
design something to be unpacked.
Discussion
• Questions?
• More folding?
Quiz on percentages?
• Any questions?