Origami

1
Origami

• Jeanine Meyer
• Mathematics/Computer Science New Media

2
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

3
Origami

• MANY websites
• use google
• Meyer family origami site http//newmedia.purchas
  e.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

4
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

5
Magazine cover box

• The 'lip' (fold over) is made using the
  difference between the width and the height
• ¼ length ¼ width
• .25length .25width
• Final dimensions
• ½length by ½width by ¼width
• .5 length by .5width by .25width
• .50 length by .50width by .25width
• Many boxes, most more sturdy!

6
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?

7
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.

8
Water bomb ornament

• Picking 3 sets of 2 of same color helps final
  assembly in 3 dimensions
• Modulars typically have 'pockets' and 'pokes'

9
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.

10
http//www.ushistory.org/betsy/flagstar.html
11
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

12
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.

13
Discussion

• Questions?
• More folding?

14
Quiz on percentages?

• Any questions?