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?