**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.**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?