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Origami

Origami. Paper folding Homework: Prepare for Final. 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

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Origami

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  1. Origami Paper folding Homework: Prepare for Final

  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.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 • http://www.origami-usa.org/ • Local clubs • Mt. Kisco Library: first Saturday of the month (usually)

  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 • Final dimensions • ½*length by ½*width by ¼*width 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. Research • Solved: given any polygon, it is possible to fold a square into a flat shape, make one cut, and produce the polygon • Betsy Ross knew how to make 5 pointed star. • 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.

  11. Another fold? • Wiggler (just 4 folds) • Traditional frog • or pick from website

  12. Topic summary • Basic skepticism about quantities. What are we talking about? What should the number(s) be? What were they before…? Why should we care? How was something measured/determined? • Definitions (subject matter and statistics terms) • Denominators • percentages • Difference (context) • Distribution • Dimension

  13. Analysis • Measures of centrality • mean (aka average), median, mode, standard deviation (square root of variance), range • Trends & limits • Rates of change • Growth on lake (doubling each day…) • Sports records • Logistic curve • Testing • 2 x 2, false positive & false negative • Condition group(s) vs control group

  14. Analysis, cont. • Correlations • Health risks • Cumulative studies • Precision and accuracy

  15. Sampling, probability • Normal distribution • Polling • Margin of error, confidence • Quality of sample • Opportunity sample • Games of chance • Lottery, numbers • Assigning people to dorm rooms • Jury selection

  16. Money • Investments: • Stocks, bonds, mutual funds • Time value of money • Social security, pensions • Insurance • Health insurance • Credit default swaps • Debt • Mortgages, subprime mortgages, securitized mortgages • Credit card • Bailout(s) • stabilization • Interconnectedness of institutions • TBTF

  17. Spreadsheet • Algebra = manipulation (references) to quantities • Unit pricing • Exercise and diet example using named cells, logical tests • Frequency distribution (midterm) • Sorting in bins • Compound growth • Investments • Debt • credit card • Mortgages • Lookup for grades

  18. Graphs and diagrams • Types of charts • Pie (not for everything) • Bar • X-Y • Small multiples • election results by demographic • Map election results

  19. Geometry • Again: election map manipulated to show electoral votes and/or population • Digital images • Maps • Greenland problem • Origami

  20. Homework • Prepare for Final • Postings: no more for the basic requirement but potential for extra credit for especially good work for new news topic!

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