Transcript 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 • 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 – http://www.origami-usa.org/ • Local clubs – Mt. Kisco Library: first Saturday of the month (usually) 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 • Final dimensions – ½*length by ½*width by ¼*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 • 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. Another fold? • Wiggler (just 4 folds) • Traditional frog • or pick from website 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 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 Analysis, cont. • Correlations • Health risks • Cumulative studies • Precision and accuracy 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 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 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 Graphs and diagrams • Types of charts – Pie (not for everything) – Bar – X-Y • Small multiples – election results by demographic • Map election results Geometry • Again: election map manipulated to show electoral votes and/or population • Digital images • Maps – Greenland problem • Origami Homework • Prepare for Final • Postings: no more for the basic requirement but potential for extra credit for especially good work for new news topic!