1. Paper folding Homework: Prepare for Final
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 Origami USA has convention in June in NYC
use google
Meyer family origami site:
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 Library: first Saturday of the month (usually)

4. Today magazine cover box business card frog water bomb
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 Trends & limits Testing
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 Games of chance
Margin of error, confidence
Quality of sample
Opportunity sample
Games of chance
Lottery, numbers
Assigning people to dorm rooms
Jury selection

16. Money Investments: Social security, pensions Insurance Debt Bailout(s)
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 Small multiples
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!