1. Making Origami the Focus of a basic Math course
Jeanine Meyer
Purchase College/SUNY

2. General Education Mathematics
At State University of New York, and many other colleges, all students are required to take courses in a variety of disciplines, including
Writing
Social science
Humanities
The Arts
Natural science
[foreign] language and Culture
Mathematics
The topic that is most disliked/feared/unnecessary/to be avoided…. Is mathematics.
Many faculty (outside of mathematics, science, economics) share these feelings.
Problems from earliest levels of education.

3. Purchase College Primarily undergraduate
Liberal Arts
Combined Mathematics/Computer Science major
Conservatories
Visual Arts, Performing arts (theater), Music, Dance
Most/many students have fears concerning math
Don’t assume the conservatory students are weak[est]

4. Purchase College math gen ed satisfiers
PreCalculus, Calculus, Statistics
Computer Science I, Programming Games, Programming for Visual Artists, Programming in Max
Mathematics for Contemporary Life
Communicating Quantitative Information
Taught by Philosophy program: Classical Logic, Modern Logic
Taught by Economics program: Microeconomics
(History of Mathematics)
New this year
Chronicles of Mathematics
The Math and Art of Origami

5. The Math and Art of Origami
Catalog description: An introduction to origami, a centuries-old art, practiced all over the world, that is constantly being expanded and is the focus of attention by mathematicians, computer scientists, and engineers. Students will learn traditional and modern models and analyze them using mathematical techniques. Students will practice preparing diagrams and teaching models, with opportunity for invention.
Enthusiastically accepted by faculty.
This could be high school or even middle school course, though I do include presentations, team work, to develop those skills.
It is NOT engineering or upper level math course!

6. Goals: explicit and implicit
Improve spatial relations sense, including 2D to 3D
Pay attention to procedures
Practice making diagrams
Calculate final dimensions
Notice symmetries
Get peek at more complex mathematics
Develop liking for origami and continue on their own
Get away from screens

7. Content by week
Introduction. Magazine cover box. Business card frog. Calculation of final dimension. Notice symmetries. Diagramming. Frog experiment.
Water bomb, variations. Twist fish. Theorem on valley and mountain folds. (Possibly hearts)
Wiggler (everyone diagrams). Water bomb modular. Collection assignment.
Traditional frog. Culture assignments (e.g., 1000 cranes, why frogs, specific folders)
Crane and flapping bird. Different folding sequences: working from crease pattern, identify correspondences. Bird in other models.

8. Weekly content, cont.
Kissy fish. Estimation of thirds. Symmetries. Caterpillar. Producing directions using programming. Building up functions. Algebra calculations.
Twisty fish. Final dimensions. Symmetries. Definition of symmetry. Presentation assignment.
Student presentations. Students also show collections.
Dollar bill: shirt, pants. Heart that can be broken. Investigate aspect ratios of money.
Dollar bill rosette. Origami-inspired adventure: improving estimate like with thirds. Nature of numbers by which procedure works.

9. Weekly content, cont.
Boxes: Masu, Sonobe, others. Polyhedra. Euler’s formula. Make variations.
Various possibilities: flowers, hexagons, rose, puppets, wallets. POSSIBLY: origami versus straight-edge and compass. POSSIBLY: Kawasaki-Justin on flat-foldability.
[More] modular models. Assignment (in teams or optional team): find model: learn, analyze, teach.
Introduction (peek) at one-cut: Betsy Ross star example. POSSIBLY: Erik Demaine video.
Student presentations. Showing of collections.

10. Grading allocation Frog study 5 First presentation. 15
First presentation: response postings
History presentation. 10
Responses to history presentations
Instructions: wiggler
Instructions: can choose media, including mixture of diagrams, photos, video. Pick or assign? From set (one dollar shirt, heart that can be broken, ?)
Variation of model.
Posting comparing ways of learning: diagrams, class demonstrations, videos, photos.
Final model presentation. 20
Presentation of personal origami collection
5 (showing mid term) + 5 (final day)
Extra credit: origami sighting report posting

11. SUNY Required Gen Ed Assessment (draft)
Interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics; 
First presentation (based on students needing to interpret diagrams=schematics)
Represent mathematical information symbolically, visually, numerically and verbally;
Students doing diagramming in the diagramming, instructions assignment.
Employ quantitative methods such as arithmetic, algebra, geometry, or statistics to solve problems;  Based on final presentation: reporting on math analysis
Estimate and check mathematical results for reasonableness; Frog homework and followup OR reply posts on first assignment.
Recognize the limits of mathematical and statistical methods.  Based on final presentations

12. First day/first model: Magazine cover box
Taught initially with copier paper, complete book folds
Ask for guess at size of lip. Note that this is a rectangle that is not a square. Calculate final dimensions.
(May do business card frog next so frog can jump into box. Note that the lack of rigidity has benefits. There are more boxes.)
Point out unused folds. Ask: what/when were they done? Why?
Solution: pinch at sides.
Choose magazine cover.
Need to decide on inside or outside.
Make box again using New Yorker covers.

13. Quick look: origami directions
On page of examples:

14. Flapping bird Compare two folding procedures Crease pattern(s)
What lines are produced by each one? Sense (mountain/valley) of folds
What are advantages and disadvantages

15. Preparation folds, then collapse
Preliminary base, petal fold

16. Aside
My initial encounter with origami: Mathematical Games section of Scientific American
My next encounter: Lillian Oppenheimer visits me, teaches me the business card frog.

17. Dollar bill rosette: origami inspired adventure
Need to divide bill into 11 parts. Do this by estimating and then improving estimate. Will show how that works.
Why 11? Must be odd; must be prime; must be ?? Will show Python computer program that produces numbers that work under 1000.
Show online search to reptend primes base 2
Show proof that the two sets of numbers of the same.

18. Betsy Ross 5 pointed star note: ok from 8.5x11

19. Comments and Suggestions??
Work in process. Check back later.
Starts 1/23. Monday/Thursday: 10:30am to 12:10pm.
Visitors welcome.