Survey of Math Chapters 19 & 20

The Portfolio Assignment

For this last section, I have decided to have you work on a series of short projects that relate to the mathematics we will be talking about in class. When completed, these projects will form a portfolio which I will grade, and replace the quizzes, assignment, and test for this final section.

Instructions:

• Each person will construct their own projects (no group work), but feel free to discuss your work with your classmates.
• I will be looking for good explanations of how your work relates to the mathematics, and also that there is a sufficient degree of creativity in your work.
• I will list the components I will be looking for in your portfolio here, and we can discuss them in class.
• Be creative! I want you to explore these topics in a way you find interesting.
• Make sure to clearly reference any sources you use, in other words a list of books, websites, and other resources you used.
• All the components of the portfolio will be due April 26, but you should work on the components as they are assigned. We will likely have some classes of peer evaluation along the way (I will give you advance notice of these).

Component 1: The Golden Ratio

Create an artifact that illustrates some aspect of the Golden Ratio, and then write a paragraph or two which explains what aspect of the golden ratio your artifact displays, and clearly explain how it shows that aspect.

Possibilities:

The links below are only to get you started, you should devise your own original project drawing upon resources you find.

• Measure body parts http://educ.queensu.ca/~fmc/october2001/GoldenBody.htm
• Draw a picture http://library.thinkquest.org/27890/applications6.html
• Take a photograph http://www.bestbydesign.com/miefaq/Photography_Tips/Golden_Rule/golden_rule.html
• Relate to architectural photos
• Do a survey of people to find which cropping of an image is ''most appealing'' (you could display your survey results using histograms!)
• or something else you devise yourself

Component 2: Strip Patterns

Create an artifact which represents a strip pattern. The artifact can be something you create yourself, or a pattern which you find on a piece of artwork, pottery, etc.

Explain clearly (with diagrams and words) what types of symmetries your strip pattern has and does not have, and then classify your strip pattern using crystallographers' notation.

Component 3: An Escher-like Tiling

Create your own Escher-like tiling from a quadrilateral, where translations and half turns are required. Clearly explain the modifications you made to the quadrilateral to get your final shape, and show how your final shape fits together to form a tiling.