### Project 7.6

Do some research on the length-to-width ratios of the packaging of common household items. Form some conclusions. Find some examples of the golden ratio in art. Do some research on dynamic symmetry.

*References:*

**Philip J. Davis** and **Reuben Hersh**, *The Mathematical Experience* (Boston: Houghton Mifflin Company, 1981), pp. 168-171

**H. E. Huntley**, *The Divine Proportion: A Study in Mathematical Beauty* (New York: Dover Publications, 1970).

### Project 7.7

In Example 2 Section 7.6, we assumed the width of the Parthenon to be 101 ft and found the height to be 62.4 (assuming the golden ratio). If you worked Problem 8, you assumed the height to be 60 ft and found the width using the golden ratio to be 97 ft. Are the numbers from Example 2 and from Problem 11 consistent? Can you draw any conclusions?

*References:*

** George Markowsk**y, “Misconceptions About the Golden Ratio,”

*The College Mathematics Journal,*January 1992.

### Project 7.8

What is the golden ratio?

What is the silver ratio? Write a paper on the silver ratio.

### Project 7.9

Write a paper on perspective. How are three-dimensional objects represented in two dimensions?

**References:**

Mathematics and Perspective

**http://mathforum.org/sum95/math_and/perspective/perspect.html**

**Morris Kline**, *Mathematics, a Cultural Approach* (Reading, MA: Addison-Wesley, 1962), Chapters 10-11.

**C. Stanley Ogilvy**, *Excursions in Geometry*(New York: Oxford University Press, 1969), Chapter 7.

### Project 7.10

Is there a “best” rectangle. If you like to do origami, which size paper best suits your needs? What are “standard” sizes for paper?

### Project 7.11

The discovery and acceptance of non-Euclidean geometries had an impact on all of our thinking about the nature of scientific truth. Can we ever know truth in general? Write a paper on the nature of scientific laws, the nature of an axiomatic system, and the implications of non-Euclidean geometries.

### Project 7.12

Find the one composite number in the following set:

31

331

3331

33331

333331

3333331

33333331

333333331