The Nature of Mathematics, 12th Edition
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Chapter 7 Projects

Section 7.6 Individual Research

Individual Research 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).

Individual Research 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 Markowsky, "Misconceptions About the Golden Ratio," The College Mathematics Journal, January 1992.

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