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THE GOLDEN RATIO

THE GOLDEN RATIO. Nika Wilcox MA 341-001. Information. What is the golden ratio? What is the actual value of phi? How do you find the actual value?. Interesting Properties. Relationship of phi squared Relationship of 1/phi Relationship of phi cubed minus 3 times phi.

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THE GOLDEN RATIO

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  1. THE GOLDEN RATIO Nika Wilcox MA 341-001

  2. Information • What is the golden ratio? • What is the actual value of phi? • How do you find the actual value?

  3. Interesting Properties • Relationship of phi squared • Relationship of 1/phi • Relationship of phi cubed minus 3 times phi

  4. The Golden Rectangle • What is it? • Important usage

  5. Important People • Johannes Kepler • Mark Burr

  6. The Golden Ratio Used in History • Greek architecture • Greek sculptures • Paintings

  7. How to Construct a Golden Rectangle from a Square • Construct square GOEN • Extend segment GO and extend segment NE • Bisect segment GO and label the midpoint M • Construct an arc intersecting line GO at point L using ME as the radius and M as the center. • Construct rectangle OLDE • Rectangle GLDN is the golden rectangle

  8. Famous Words • Geometry has two great treasures: one is the theorem of Pythagoras; the other is the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel. -Johannes Kepler

  9. Sources • Gardner, Martin. The Second Scientific American Book of Mathematical Puzzles and Diversions. New York, 1961. • High School Geometry Book

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