THE GOLDEN RATIO

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THE GOLDEN RATIO

• Nika Wilcox
• MA 341-001

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Information

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

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Interesting Properties

• Relationship of phi squared
• Relationship of 1/phi
• Relationship of phi cubed minus 3 times phi

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The Golden Rectangle

• What is it?
• Important usage

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Important People

• Johannes Kepler
• Mark Burr

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The Golden Ratio Used in History

• Greek architecture
• Greek sculptures
• Paintings

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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

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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

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Sources

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