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?

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Presentation transcript:

THE GOLDEN RATIO Nika Wilcox MA

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

The Golden Rectangle What is it? Important usage

Important People Johannes Kepler Mark Burr

The Golden Ratio Used in History Greek architecture Greek sculptures Paintings

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

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

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