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

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, 1961.

• High School Geometry Book