Investigation 11Golden Ratio

The Golden Ratio

Two numbers display the golden ratio when their sum divided by the larger number is equal to the ratio of the larger number to the smaller number

We can do some algebra to find the value of this ratio so it can be used in calculations

Find the Golden Ratio

Now we will need to complete the square for a

Find the Golden Ratio

Now we will need to complete the square for a

Since the number can only be positive, we can eliminate the negative

or

Golden Ratio/The Divine Proportion/Golden Mean/Golden

Section

Since this is an irrational number the Greek letter phi (Φ,φ) is commonly used to represent the ratioThe golden ratio is commonly found in nature, spirals, petals of flowers, and is use in art and architecture

If AC=12, find CB to the tenth

If CB=178, find AB to the hundredth

If AB=36, find AC to the hundredth

The Golden Rectangle

The golden rectangle’s ratio of length to width is equal to φ

or

This is a golden rectangle, find x

Questions?Just about every architecture design of the Greek Parthenon comes from the golden ratioFrom the shape and actual size all the way down to the space between columns and the size of the sculptures used for accents