Exercises

7. The golden rectangle is considered to be pleasing to the human eye. Of the following rectangles, which do you prefer? Is it a golden rectangle?
   

   Rectangle 1

   

   Rectangle 2

   

   Rectangle 3

   

   Rectangle 4

8. A drone is a male honeybee. Drones have only one parent, a queen. Workers and queens are female honeybees. Females have two parents, a drone and a queen. Part of the family tree showing the ancestors of a drone is shown below, where D represents a drone and Q represents a queen.

   
   Image Long Description

   1. Continue the family tree for three more generations of ancestors.
   2. Count the number of honeybees in each generation. What pattern do you notice?
9. What is the relationship between the flowers and the Fibonacci sequence?
   

10. In △ A B C , white up pointing triangle eh b c comma  point D divides the hypotenuse into the golden ratio. That is, A D : D B eh d colon d b  is about 1.618 : 1. C D ¯ c d bar  is an altitude. Using the value 1.618 for AD and the value 1 for DB, solve for x. What do you notice?

    

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