1. The Golden Rectangle and Powers of Phi
November 18, 2004
Whitney Lamm & Allison Trask

2. Interest in Phi Modern College Geometry Class Thesis Research
Topic of Interest

3. History of Phi Phi originated from Greek art and architecture.
The Golden Rectangle, with dimensions , was thought to be aesthetically pleasing to the eye.
Therefore, the Golden Rectangle appears in many well known works of art and architecture throughout history.
The Parthenon
Leonardo da Vinci’s Work
St. Jerome
Michelangelo
David

4. What is Phi and phi?
Phi is equal to:
phi is equal to:

5. What is Phi and phi? We rarely represent and in terms of
its’ numerical value.
Thus, we always write the powers of
and in terms of

6. Patterns of Phi and phi Phi: Increasing by Fibonacci Numbers
phi: Alternating Signs AND Fibonacci Numbers
Fibonacci Numbers:
1, , 2, 3, 5, 8, 13, 21, 34, …
F1, F2, F3, F4, F5, F6, F7, F8, F9, …

7. The Golden Rectangle We think that and
when looking at the Golden Rectangle in terms of .
Is this true?

8. The Golden Rectangle
We will now explore the picture below:
A-HA!

9. Powers of phi
We will now explore the areas of the shapes in the picture below:

10. Powers of phi
We will now explore the volumes of the shapes below:

11. Powers of phi
We will now explore the figure below:

12. Further Research Questions
In 3-D, could we use powers of phi to find the volume of a rectangular prism?
Any other shapes in 3-D?
Is there an example of a Golden Rectangle on the campus of Meredith College?

13. Thank you for listening to our presentation!
Are there any questions?