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

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

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

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

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 .

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

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

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

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

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

Powers of phi We will now explore the figure below:

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?

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