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Golden Rectangle

Golden Rectangle. A golden rectangle is a rectangle whose side lengths are in the golden ratio , 1: φ. The golden ratio , φ , is pronounced “Fee” and is approximately 1.618. 1. φ. Constructing a Golden Rectangle. 1.) Construct a unit square.

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Golden Rectangle

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  1. Golden Rectangle • A golden rectangle is a rectangle whose side lengths are in the golden ratio, 1:φ. • The golden ratio, φ, is pronounced “Fee” and is approximately 1.618. 1 φ

  2. Constructing a Golden Rectangle 1.) Construct a unit square 2.) Draw a line from the midpoint of one side to an opposite corner. 3.) Use that line as the radius to draw an arc that defines the long dimension of the rectangle. Midpoint Square

  3. Constructing a Golden Rectangle The Golden Rectangle φ 1

  4. Proving a Golden Rectangle • We will have to use the Pythagorean Theorem Longer Side = = Ratio = 1.618 Shorter Side Which is the “Golden Ratio” or “Phi”

  5. “Golden Rectangle”, GSP, and Pictures 1.) Construction of the Golden Rectangle using GSP. 2.) Parthenon (using pictures). 3.) Mona Lisa (using pictures).

  6. Quadrature of the Rectangle

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