Cynthia Lanius Building a Golden Rectangle Golden Ratio 1.61803

Golden Ratio Table of Contents Introduction Find golden rectangles. Build golden rectangles. Confirm the ratio using algebra. Let's build an approximation of the golden rectangle using square grid paper. At each step we will calculate the ratio of length to width. Remember the Golden Ratio is approximately 1.61803. Step 1:  Start with a square 1 by 1. Ratio of Sides 1/1 = 1     Step 2:  Add another 1 by 1 square. Ratio of Sides 2/1=2    Step 3:  Add a 2 X 2 square. Ratio of Sides 3/2=1.5     Step 4:  Add a 3 X 3 square. Ratio of Sides 5/3=1.667     Step 5:  Add a 5 X 5 square. Ratio of Sides 8/5=1.6     Step 6:  It's Your Turn! Build the next approximation on square grid paper. Then observe the pattern and answer the following: Lengthn = Answer width of n+1 Lengthn + widthn = Answer Length of n+1 The lengths of the various rectangles are 1, 2, 3, 5,..., Notice that each term is found by adding the 2 previous ones, the sequence known as the Answer Fibonacci Sequence Every step of the rectangle will produce a ratio closer and closer to the golden ratio of approximately Answer 1.61803 Golden Ratio Table of Contents Introduction Find golden rectangles. Build golden rectangles. Confirm the ratio using algebra. Geometry Online Email any comments to lanius@math.rice.edu Copyright 1998-2008 Cynthia Lanius

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