URL http://math.rice.edu/~lanius/Geom/building.html

## Cynthia Lanius

## Building a Golden Rectangle

Golden Ratio 1.61803

Golden Ratio Table of ContentsIntroduction 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.

Step 2:Add another 1 by 1 square.

Step 3:Add a 2 X 2 square.

Step 4:Add a 3 X 3 square.

Step 5:Add a 5 X 5 square.

Step 6:It's Your Turn! Build the next approximation on square grid paper.

Then observe the pattern and answer the following:

- Length
_{n}=

- Length
_{n}+ width_{n}=

- 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

- Every step of the rectangle will produce a ratio closer and closer to the golden ratio of approximately

Golden Ratio Table of ContentsIntroduction Find golden rectangles. Build golden rectangles. Confirm the ratio using algebra.

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