Name: _______________________________   
Date: _______________________

Calculating the Golden Ratio

A Cooperative Learning Activity (Suggested groups of 3)
Objective: Students will find the value of the golden ratio
Materials needed: graph paper (centimeter ruled), ruler, scissors, calculator

Step 1. Draw a rectangle on the graph paper that is 34 squares long and 21 squares wide and then cut out this rectangle. Calculate the ratio by dividing the length by the width. The answer should be about 1.62.

Step 2. Draw a line on the rectangle that will give the largest possible square. What is the shape of the remaining figure? (A rectangle) Cut the original rectangle along this line. Measure the length and width of the remaining rectangle to the nearest tength of a centimeter. Record this in the table below. What is the ratio of its length and width? Express this as a decimal.

Step 3. Repeat Step 2 and cut the rectangle into a square and a smaller rectangle until the remaining rectangle is 1 square by 2 squares. Fill in the table below to record your findings.

Discussion Questions:

1. Describe the pattern in the ratios you calculated.

2. The rectangles that you cut out are called golden rectangles. What do you think is the value of the golden ratio?

3. Write a definition of a golden rectangle. Use the word ratio as part of your definition.

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