## Find the Golden Ratio

Summary: Many rectangular objects have a length-to-width ratio that is close to the Golden Ratio, which is approximately 1.618 to 1. The Golden Ratio has been used in art and architecture for centuries because many people find this proportion pleasing to the eye.

1. Plan It

A. Measure the front panel of several cereal boxes. Find the length-to-width ratio of each front panel by dividing the length of the rectangle by the width. Record the length-to-width ratio for each front panel. Which panel had a ratio closest to the Golden Ratio?

Our planning completed

2. Put It Together

A. Draw Golden Rectangles. The pattern on page 341 of the Math Central textbook is made of squares of different sizes. You'll find a similar pattern here. Your group will find the hidden Golden Ratio in this pattern. Remember that the square labeled 1 measures 1 unit by 1 unit. Find the dimensions of each square in the pattern. Remember that proportions remain the same in drawings to scale, if you wish to use a measurement other than inches for your drawing.

Find all the rectangles in the pattern. Determine their measurements. Calculate and record their length-to-width ratios first as fractions and then as ratios. What did you notice? Rectangles with a length-to-width ratio the same as the Golden Ratio are called Golden Rectangles.

Our drawings and calculations completed

3. Wrap It Up

Design a cereal box. On the other side of your rectangle pattern, design a front panel for a box of your favorite cereal. Try to use Golden Rectangles in your design. Can you use the Golden Ratio to determine side lengths of rectangles in your design?

Our designs completed

• How did you figure out the length of the sides of squares in the pattern?
• How well did you keep track of the rectangles and the ratios of the lengths of their sides?
• Did you notice any patterns with the rectangles in the figure you copied?
• How well did you incorporate Golden Rectangles in your cereal box design?
• How well did you use ratio in the investigation?

Review completed