The following questions review the main ideas of this chapter. Write your answers to the...

The following questions review the main ideas of this chapter. Write your answers to the questions and then refer to the pages listed by number to make certain that you have mastered these ideas.

What is the golden ratio and how are the Fibonacci numbers related to the golden ratio? pg. 121 How can you determine if a rectangle is a golden rectangle? pg. 121 How can you construct a golden rectangle? pgs. 122–123

Reference:

The rectangle enclosing the diagram of the Parthenon in Figure 2.79 is an example of a golden rectangle. A golden rectangle is a rectangle in which the ratio of the dimensions is the golden ratio. In Example 2.14, we constructed a sequence of rectangles whose dimensions were Fibonacci numbers. We noticed in Table 2.11 that the ratios of those dimensions approached the golden ratio. Thus, the rectangles constructed in Example 2.14 got closer and closer to the shape of a golden rectangle.

The Greeks were able to construct a golden rectangle using the Pythagorean theorem, which was discussed in Section 2.1. We next describe in detail how to create a golden rectangle. We will start with a square WXYZ that measures 1 unit on a side (Figure 2.80).