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 geometric recursion? pgs. 118–120

Reference:

GEOMETRIC RECURSION

We have seen how a recursion formula may be used to generate the numbers in the Fibonacci sequence. The process of recursion may also be used to create shapes. Figures can be built step by step by repeating some rule or set of rules, a process called geometric recursion. Geometric recursion can lead to interesting figures and to new mathematics.

Beginning with a rectangle, we can form a new rectangle by adding a square to one side of the rectangle or to its top or bottom, where the side of the added square has the same length as one dimension of the rectangle (Figure 2.76). If we add the square on one of the sides of the rectangle, the rectangle becomes wider [Figure 2.76(a)]. If we add the square on the top or the bottom of the rectangle, the rectangle becomes taller [Figure 2.76(b)].

If we alternate between adding a square to the side and to the top or bottom of the figure, the resulting shape is very interesting, as will be shown in the next example. However, in this example, we will begin with a square and add more squares to build rectangular shapes rather than starting with a nonsquare rectangle and adding squares