The answers to exercises marked [BB] can be found in the Back of the Book.Select two point...

The answers to exercises marked [BB] can be found in the Back of the Book.

Select two points on a circle and join them with a straight line. The circle has been divided into regions. Select three points and join each pair with a line; the circle is divided into four regions. Select four points and join each pair; the circle is divided into eight regions.

(a) If five points are selected on a circle and each pair is joined with a line, into how many regions has the circle been divided?

(b) What do you think happens in general with n points? Guess a formula and investigate with n = 6.

[This exercise emphasizes the need for care when drawing inferences from “obvious” patterns.]