### Assignment #6

**Due: 25 January,1999**

**1.** Suppose two cylinders, each of radius 1, intersect at a right angle. What is the volume of the region of intersection? *[5]*
**2.** In 1228 Leonardo of Pisa, known as Fibonacci, posed the following problem in his Liber Abaci:

A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?

Suppose rabbits never die. Let f_{n} be the number of pairs of rabbits after n months.

**a.** How is f_{n+2} related to f_{n+1} and f_{n}? Why? *[3]*

**b.** Find the answer to Leonardo's question. *[2]*

Department of Mathematics
Trent University

Maintained by Stefan Bilaniuk. Last updated 1999.12.03.