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 fn be the number of pairs of rabbits after n months.

a. How is fn+2 related to fn+1 and fn? Why? [3]

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

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