Answer the following question in sentence form.

1. In the Fibonacci Sequence:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...

which of these numbers are divisible by 2?

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...

The answer is every third number, and 2 is the third Fibonacci number.

How about the ones divisible by 3?

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...

The answer is every fourth number, and 3 is the fourth Fibonacci number.

Could these be just a coincidence? Examine if this pattern goes on forever.

2 The golden triangle, sometimes also called the sublime triangle, is an isosceles triangle such that the ratio of the hypotenuse a to base b is equal to the golden ratio, a/b = ?. What is the measure of the vertex angle of the triangle?

3. Suppose a newly-born pair of rabbits, one male and one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. How many pairs will there be in one year?

4. Henry Dudeny, an English puzzle book author in the early 1900s, came up with the following simplified version of Fibonacci's logic:

If a cow produces its first female calf at age two years and produces another female calf every year after that, how many female calves are there after five years if we start with one newborn female calf and no calves die?

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