ANSWER SHEET
EXERCISES 1, 2, 3, 4, 6: Check by inspection for completeness
EXERCISE 5: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233
ADDITIONAL EXERCISES
Calculating the Golden Mean
| length | 34 | 21 | 13 | 8 | 5 | 3 | 2 |
| width | 21 | 13 | 8 | 5 | 3 | 2 | 1 |
| ratio | 34/21 | 21/13 | 13/8 | 8/5 | 5/3 | 3/2 | 2/1 |
| decimal | 1.62 | 1.62 | 1.63 | 1.6 | 1.67 | 1.5 | 2 |
Discussion Questions:
1. Describe the pattern in the ratios you calculated.
Except for 2, all are near 1.6
2. The rectangles that you cut out are called golden
rectangles. What do you think is the value of the golden
ratio?
The value of the golden ratio is about 1.6.
3. Write a definition of a golden rectangle. Use the
word ratio as part of your definition.
A golden rectangle is a rectangle in which the ratio of the
length to the width is 1.6.
The Golden Ratio in Our World
Check by inspection for completeness
Calculating Fibonacci Numbers
1
1 1
2 2
3 1.5
5 1.666667
8 1.6
13 1.625
21 1.615385
34 1.619048
55 1.617647
89 1.618182
144 1.617978
233 1.618056
377 1.618026
610 1.618037
987 1.618033
1597 1.618034
2584 1.618034
4181 1.618034
6765 1.618034
10946 1.618034
17711 1.618034
28657 1.618034
46368 1.618034
75025 1.618034
121393 1.618034
196418 1.618034
317811 1.618034
514229 1.618034
832040 1.618034
1346269 1.618034
2178309 1.618034
3524578 1.618034
5702887 1.618034
9227465 1.618034
14930352 1.618034
24157817 1.618034
39088169 1.618034
63245986 1.618034
State these terms of the Fibonacci sequence:
10th _55___________
15th _610__________
20th _6765_________
25th _75025________
30th _832040_______
39th _63245986_____