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Learning Math Home
Session 9, Part C: Fibonacci Numbers
 
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Session 9, Part C:
Fibonacci Numbers (30 minutes)

In This Part: The Fibonacci Sequence | Ratios of Fibonacci Numbers
The Golden Mean and the Golden Rectangle

For the final activity in this session, we'll look at an interesting application of ratios that again demonstrates the amazing patterns that emerge when we examine mathematics.

Fibonacci was the nickname of Leonardo de Pisa, an Italian mathematician. He is best known for a sequence of numbers that bears his name. The Fibonacci sequence begins with 1, 1. Each new number is then found by adding the two preceding numbers:

 Fibonacci Number

1

1

2

3

5

8

13

21

34

55

...

 Index of Numbers

1

2

3

4

5

6

7

8

9

10

...

The Fibonacci numbers are found in art, music, and nature. You can find them in the number of spirals on a pine cone or a pineapple. The numbers of leaves or branches on many plants are Fibonacci numbers. The center of a sunflower has clockwise and counterclockwise spirals; the numbers of these spirals are consecutive Fibonacci numbers.

Problem C1

Solution  

Examine a pineapple, looking for its three different sets of spirals. Use a toothpick to mark a starting place, and hold a pencil at the bottom of one spiral. Count the number of spirals of this type, moving the pencil as you count. Stop when you get back to your starting place. Now count the spirals in a different direction. See if you can find the third direction. Record the number of spirals in each of the directions. What do you notice about these numbers?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
If you don't notice anything, try again, or try it with a different pineapple. The pattern should be apparent on most pineapples. If you don't have access to a pineapple, try this with a pine cone, or examine a nearby tree to see if you can find a Fibonacci pattern.   Close Tip

Next > Part C (Continued): Ratios of Fibonacci Numbers

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