### 7.4 Fibonacci & Other Patterns

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• 1. Daisies

Use the Internet to describe how the Fibonacci sequence is related to the object shown. (See Example 1 and Example 2.)

Daisies

• Worked-Out Solution

Ordinary field daisies have 34 petals. It is common for other members of the daisy family to have 13, 21, 55, or even 89 petals. All of these numbers are in the Fibonacci sequence.

In the arrangement of tiny florets in the core of a daisy, you can see 21 counterclockwise spirals and 34 clockwise spirals. In any daisy, the combination of counterclockwise and clockwise spirals generally consists of successive terms of the Fibonacci sequence.

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```  ______   __   __   __   _    __   __    _  _
/_   _//  \ \\/ // | || | ||  \ \\/ //  | \| ||
`-| |,-    \ ` //  | '--' ||   \ ` //   |  ' ||
| ||      | ||   | .--. ||    | ||    | .  ||
|_||      |_||   |_|| |_||    |_||    |_|\_||
`-`'      `-`'   `-`  `-`     `-`'    `-` -`

```
• 2. Phyllotaxis

Use the Internet to describe how the Fibonacci sequence is related to the object shown. (See Example 1 and Example 2.)

Phyllotaxis

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```  _  _    __   __    ______   __   __    _____
| \| ||  \ \\/ //  /_   _//  \ \\/ //  / ____||
|  ' ||   \ ` //     | ||     \ ` //  / //---`'
| .  ||    | ||     _| ||      | ||   \ \\___
|_|\_||    |_||    /__//       |_||    \_____||
`-` -`     `-`'    `--`        `-`'     `----`

```
• 3. Pineapple

Use the Internet to describe how the Fibonacci sequence is related to the object shown. (See Example 1 and Example 2.)

Pineapple

• Worked-Out Solution

Pineapple scales are patterned into spirals and because they are hexagonal, there are 3 sets of spirals.

There is one set of 5 paralllel spirals.

There is a second set of 8 parallel spirals.

And there is a third set of 13 parallel spirals.

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```  _  __    _____      _____    ______     _____
| |/ //  |  ___||   / ___//  /_   _//   / ___//
| ' //   | ||__     \___ \\   -| ||-    \___ \\
| . \\   | ||__     /    //   _| ||_    /    //
|_|\_\\  |_____||  /____//   /_____//  /____//
`-` --`  `-----`  `-----`    `-----`  `-----`

```
• 4. Pinecone

Use the Internet to describe how the Fibonacci sequence is related to the object shown. (See Example 1 and Example 2.)

Pinecone

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```  _  _     _____     _____      ___     __   _
| \| ||  |  ___||  /  ___||   / _ \\  | || | ||
|  ' ||  | ||__   | // __    | / \ || | '--' ||
| .  ||  | ||__   | \\_\ ||  | \_/ || | .--. ||
|_|\_||  |_____||  \____//    \___//  |_|| |_||
`-` -`   `-----`    `---`     `---`   `-`  `-`

```
• 5. Sneezewort

Use the Internet to describe how the Fibonacci sequence is related to the object shown. (See Example 1 and Example 2.)

Sneezewort

• Worked-Out Solution

The branches and leaves on a sneezewort plant grow in a Fibonnaci pattern as shown in the diagram below.

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``` _    _      ___     _    _    _    _
| || | ||   / _ \\  | |  | || | || | ||   ____
| || | ||  | / \ || | |/\| || | || | ||  |    \\
| \\_/ ||  | \_/ || |  /\  || | \\_/ ||  | [] ||
\____//    \___//  |_// \_||  \____//   |  __//
`---`     `---`   `-`   `-`   `---`    |_|`-`
`-`
```
• 6. Human Body

Use the Internet to describe how the Fibonacci sequence is related to the object shown. (See Example 1 and Example 2.)

Human Body

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```  ______   _    _     ______     ___      _____