The document discusses how the Fibonacci sequence appears frequently in nature. It introduces Leonardo Fibonacci, the Italian mathematician who documented the sequence, and describes how the sequence is formed by adding the previous two numbers. It then gives several examples of how the Fibonacci sequence shows up in patterns of plant life like flowers, fruit, vegetables, and phyllotaxis. Finally, it explains how the Golden Ratio, a ratio derived from the Fibonacci sequence, is commonly found in art, architecture, nature, and proportions of the human body.

1. Fibonacci in Real Life Jody Hollister

2. Fibo-who? - Leonardo Fibonacci - Italian Mathematician - Wrote Liber Abaci - Did not discover sequence - Used famous sequence as example in book

3. Fibonacci Sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, ... - Formed by adding the preceding two numbers together. - Ex: Fifth number (5) is formed by adding third and fourth (2 + 3)

4. Fibonacci in Nature - Fibonacci numbers are all around us - "Nature's Mystery" - Show up in other art, arcitecture, and nature

5. Fibonacci in Flowers - Number of petals - Pattern of leaves - Spirals in center

6. Fibonacci in Fruit - Number of seeds - Patterns on outer layer

7. Fibonacci in Vegetables - Spirals in certain vegetables - Fractal patterns

8. Fibonacci and the Golden Ratio - Ratio derived from Fibonacci Sequence - Found in: - art - architecture - nature

9. Golden Ratio - 1 : 1.61... - Derived from Fibonacci and denoted by the Greek letter "phi"

10. Golden Ratio in Humans - Ratio of bones - Ratio of facial features