1. Basic Practice of Statistics - 3rd Edition
Lecture 4
1. Fibonacci Sequence
2. Golden ratio
Chapter 2

2. Basic Practice of Statistics - 3rd Edition
Fibonacci Sequence
Recap:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …
Finding Patterns in Nature that exhibit numbers
in the sequence: your project.
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3. Basic Practice of Statistics - 3rd Edition
Plants
White Calla Lily
One Petal
Euphorbia
Two Petals
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4. Plants Bloodroot Shasta daisy with 21 petals
Basic Practice of Statistics - 3rd Edition
Plants
Bloodroot
8 petals are not very common
Shasta daisy with 21 petals 4
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5. Basic Practice of Statistics - 3rd Edition
Pine cone
A pine cone’s petals spiral in two directions. The number of petals to go around once is always a Fibonacci number. 5
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6. Sunflower Seeds on a sunflower also show the Fibonacci spiral. 6
Basic Practice of Statistics - 3rd Edition
Sunflower
Seeds on a sunflower also show the Fibonacci spiral. 6
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7. Pineapple The sequence is found in pineapples. 7
Basic Practice of Statistics - 3rd Edition
Pineapple
The sequence is found in pineapples. 7
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8. Fibonacci Spirals Draw the spirals on the sheets provided. 8
Basic Practice of Statistics - 3rd Edition
Fibonacci Spirals
Draw the spirals on the sheets provided. 8
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9. Fibonacci Spirals 9 Basic Practice of Statistics - 3rd Edition
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10. Fibonacci Spirals 10 Basic Practice of Statistics - 3rd Edition
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11. Fibonacci Spirals Draw a spiral that matches the shell below: 11
Basic Practice of Statistics - 3rd Edition
Fibonacci Spirals
Draw a spiral that matches the shell below: 11
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12. Basic Practice of Statistics - 3rd Edition
Fibonacci Spirals 12
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13. The Golden Ratio Golden Ratio - Phi φ = 1.618033989
Basic Practice of Statistics - 3rd Edition
The Golden Ratio
Your project report: discuss your findings with your group. Give a short presentation on your findings.
Golden Ratio - Phi φ = 13
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14. Golden Ratio 14 Basic Practice of Statistics - 3rd Edition Chapter 2

15. Basic Practice of Statistics - 3rd Edition
Golden Ratio
Mona Lisa
Mona Lisa's face is a perfect golden rectangle, according to the ratio of the width of her forehead compared to the length from the top of her head to her chin. 15
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16. Golden Ratio The Great Pyramid at Giza 16
Basic Practice of Statistics - 3rd Edition
Golden Ratio
The Great Pyramid at Giza
Half of the base, the slant height, and the height from the vertex to the center create a right triangle. When that half of the base equal to one, the slant height would equal to the value of Phi and the height would equal to the square root of Phi. 16
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17. Basic Practice of Statistics - 3rd Edition
The Golden Ratio
Activity: Find the ratio of the length to the width of your credit card.
What value did you get?
Find other objects that exhibit the Golden Ratio or Golden Rectangle.
Internet Sources: 17
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