1 1. Fibonacci Sequence 2. Golden ratio Lecture 4

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1. Fibonacci Sequence2. Golden ratio

Lecture 4

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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.

Fibonacci Sequence

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Plants

White Calla LilyOne Petal

Euphorbia Two Petals

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Plants

Bloodroot8 petals are not very common

Shasta daisy with 21 petals

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Pine cone A pine cone’s petals spiral in two directions. The

number of petals to go around once is always a Fibonacci number.

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Sunflower Seeds on a sunflower also show the Fibonacci

spiral.

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Pineapple The sequence is found in pineapples.

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Fibonacci Spirals

Draw the spirals on the sheets provided.

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Fibonacci Spirals

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Fibonacci Spirals

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Fibonacci SpiralsDraw a spiral that matches the shell below:

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Fibonacci Spirals

http://www.shallowsky.com/blog/science/fibonautilus.html

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The Golden Ratio

Your project report: discuss your findings with your group. Give a short presentation on your findings.

Golden Ratio - Phi φ = 1.618033989

http://library.thinkquest.org/trio/TTQ05063/phibeauty1.htm

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Golden Ratio

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Golden RatioMona 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.

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Golden RatioThe 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.

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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:http://www.shallowsky.com/blog/science/fibonautilus.htmlhttp://jwilson.coe.uga.edu/emt669/Student.Folders/Lewis.Millard/fibonacci/Fib.htmlhttp://britton.disted.camosun.bc.ca/fibslide/jbfibslide.htmhttp://4.bp.blogspot.com/_qC54jayKgko/SPtql92PbgI/AAAAAAAACH4/pn0vY4yIrm0/s1600-h/tiling8.gifhttp://library.thinkquest.org/trio/TTQ05063/phibeauty3.htm