1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

17
1 1. Fibonacci Sequence 2. Golden ratio Lecture 4
  • date post

    19-Dec-2015
  • Category

    Documents

  • view

    239
  • download

    1

Transcript of 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

Page 1: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

1

1. Fibonacci Sequence2. Golden ratio

Lecture 4

Page 2: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

2

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

Page 3: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

3

Plants

White Calla LilyOne Petal

Euphorbia Two Petals

Page 4: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

4

Plants

Bloodroot8 petals are not very common

Shasta daisy with 21 petals

Page 5: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

5

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

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

Page 6: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

6

Sunflower Seeds on a sunflower also show the Fibonacci

spiral.

Page 7: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

7

Pineapple The sequence is found in pineapples.

Page 8: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

8

Fibonacci Spirals

Draw the spirals on the sheets provided.

Page 9: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

9

Fibonacci Spirals

Page 10: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

10

Fibonacci Spirals

Page 11: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

11

Fibonacci SpiralsDraw a spiral that matches the shell below:

Page 12: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

12

Fibonacci Spirals

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

Page 13: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

13

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

Page 14: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

14

Golden Ratio

Page 15: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

15

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.

Page 16: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

16

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.

Page 17: 1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.

17

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