MATH IN OUR
WORLD
MATH IS EVERYWHERE!
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MATH IS EVERYWHERE!
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MATH IS EVERYWHERE!
Space Shuttle
Challenger Disaster
(1986)
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MATH IS EVERYWHERE!
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MATH IS EVERYWHERE!
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MATH IS EVERYWHERE!
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MATH IS EVERYWHERE!
https://youtu.be/PMerSm2ToFY
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HOW ABOUT IN
NATURE?
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MATH IS EVERYWHERE!
https://youtu.be/kkGeOWYOFoA
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MATH IS EVERYWHERE!
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FIBONACCI SEQUENCE
How did the Fibonacci sequence come about?
Leonardo of Pisa aka “Fibonacci”
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FIBONACCI SEQUENCE
Fibonacci asked, “How do rabbits breed?”. He observed…
young pair of rabbits
adult pair of rabbits
Idea:
- It takes a month for a young rabbit to become adult.
- It takes a month before an adult rabbit bears a young rabbit.
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FIBONACCI SEQUENCE
Month 0
1
Month 1
1
Month 2
2
Month 3
3
Month 4
5
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FIBONACCI SEQUENCE
How is the Fibonacci sequence derived?
1. First two terms of the sequence is 𝟏 and 𝟏.
2. Add two consecutive terms to get the next term.
𝟏 𝟏 𝟐 𝟑 𝟓
𝟖 𝟏𝟑 𝟐𝟏 𝟑𝟒 …
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FIBONACCI SEQUENCE
“Fibonacci numbers are said as one of the Nature's numbering systems …”
•
1
2
3
5
White calla lily
Euphorbia
Trillium
Hibiscus
Akhtaruzzaman, Md. (2011). Geometrical Substantiation of Phi, the Golden Ratio and the Baroque
of Nature, Architecture, Design and Engineering. International Journal of Arts. 1.
10.5923/j.arts.20110101.01
16
FIBONACCI SEQUENCE
“Fibonacci numbers are said as one of the Nature's numbering systems …”
8
Bloodroot
•
13
21
34
Black Eyed Susan
Shasta Daisy
Daisy
Akhtaruzzaman, Md. (2011). Geometrical Substantiation of Phi, the Golden Ratio and the Baroque
of Nature, Architecture, Design and Engineering. International Journal of Arts. 1.
10.5923/j.arts.20110101.01
17
FIBONACCI SEQUENCE
Fibonacci Sequence:
𝟏 𝟏 𝟐 𝟑 𝟓
𝟖 𝟏𝟑 𝟐𝟏 𝟑𝟒 …
Use your calculator and observe:
𝟏
𝟏
𝟐
𝟏
𝟑
𝟐
𝟓
𝟑
𝟖
𝟓
𝟏𝟑
𝟖
𝟐𝟏
𝟏𝟑
𝟑𝟒
𝟐𝟏
⟹ approaches to 𝝋 = 𝟏. 𝟔𝟏𝟖 …
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GOLDEN RATIO
CONCEPT: A line is divided into two sections containing a unique property such
that the ratio between the bigger segment and the shorter segment should be
equal to the ratio between the line and its bigger segment
S
B
𝐁 𝐒+𝐁
=
=𝝋
𝐒
𝐁
𝟏+ 𝟓
=
≈ 𝟏. 𝟔𝟏𝟖𝟖𝟎𝟑𝟑𝟗𝟖𝟖𝟕 = 𝛗
𝟐
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GOLDEN RATIO
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GOLDEN RATIO
"Non mi legga chi non e matematico.“
– Leonardo Da Vinci
(“Let no one read me who is not a
mathematician.”)
“Mona Lisa”
aka “La Gioconda”
* http://monalisa.org/2012/09/12/leonardo-and-mathematics-in-his-paintings/
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GOLDEN RATIO
Parthenon (in Greece)
* https://www.goldennumber.net/parthenon-phi-golden-ratio/
The quotient of the length from foot to the top of the arch and the length from the
top of the arch to the tip of the roof is close to the Golden Ratio.
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GOLDEN RATIO
•
Akhtaruzzaman, Md. (2011). Geometrical
Substantiation of Phi, the Golden Ratio and the
Baroque of Nature, Architecture, Design and
Engineering. International Journal of Arts. 1.
10.5923/j.arts.20110101.01
23
GOLDEN RATIO
https://youtu.be/0hvD5kLqjuw
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NOTE
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