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Ratio
Golden Ratio
Fibonacci
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Ratio
• Ratio is a way of showing the connection
between two or more numbers.
• A ratio can be written as a fraction, a decimal
or as numbers with : between them.
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There are 30 students in a class;
18 are girls and 12 are boys.
Express this as a ratio.
• The ratio of girls to boys is: 18 : 12 or
• 3 : 2 (simplifying) or
3
• –– (fraction) or
2
• 1·5 (decimal)
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The Golden Ratio
• At least since the Renaissance, many artists and
architects have proportioned their works to
approximate the Golden Ratio, believing this
proportion to be aesthetically pleasing.
• Leonardo da Vinci’s drawings of the human body
emphasised its proportion.
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The Golden Ratio
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The Golden Ratio
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w
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The Golden Ratio
• This Golden Ratio has many unusual properties. We
will take the number as 1·618.
• Remember, this is an approximation. The number is
irrational.
1
––––– = 0·618
1·618
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Fibonacci
• Fibonacci, an Italian mathematician, developed
a famous series in the thirteenth century.
• Start with 1, 1.
• Every number is calculated by adding the two
previous numbers together.
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Fibonacci Series
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1
1
2
3
5
8
Golden Ratio
• Compute the ratio of Fibonacci numbers:
2÷1= 2
3 ÷ 2 = 1·5
5÷3=
8÷5=
13 ÷ 8 =
21 ÷ 13 =
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1·666…
1·6
1·625
1·615…
Fibonacci in Nature
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Spirals
13
21
2 3
1 1
8
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5
Spirals
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Golden Ratio in Nature
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Golden Ratio in Architecture
Great Wall of China
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Parthenon, Greece
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