the golden curve maths, art and nature. it’s surprising who uses maths many of the writers for the...
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The Golden CurveThe Golden Curve
Maths, art and natureMaths, art and nature
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It’s surprising who uses It’s surprising who uses mathsmaths
Many of the writers for The Simpsons have maths degrees.
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Maths helps us…Maths helps us…
DesignDesign
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Maths helps us…Maths helps us…
DesignDesign
PlanPlan
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Maths helps us…Maths helps us…
DesignDesign
PlanPlan
UnderstandUnderstand
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Where’s the maths?Where’s the maths?
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Where’s the maths? (1)Where’s the maths? (1)
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Where’s the maths? (2)Where’s the maths? (2)
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Where’s the maths? (3)Where’s the maths? (3)
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Where’s the maths? (4)Where’s the maths? (4)
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The “Golden Curve”The “Golden Curve”
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The Fibonacci sequenceThe Fibonacci sequence
• 1, 1, 2, 3, 5, 8, 13, 21, 34, ….1, 1, 2, 3, 5, 8, 13, 21, 34, ….
• What comes next?What comes next?
21 + 34 = 5521 + 34 = 55 34 + 55 = 8934 + 55 = 89
55 + 89 = 14455 + 89 = 144 89 + 144 = 233 89 + 144 = 233
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The The ratiosratios of the sequence of the sequence
• 1 1 ÷ ÷ 1 = 11 = 1
• 2 2 ÷÷ 1 = 2 1 = 2
• 3 3 ÷÷ 2 = 1.5 2 = 1.5
• 5 ÷5 ÷ 3 = 1.6666666666… 3 = 1.6666666666…
• 8 8 ÷÷ 5 = 1.6 5 = 1.6
• 13 13 ÷÷ 8 = 1.625 8 = 1.625
• 21 21 ÷÷ 13 = 1.615384615384615384615… 13 = 1.615384615384615384615…
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The The ratiosratios of the of the sequence…sequence…
• 8 8 ÷÷ 5 = 1.6 5 = 1.6
• 13 13 ÷÷ 8 = 1.625 8 = 1.625
• 21 21 ÷÷ 13 = 1.615384615384615384615… 13 = 1.615384615384615384615…
• 34 34 ÷÷ 21 = 1.619047619047619047619… 21 = 1.619047619047619047619…
• 55 55 ÷÷ 34 = 1.6176470588235294117647… 34 = 1.6176470588235294117647…
• 89 89 ÷÷ 55 = 1.6181818181818181818… 55 = 1.6181818181818181818…
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The ratios tend to a The ratios tend to a number!number!
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
0 2 4 6 8 10 12
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The golden ratioThe golden ratio
• The number that these ratios tend The number that these ratios tend towards is called the towards is called the golden ratiogolden ratio::
1.618033988749…1.618033988749…
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Why golden?Why golden?
• It has lots of special propertiesIt has lots of special properties
• People have studied it for over 2000 yearsPeople have studied it for over 2000 years
• It occurs in art, architecture and natureIt occurs in art, architecture and nature
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Golden rectanglesGolden rectangles
• A golden rectangle has A golden rectangle has one side which is one side which is 1.618033… times the 1.618033… times the length of the otherlength of the other
• The United Nations The United Nations building in New York building in New York has this shape has this shape
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People like golden People like golden rectanglesrectangles
• Too long? Too short? Just right!Too long? Too short? Just right!
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Nature and the golden ratioNature and the golden ratio
• Sunflowers use the Fibonacci sequenceSunflowers use the Fibonacci sequence
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Shells and the golden curveShells and the golden curve
• The shell of a nautilus (sea creature)The shell of a nautilus (sea creature)