THE Golden Ratio
Razielle D., Jee Woo P., Danielle S., Alice C.
do these Images look familiar?
They all have one thing in common...
They all have one thing in common
The Golden Ratio
Also known as
Seems to be found EVERYWHERE...
THE GOLDEN MEAN,
THE GOLDEN NUMBER,
THE GOLDEN PROPORTION,
THE DIVINE PROPORTION,
THE DIVINE SECTION,
THE GOLDEN NUMBER,
THE DIVINE NUMBER.
What is The Golden ratio?
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An irrational number
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PHI (φ)=1.61803398874989484820...
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The ratio of two numbers is a:a+b
Relationship with
the Fibonacci Sequence
Relationship of
the Fibonacci Sequence with the pascal triangle
In summary: it is
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a sequence of numbers created by adding the two numbers before it
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1, 1, 2, 3, 5, 8, 13, 21, 34, 55...
Relationship with
the Fibonacci Sequence
Relationship:
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take two successive Fibonacci numbers
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ratio them (ex. 1/2, 2/3, 3/5, 5/8, 8/13...)
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the bigger the number, the closer it gets to the Golden Ratio
that have the golden ratio
golden ratio shapes
Isosceles Triangle
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the ratio a:b is equivalent to the golden ratio
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bisecting an isosceles triangle made with 36° and 72° from the larger angle will get another isosceles triangle
Isosceles Triangle
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if the process continues, a spiral will form with an infinite amount of isosceles triangles
Golden Ratio Pentagram
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contains five golden triangles
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made by joining two non-adjacent corners to the central pentagon
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Construct a simple square
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Draw a line from the midpoint of one side of the square to an opposite corner
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Use that line as the radius to draw an arc that defines the height of the rectangle
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Complete the golden rectangle
Golden Ratio rectangle
TRY IT YOURSELF
The Golden Ratio is found in your daily life too
Other examples of Golden Ratio in life
