Download Introduction to the Golden Mean

INTRODUCTION TO THE
GOLDEN MEAN
… and the Fibonacci Sequence
The Golden Mean
Aristotle defined it as…
the desirable middle between two extremes, one of
excess and the other of deficiency
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In Art,
a term used to describe aesthetically pleasing
proportioning within a piece.
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It is not merely a term -- it is an actual ratio.
So what is the Golden Ratio?
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The golden ratio is 1 to 1.618034.
The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13,
... (add the last two numbers to get the next)
The GOLDEN RATIO and FIBONACCI NUMBERS
 sea
shell shapes, branching plants, flower petals and
seeds, leaves and petal arrangements all involve the
Fibonacci numbers.
The Golden Mean also known as…
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The Golden Ratio
The Golden Section
The Golden Rectangle
The Golden Number
The Golden Spiral
The Divine Proportion
Wait… this is Math
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The line AB is divided
at point M so that the
ratio of the two parts,
(the smaller MB to the
larger AM) is the same
as the ratio of the
larger part AM to the
whole AB.
This is kind of like geometry…
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Given a rectangle having
sides in the ratio 1:1.6
Dividing the original
rectangle into a square
and new rectangle results
in a new rectangle having
sides with a ratio 1:1.6.
This is called a Golden
Rectangle
Every other division of the
rectangle into squares
results in a spiral
This figure is known as a
whirling square.
Fibonacci Sequence
& the Golden Rectangle
Golden Rectangle
Golden Spiral
What is this called again?
The Golden Mean and Art
Throughout history, the ratio for length to width
of rectangles of 1.61 has been considered the
most pleasing to the eye.
The Parthenon
The exterior
dimensions of
the Parthenon
in Athens,
built in about
440BC, form
a perfect
golden
rectangle.
The Parthenon
With the Golden Rectangle
Leonardo Da Vinci’s Mona Lisa
Try drawing a
rectangle around
her face.
Are the
measurements in a
golden proportion?
Mona Lisa
With Divine Proportion
Modern Day Examples
Today, where might you want to use the Golden Mean
to create an image that is pleasing to the eye?
TWITTER
Apple Logo
iCLOUD Logo
Look at your own hand
2 hands each of which has ...
5 fingers
3 parts
2 knuckles
Your turn… finger, hand, arm, foot
Grab a ruler from the center of the table
The Golden Mean in Nature
It can be found EVERYWHERE!!!!
Nautilus Shell
The spiral is created by the Golden Rectangle
divisions.
Seeds
The Golden Spiral can be seen in the
arrangement of seeds on flower heads.
Pine Cones
Pine cones show the Golden Spirals clearly. Here is
a picture of an ordinary pinecone seen from its base
where the stalk connects it to the tree.
Flower Petals
On many plants, the number of petals is a Fibonacci number:
Buttercups have 5 petals; Lilies and Iris have 3 petals; some Delphiniums
have 8; sorne Marigolds have 13 petals; some Asters have 21 and Daisies
can be found with 34, 55 or even 89 petals.
Two days from now…
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You will choose a pattern from nature which is
created through the phenomenon of the
Golden Mean such as the pattern in a Nautilus
Shell and create an original design.
The Possibilities are infinite…
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The pattern of a butterfly wing….
Patterns of sea creatures……
Close ups of patterns from nature…..
Leaf arrangements, leaf veins, petal patterns….
Feather patterns from birds such as one feather, or
the entire tail pattern of a peacock….
Look at animals, bugs, fish, and plants to get
ideas…..
Quick Rubric
The design must be original.
The painting must use a pattern found in nature to inspire the
design.
The project is to be done in tempura paint.
The design must show technical craftsmanship.
The student must make good use of class time and take proper
care of tools and supplies.
THE DESIGN MUST USE THE GOLDEN MEAN