grace golden mean

8/2/2019 Grace Golden Mean

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The Golden MeanThe Mathematical Formula of

Life


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The Golden Mean

The Golden Mean is a ratio which

has fascinated generation after

generation, and culture after culture.It can be expressed succinctly in the

ratio of the number "1" to the

irrational l.618034.


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The Golden Mean

Also known as:

The Golden Ratio

The Golden Section The Golden Rectangle

The Golden Number

The Golden Spiral Or the Divine Proportion


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The Golden Mean

The golden ratio is 1618034. It is oftenrepresented by a Greek letter Phi .

The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8,

13, ... (add the last two to get the next) The golden ratio and Fibonacci numbers relate

in such that sea shell shapes, branching plants,

flower petals and seeds, leaves and petalarrangements, all involve the Fibonaccinumbers.
http://www.goldennumber.net/http://www.goldennumber.net/


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A M B

The line AB is divided at point M so that theratio of the two parts, the smaller MB to the

larger AM is the same as the ratio of thelarger part AM to the whole AB. Does thatmake sense?

One Way to Understand It


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OR

Given a rectangle having sidesin the ratio 1:phi , phi is definedsuch that partitioning theoriginal rectangle into a square

and new rectangle results in anew rectangle having sides witha ratio 1: phi. Such a rectangleis called a golden rectangle,

and successive points dividinga golden rectangle into squareslie on a logarithmic spiral. Thisfigure is known as a whirlingsquare.


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Have You Seen This?

Note that eachnew squarehas a side

which is aslongas the sum ofthe latesttwo square'ssides.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.htmlhttp://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.htmlhttp://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.htmlhttp://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.htmlhttp://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.htmlhttp://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.htmlhttp://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.htmlhttp://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.htmlhttp://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.htmlhttp://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html


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The Golden Mean and Aesthetics

Throughout history, the ratio for length to

width of rectangles of 1.61803 39887 49894

84820 has been considered the most

pleasing to the eye.

Artists use the Golden Mean in the creation

of great works.
http://students.bath.ac.uk/ma1caab/art.htmlhttp://students.bath.ac.uk/ma1caab/art.htmlhttp://students.bath.ac.uk/ma1caab/art.htmlhttp://students.bath.ac.uk/ma1caab/art.html


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The Parthenon

Phi was named

for the Greek

sculptor Phidias.

The exterior

dimensions of the

Parthenon in

Athens, built in

about 440BC,

form a perfectgolden rectangle.


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Leonardo Da Vinci

Many artists who lived afterPhidias have used thisproportion. Leonardo DaVinci called it the "divineproportion" and featured it

in many of his paintings, forexample in the famous"Mona Lisa". Try drawing arectangle around her face.Are the measurements in a

golden proportion? You canfurther explore this bysubdividing the rectangleformed by using her eyes asa horizontal divider.


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The Vitruvian

Man

Leonardo did an entire

exploration of the

human body and the

ratios of the lengths ofvarious body parts.

Vitruvian Man

illustrates that the

human body isproportioned according

to the Golden Ratio.


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Look at your own hand:

You have ...

2 hands each of which has ...5 fingers, each of which has ...3 parts separated by ...

2 knucklesIs this just a coincidence or not?????


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The Golden

Mean isAlso Found

in Nature


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The Golden Spiral can be seen in the arrangement ofseeds on flower heads.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/coneflower.jpg


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Pine cones

show theFibonacciSpiralsclearly. Here

is a picture ofan ordinarypineconeseen from itsbase wherethe stalkconnects it tothe tree.


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On many plants, thenumber of petals is a

Fibonacci number:buttercups have 5petals; lilies and irishave 3 petals; some

delphiniums have 8;corn marigolds have13 petals; some astershave 21 whereas

daisies can be foundwith 34, 55 or even 89petals.


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Patterns of Nature

In this assignment students 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. Students will use this pattern, or the one

demonstrated in the Last Supper to create an

original work of art using the Golden Mean to create

the composition.

The solutions to this problem are infinite.


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Ideas for Designs

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 onefeather, or the entire tail pattern of a

peacock. Look at animals, bugs, fish, and plants to get

ideas..


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Rubric

The design must be original. The composition must use the Golden Mean.

The painting must use a pattern found in nature toinspire the design.

The design must demonstrate knowledge of space asan element of design.

The project is to be done in acrylic paint.

The design must show technical craftsmanship.

The student must use proper care and conservation oftools and supplies.


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The fairest thing we can experience

is the mysterious. It is thefundamental emotion which stands

at the cradle of true art and

science. He who knows it not andcan no longer wonder, no longer

feels amazement, is as good as

dead, a snuffed-out candle.

Albert Einstein

grace golden mean

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