grace golden mean
TRANSCRIPT
-
8/2/2019 Grace Golden Mean
1/20
The Golden MeanThe Mathematical Formula of
Life
-
8/2/2019 Grace Golden Mean
2/20
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.
-
8/2/2019 Grace Golden Mean
3/20
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
-
8/2/2019 Grace Golden Mean
4/20
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/ -
8/2/2019 Grace Golden Mean
5/20
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
-
8/2/2019 Grace Golden Mean
6/20
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.
-
8/2/2019 Grace Golden Mean
7/20
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 -
8/2/2019 Grace Golden Mean
8/20
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 -
8/2/2019 Grace Golden Mean
9/20
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.
-
8/2/2019 Grace Golden Mean
10/20
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.
-
8/2/2019 Grace Golden Mean
11/20
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.
-
8/2/2019 Grace Golden Mean
12/20
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?????
-
8/2/2019 Grace Golden Mean
13/20
The Golden
Mean isAlso Found
in Nature
-
8/2/2019 Grace Golden Mean
14/20
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 -
8/2/2019 Grace Golden Mean
15/20
Pine cones
show theFibonacciSpiralsclearly. Here
is a picture ofan ordinarypineconeseen from itsbase wherethe stalkconnects it tothe tree.
-
8/2/2019 Grace Golden Mean
16/20
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.
-
8/2/2019 Grace Golden Mean
17/20
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.
-
8/2/2019 Grace Golden Mean
18/20
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..
-
8/2/2019 Grace Golden Mean
19/20
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.
-
8/2/2019 Grace Golden Mean
20/20
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