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The Mathematical Formula of Art
Questions
 Did you know that math and geometry are very closely
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related to art? Brainstorm different ways that math
and geometry could be used in art.
Do you know of any artists who use math in their
artwork?
How might science and art be related? Brainstorm
ways artists may use science to inspire artwork.
Do you know of any artists who have used science in
their artwork?
Do you think a rectangle is more interesting that a
square in art? Explain why.
The Golden Mean
The Golden Mean is a
mathematical ratio which has
fascinated people for many years in
several different cultures.
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
The Golden Mean
 The golden ratio is 1·618034. It is often represented
by a Greek letter Phi Φ.
 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 petal arrangements, all involve
the Fibonacci numbers.
Have You Seen This?
Note that each
new square has a
side which is as
long as the sum
of the latest
two square's
sides.
The Parthenon
 “Phi“ was named
for the Greek
sculptor Phidias.
 The exterior
dimensions of
the Parthenon
in Athens, built
in about 440BC,
form a perfect
golden
rectangle.
Leonardo Da Vinci
 Many artists who lived after
Phidias have used this
proportion. Leonardo Da
Vinci called it the "divine
proportion" and featured it
in many of his paintings, for
example in the famous
"Mona Lisa". Try drawing a
rectangle around her face.
Are the measurements in a
golden proportion?
The “Vitruvian Man”
 Leonardo did an entire
exploration of the
human body and the
ratios of the lengths of
various body parts.
“Vitruvian Man”
illustrates that the
human body is
proportioned
according to the
Golden Ratio.
The Golden Mean is Also
Found in Nature
The Golden Spiral can be seen in the
arrangement of seeds on flower heads and in
pinecones.
Golden Self Portraits
 Using what you have
learned so far, you will
now get to try and make
your own golden section.
13 inch
 Draw squares on the big
paper that fit together
using these
inch
____
3 inch
____
measurements.
inch
8 inch
inch
|
5 inch
Golden Self Portraits
 Using your Golden
section, look at your
picture and find squares
of the same size that
you think have an
interesting
composition.
Golden Self Portraits