The Mathematical Formula of Art

QuestionsDid you know that math and geometry are very

closely 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 RatioThe Golden SectionThe Golden RectangleThe Golden NumberThe Golden SpiralOr 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 VinciMany 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 PortraitsUsing what you have

learned so far, you will now get to try and make your own golden section.

Draw squares on the big paper that fit together using these measurements.

inch

inch inch

13 inch

8 inch

____

____

|

5 inch

3 inch

Golden Self PortraitsUsing your Golden

section, look at your picture and find squares of the same size that you think have an interesting composition.

Golden Self Portraits