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The Golden Mean

The Golden Mean. The Mathematical Formula of Art. Questions. Did 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?

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The Golden Mean

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  1. The Golden Mean The Mathematical Formula of Art

  2. Questions • Did 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.

  3. The Golden Mean • The Golden Mean is a mathematical ratio which has fascinated people for many years in several different cultures.

  4. 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

  5. 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.

  6. 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.

  7. 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.

  8. 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?

  9. 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.

  10. The Golden Mean is Also Found in Nature

  11. The Golden Spiral can be seen in the arrangement of seeds on flower heads and in pinecones.

  12. Golden Self Portraits • Using 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. 13 inch inch ____ 3 inch ____ inch inch 5 inch | 8 inch

  13. 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.

  14. Golden Self Portraits

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