Golden mean presentation_01


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Golden Mean Presentation: BCC - 2D Design

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  • I enjoyed seeing 3 of my pictures on your site with my golden mean gauge. The insect, the peacock feather and the teeth. See
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Golden mean presentation_01

  1. 1. The  Golden  Mean   The  Mathema)cal  Formula…   of  Life?  
  2. 2. 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
  3. 3. The  Golden  Mean    The Golden Mean is a ratio whichhas fascinated generation aftergeneration, and culture after culture.
  4. 4. The  Golden  Mean    It can be expressed succinctly in theratio of the number “1” to theirrational 1.618034. 1.618034 1
  5. 5. The  Golden  Mean      •  The golden ratio is 1·618034. It is often represented by a Greek letter Phi Φ.    Phi  pronuncia)on:  Linguis)c  purist  might  opt  for  the  original  Greek  fee,   most  mathema)cians  know  phi  as  fi.  •  The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ... (add the last two to get the next and so on)•  The golden ratio and Fibonacci numbers also exist in nature… more on that in a bit.
  6. 6.  The Golden Ratio
  7. 7. One Way to Understand It Is A                                M              B        A B A MThe line AB is divided at point M so thatthe ratio of the two parts,the smaller MB to the larger AM is thesame as the ratio of the larger part AM tothe whole AB. Does that make sense?
  8. 8. What?  
  9. 9. OK try this  
  10. 10. Fibonacci Sequence Expressed as aGolden Rectangle   1+ 1 =2 1 2 2 1
  11. 11. Fibonacci Sequence Expressed as aGolden Rectangle   1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 37 1+1= 2 2+3=5 3+5=8 5+8=13  
  12. 12. So the Golden Ratio is…  Given a rectangle having sides inthe ratio 1:phi, phi is defined suchthat partitioning the originalrectangle into a square and newrectangle results in a newrectangle having sides with a ratio1: phi. Such a rectangle is calleda golden rectangle, andsuccessive points dividing agolden rectangle into squares lieon a logarithmic spiral. This figureis known as a whirling square.
  13. 13. Whirling Square  
  14. 14. The  Golden  Mean  &  Aesthe1cs  •  Throughout history, the ratio for length to width of rectangles of 1: 1.61803 39887 49894 84820 has been considered the most pleasing to the eye
  15. 15. The  Parthenon  The exteriordimensions ofthe Parthenon inAthens
  16. 16. The  Parthenon  The exteriordimensions ofthe Parthenon inAthens, built inabout 440BC …
  17. 17. The  Parthenon  The exteriordimensions ofthe Parthenon inAthens, built inabout 440BC …form a perfectgolden rectangle.
  18. 18. Golden SpiralLogarithmic Spiral: The Whirling Square.Note that each new square has a side which is as long as the sum ofthe latest two squares sides.
  19. 19. Leonardo  Da  Vinci  •  Leonardo Da Vinci called it the "divine proportion" and featured it in many of his paintings.
  20. 20. Leonardo  Da  Vinci  •  Leonardo Da Vinci called it the "divine proportion" and featured it in many of his paintings.•  In the famous "Mona Lisa". Try drawing a rectangle around her face. You can further explore this by subdividing the rectangle formed by using her eyes as a horizontal divider, etc.  
  21. 21. 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.
  22. 22. Look at your own hand:You have ...• 2 hands each of which has ...• 5 fingers, each of which has ...• 3 parts separated by ...• 2 knucklesAnd…
  23. 23. The Golden Ratio A                              M              B         A B A M
  24. 24. The  Golden  Mean  is  also   Found  in   Nature  
  25. 25. On many plants, the number ofpetals is a Fibonacci number:buttercups have 5 petals;lilies and iris have 3 petals;some delphiniums have 8;corn marigolds have 13 petals;some asters have 21 whereasdaisies can be found with 34,55 or even 89 petals.
  26. 26. The Golden Spiral can be seen in thearrangement of seeds on flower heads.
  27. 27. Pine cones showthe FibonacciSpirals clearly.Here is a pictureof an ordinarypinecone seenfrom its basewhere the stalkconnects it tothe tree.
  28. 28. And In Shells
  29. 29. And In Insects
  30. 30. And In Space
  31. 31. So?  Where and how can I use it?
  32. 32. In Compositions
  33. 33. A Pretty Picture
  34. 34. A Pretty Balanced Picture
  35. 35. In Design
  36. 36. Project  8  •  Objectives We will explore geometric relationships within the Picture plane derived from the Golden Section, or the Golden Rectangle. This system provides a way to place and organize shapes based on using mathematical ratios and rational proportions. We will also explore how to direct the viewer s eye by contrasts of value, shape and size.
  37. 37. But  first    an  in-­‐class  project  to  warm  up