1. The Golden Mean and Human Proportion  Inspired by Leonardo DaVinci by Valerie Xanos

2. The Golden Mean Phi  is simply the ratio of the line segments that result when a line is divided in one very special way. 1:1.618a line is divided Divide a line so that:

3.   Phi appears in: The proportions of the human bodyhuman body The proportions of many other animalsother animals Plants DNA The solar systemsolar system Art and architecture Music Population growth The stock marketstock market Copyright 1997-2007 PhiPoint Solutions, LLC

4. Antiochos (signed), copy of Phidias Athena of the Parthenos

10. Golden Mean in Art Ancient Greeks used it in sculpture and architecture (Phidias) Ancient Greeks used it in sculpture and architecture (Phidias) Renaissance artists created a revival of its use, calling it Divine Proportion. Renaissance artists created a revival of its use, calling it Divine Proportion. Da Vinci used this technique in all of his paintings. Da Vinci used this technique in all of his paintings. Artists to this day continue to use the Golden Mean. Artists to this day continue to use the Golden Mean.

11. The Parthenon, Acropolis, Athens, Greece

13. Leonardo Da Vinci, The Last Supper

15. Leonardo Da Vinci, Mona Lisa

16. Sandro Botticelli, The Birth of Venus

18. Golden Mean and Life "All life is biology. All biology is physiology. All physiology is chemistry. All chemistry is physics. All physics is math." Dr. Stephen Marquardt "All life is biology. All biology is physiology. All physiology is chemistry. All chemistry is physics. All physics is math." Dr. Stephen Marquardt The Golden Mean is found in all Life Forms The Golden Mean is found in all Life Forms

19. Golden Mean and Life The DNA spiral is a Golden Section The DNA spiral is a Golden Section The DNA molecule, the program for all life, is based on the golden section. It measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral.

20. Our Solar System corresponds to the Golden Mean in measurement of distance from each other, even the rings of Saturn.

21. Fibonacci Numbers "Without mathematics there is no art." --Luca Pacioli "Without mathematics there is no art." --Luca Pacioli Leonard of Pisa (1170- 1250), better known as Fibonacci, introduced the Fibonacci Series, a sequence of numbers; 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … in which any number is the sum of the two preceding members. 0 + 1 = 1 1 + 1 = 2 1 + 2 = 3 2 + 3 = 5 3 + 5 = 8 5 + 8 = 13 etc.

22. Fibonacci Numbers The Fibonacci Series and the Golden Mean are intimately connected. The Fibonacci Series numbers increase at a rate equal to (actually, oscillating round) the Golden mean. (The larger the numbers, the closer to the Golden Mean.) The Fibonacci Series and the Golden Mean are intimately connected. The Fibonacci Series numbers increase at a rate equal to (actually, oscillating round) the Golden mean. (The larger the numbers, the closer to the Golden Mean.)

23. Notice that the proportionate length of each part of a finger bone corresponds with the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8, 13, 21,

24. Golden Spiral Golden Spiral Draw a golden rectangle Draw a golden rectangle Taking the smaller of the sections, draw another golden rectangle Taking the smaller of the sections, draw another golden rectangle Keep doing that ad infinitum Keep doing that ad infinitum A spiral can be drawn through the corners of each golden section. A spiral can be drawn through the corners of each golden section. These spirals are found everywhere!!! (shells, galaxies, hurricanes, human ear) These spirals are found everywhere!!! (shells, galaxies, hurricanes, human ear)

31. Golden Mean and the Human Body The Golden Mean and Golden Spiral are evident in the proportions of the human body. The Golden Mean and Golden Spiral are evident in the proportions of the human body.

32. A template for human beauty is found in phi and the pentagon

34. The rules of human proportion are often simplified To correspond to the size of the head. Adult humans are about 8 heads tall

35. The proportion of infants, children, And adolescents is very different from the adult. Infant: Toddler: Child: Adolescent:

36. Leonardo DaVinci

37. Vitruvian Man The Vitruvian Man is a world renowned drawing with accompanying notes created by Leonardo da Vinci around the year 1492 as recorded in one of his journals. It depicts a nude male figure in two superimposed positions with his arms and legs apart and simultaneously inscribed in a circle and square. The drawing and text are sometimes called the Canon of Proportions or, less often, Proportions of Man. It is on display in the Gallerie dell' Accademia in Venice, Italy The Vitruvian Man is a world renowned drawing with accompanying notes created by Leonardo da Vinci around the year 1492 as recorded in one of his journals. It depicts a nude male figure in two superimposed positions with his arms and legs apart and simultaneously inscribed in a circle and square. The drawing and text are sometimes called the Canon of Proportions or, less often, Proportions of Man. It is on display in the Gallerie dell' Accademia in Venice, Italy drawingLeonardo da Vinci 1492AccademiaVenice drawingLeonardo da Vinci 1492AccademiaVenice http://en.wikipedia.org/wiki/Vitruvian_man

41. DaVinci filled sketchbooks with studies and research about the human body and the natural world. He even wrote in his own code, backwards (mirror- writing).

42. Leonardo DaVinci

43. Michelangelo

45. http://www.byzarium.com/images/ flashImages/Odd_Nerdrum_small.jpg Odd Nerdrum Return of the Sun

46. Artemisia Gentileschi Susanna and the Elders

47. Frida Kahlo Two Fridas

48. http://www.ibiblio.org/wm/paint/auth/moreau/orpheus.jpg Gustave Moreau Orpheus

49. http://religion-cults.com/Cults/Other/CRISTO2DALI71.JPG Salvador Dali Christ Crucified 2

50. http://odin.himinbi.org/reading_list/dali%20-%20last%20supper.jpg

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