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The math behind beauty


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Published in: Education, Technology

The math behind beauty

  1. 1. Today you will learn about the Golden Ratio and study Leonardo’s famous painting Mona Lisa.<br />You will then recreate your own version of a modern day Mona Lisa painting of either yourself or a partner. <br />
  2. 2. How does mathematics relate to beauty? <br />What is “beauty”? <br /><ul><li>Brainstorm how you think math is related to beauty.
  3. 3. Share with your neighbor.</li></ul>Physical attraction depends on ratio.<br />
  4. 4. How does mathematics relate to beauty?<br />Many scientists agree that beauty is found in symmetry and proportion.<br />If a face is in proportion we are likely to find it beautiful.<br />Scientists believe that we perceive proportional bodies to be more healthy.<br />
  5. 5. Why do many people feel that Jessica Simpson is beautiful?<br />
  6. 6. This mask of the human face is based on the Golden Ratio. The proportions of the length of the nose, the position of the eyes and the length of the chin, all conform to some aspect of the Golden Ratio.<br />
  7. 7. Leonardo Da Vinci used mathematical ratios <br />Leonardo da Vinci's drawings of the human body focused on proportion. <br />The ratio of the following distances is the Golden Ratio:<br />(foot to navel) : (navel to head) <br />
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  9. 9. Beauty Analysis Website<br /><br />VIDEO<br />
  10. 10. What is the Golden Ratio?<br />
  11. 11. The Golden Ratio<br />Introduced in text by Pythagoras, a Greek mathematician<br />Also used by Euclid in the 5th century BC.<br />Aristotle also mentioned its aesthetic properties<br />Authors have reported the golden ratio in Egyptian, Summerian and Greek vases, Chinese artifacts<br />
  12. 12. Renaissance artists became some of the best applied mathematicians of their times.<br />The Renaissance saw a rebirth of Classical Greek and Roman culture and ideas and were very into mathematics. <br /> Two reasons why they were interested in math:<br />Painters needed to figure out how to portray three-dimensional scenes on a two-dimensional canvas.<br />“Philosophers and artists alike believed that mathematics was the true essence of the physical world and that the entire universe, including the arts, could be explained in geometric terms.” <br />
  13. 13. What is the Golden Ratio?<br />Fibonacci Numbers<br />1, 1, 2, 3, 5, 8, 13, 21, ...<br />
  14. 14. The ratio of each number in the Fibonacci sequence to the one before it:<br />1/1 = 1<br />2/1 = 2<br />3/2 = 1.5<br />5/3 = 1.666...<br />8/5 = 1.6<br />13/8 = 1.625<br />21/13 = 1.61538...<br />34/21 = 1.61905...<br />55/34 = 1.61764...<br />89/55 = 1.61861…<br />
  15. 15. Golden Ratio<br />If we keep going, we produce a number which mathematicians call "phi" (Golden Ratio)<br />Φ = 1.618 033 988 7...<br />
  16. 16. Golden Ratio<br />The Golden Rectangle is thought to be the most aesthetically pleasing of all possible rectangles. <br />The Golden Ratio have been used in art and architecture for thousands of years.<br />
  17. 17. Leonardo Da Vinci<br />1452-1519<br />Italian<br />Scientist, mathematician, engineer, inventor, anatomist, painter, sculptor, and architect. <br />Most well known uses of the Golden Rectangle in art were created Leonardo da Vinci.<br />
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  19. 19. The Mona Lisa<br />Filled with Golden Rectangles<br />Leonardo, a mathematician, made this painting to line up with Golden Rectangles to incorporate mathematics into art.<br />
  20. 20. Mona LisaGolden Ratio<br />
  21. 21. Mona Lisa1503 or 1504 Florence,Italy<br />