1. WHO SAID MATH WASN’T FUN? Tara Kerr, Liz So, Deena Douara

2. A B C

3. A C B

4. A C B

5. A C B

6. B A C A

8. YouTube

9. the Golden Ratio: the math the Golden Ratio is a special number approximately equal to 1.6180339887498948482 one way to visually understand it is with a line segment

10. the Golden Ratio: the math then a mathematical equation can be established through the ratio b=a aa + b solving for a, we end up with a=(1 + sqrt(5)) 2 = phi  =1.618033988749 by cross-multiplying we get ab + b 2 = a 2 or if we substitute 1 for b, then a 2 = a + 1

11. the Golden Ratio: the math Fibonacci sequence = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... where 5/3 = 1.6666… and 8/5 = 1.6 and 13/8 = 1.625 and 21/13 = 1.615… and 34/21 = 1.61904… and so on, each more closely approximating the Golden Ratio

12. In History...

13. Ancient Egypt Pyramids

14. Ancient Greece Pythagoras  concept  geometry Euclid  definition Phidias (phi, Φ )  sculptor  Parthenon

15. “Middle” Ages Leonardo of Pisa aka "Fibonacci“  Fibonacci sequence Great Mosque of Kairouan (Tunisia)

16. Renaissance Leonardo da Vinci “divine proportion” (Luca de Pacioli) Johannes Kepler  Kepler triangle decimal (Maestlin) Taj Mahal

17. post-Renaissance “φ “ named Oprah, plastic surgery & cult of beauty Painters  Mondrian, Dali Modern architecture  Le Corbusier

18. Nature plants & flowers human body animals

19. Further Reading Mario Livio, The Golden Ratio: The Story of Phi, The World's Most Astonishing Number Mario Livio YouTube videos, Discover Channel