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

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

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  = by cross-multiplying we get ab + b 2 = a 2 or if we substitute 1 for b, then a 2 = a + 1

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

In History...

Ancient Egypt Pyramids

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

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

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

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

Nature plants & flowers human body animals

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