WHO SAID MATH WASNT FUN Tara Kerr Liz

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 1. 6180339887498948482 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 a by cross-multiplying we get ab + b 2 = a 2 a+b or if we substitute 1 for b, then a 2 = a + 1 solving for a, we end up with a = (1 + sqrt(5)) 2 = phi = 1. 618033988749

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

In History. . .

Ancient Egypt n Pyramids

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

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

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

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

Nature n plants & flowers n human body n animals

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