190 likes | 286 Views
WHO SAID MATH WASN’T FUN?. Tara Kerr, Liz So, Deena Douara. A. B. C. A. B. C. A. B. C. A. B. C. B. C. A. A. YouTube. the Golden Ratio: the math. the Golden Ratio is a special number approximately equal to 1.6180339887498948482
E N D
WHO SAID MATH WASN’T FUN? Tara Kerr, Liz So, Deena Douara
A B C
A B C
A B C
A B C
B C A A
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 by cross-multiplying we get ab + b2 = a2 or if we substitute 1 for b, then a2 = a + 1 solving for a, we end up with
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
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 • YouTube videos, Discover Channel