who said math wasn’t fun?
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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 - PowerPoint PPT PresentationTRANSCRIPT
WHO SAID MATH WASN’T FUN?
Tara Kerr, Liz So, Deena Douara
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B
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C
B
A
C
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YouTube
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 a + b
solving for a, we end up with
a = (1 + sqrt(5))
2
= phi
= 1.618033988749
by cross-multiplying we get ab + b2 = a2
or if we substitute 1 for b, then a2 = a + 1
the Golden Ratio: the mathFibonacci 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
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