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 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