WHO SAID MATH
WASN’T FUN?
Tara Kerr, Liz So, Deena Douara
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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
by cross-multiplying we get ab + b2 = a2
a+b
or if we substitute 1 for b, then a2 = 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

Pyramids
Ancient Greece

Pythagoras



Euclid


concept
geometry
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