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Golden Ratio

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by

Samuel Khzym

on 4 June 2015

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Transcript of Golden Ratio

TREASURE?!!
What is zero?
The Golden Ratio: Is it really gold?!
By: Samuel Khzym
What is the golden ratio?
-The golden ratio is an irrational number. Which means it is infinite, like pi.
- 0 or 1 : 1.61803398874989484820... (rounded to 1.618.)
-The golden ratio pops up everywhere in ancient and modern architecture, art, geometry, and even nature itself.
-The golden ratio is represented by the greek letter phi. φ
Arr, the golden ratio be confusing for my pirate brain
Historical uses of the golden ratio
-Phidias

-Euclid

-Leonardo da Vinci

-Johannes Keppler
Phidias
Statues of Parthenon

-A ratio is a comparison of two numbers. Normally recognized by a colon.
Euclid of Alexandria
ἄκρος καὶ μέσος λόγος
"the extreme and mean ratio"
Leonardo da Vinci
CENSORED
-The golden ratio links very closely with the Fibonacci sequence.
Fibonacci and phi
1, 1, 2, 3, 5, 8,13 ,21 ,35, 44 ,79 ,144...
GOLDEN RECTANGLE!!!!
Johannes Kepler
“Geometry has two great treasures: one is the theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.”
~Johannes Kepler
1571-1630
365 BC – 300 BC
1459-1519
Architecture and phi
Pyramids
Parthenon
CN tower
Taj Mahal

φ
= φ

+ 1
1
√φ
φ
a
÷b = (a+b) ÷ a = φ
B
A
GOLDEN RECTANGLES EVERYWHERE!
Nature and phi
The face
Spiral Galaxies
REASON 1
REASON 2
1, 1, 2, 3, 5, 8,13 ,21 ,35, 44 ,79 ,144...
144/79
= 1.82278481013
≈ φ
223/144
= 1.54861111111
≈ φ
367/223
= 1.64573991031
≈ φ
SLOWLY GOES TO PHI
The human arm
sea stars
Fun Facts!
φ

PHI DAY!!!
June 18
= 6/18
Conclusion
Overall, phi is everywhere in our lives, from the outer depths of space to the microbiological level itself. So enjoy it while you can.
Websites
Videos
http://www.goldennumber.net/
http://en.wikipedia.org/wiki/Golden_ratio
http://en.wikipedia.org/wiki/Phidias
http://en.wikipedia.org/wiki/Johannes_Kepler
Another name, another number
Phidias
φ
http://jwilson.coe.uga.edu/emt668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html
The End!
1.6180339887498948482045868343656381177203091798
(If you can memorize all this, you are a genius!)
Interactive COMPETITION!
Golden Shapes
61.8 cm
38.2 cm
1 : 1.618...
Golden Rectangle
Golden Pentagram
a ­≈ 216

b ≈ 133

c ≈ 82

d ≈ 51
a/b = b/c = c/d = φ
1.618033988749894848204586834365638117720309179805762862135448622705260462818
Interactive Activity
Bibliography
Full transcript