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

=τ

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