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The Fibonacci Sequence

by

Blake Andert

on 6 November 2014

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Transcript of The Fibonacci Sequence

The Fibonacci Sequence
By Blake Andert
0+1
=1
1+1
=2
1+2
=3
2+3=5
3+5=8
5+8=13
...
Green, Hank. "The Fibonacci Sequence: Nature's Code." Video blog post. SciShow. N.p., 17 Aug. 2012. Web. 24 Jan. 2014.
Bibliography
Hart, Vi. "Doodling in Math Class: Spirals, Fibonacci, and Being a Plant [2 of 3]." Video blog post. Vihart. N.p., 9 Jan. 2012. Web. 24 Jan. 2014.
Viatour, Luc. Da Vinci Vitruve Luc Viatour. Digital image. Wikipedia. N.p., 8 Sept. 2007. Web. 24 Jan. 2014.
Ida, Takashi. "“Vitruvian Man” by Leonardo Da Vinci and the Golden Ratio." “Vitruvian Man” by Leonardo Da Vinci and the Golden Ratio. Advanced Ceramics Research Center, 18 June 2012. Web. 24 Jan. 2014.
Uses of Phi
In Da Vinci's famous Vitruvian Man, the ratio of the square's side to the radius of the circle is golden.
Examples of the golden ratio in the human body include:
the ratio of the height of your face to the width of your face
the ratio of the length of your eye to the width of your eye
What happens when you divide adjacent Fibonacci Numbers?
1/1=1
2/1=2
3/2=1.5
5/3=1.666
8/5=1.6
13/8=1.625
...
377/233=1.618
610/377=1.618
1+(5 )
1/2
_______
2
Dcotezee. Phi Uc Lc. Digital image. Wikipedia. N.p., 10 Aug. 2007. Web. 24 Jan. 2014.
"The Golden Ratio in the Human Body." Modern Energy Research Library. N.p., n.d. Web. 25 Jan. 2014.
Architecture
"Architecture." Phi 1618 The Golden Number RSS. N.p., 5 Aug. 2013. Web. 23 Jan. 2014.
The pentagram naturally shows the Golden Ratio, as the ratio of its midsegments to the outer edges always equals phi. Pythagoras loved it so much that it became the symbol of the Pythagoreans.
Torra, Marc. Sacred Time. Digital image. Andean Spirituality. N.p., 2012. Web. 24 Jan. 2014.
Mona Lisa. Digital image. Wikipaintings. N.p., n.d. Web. 25 Jan. 2014.
Terrich, Matt. Mond Crucifixion. Digital image. Renaissance Art Project. N.p., 7 Oct. 2013. Web. 25 Jan. 2014.
Britton, Jill. Mond Crucifixion Pentacle. Digital image. Golden Section in Art and Architecture. N.p., 6 May 2012. Web. 25 Jan. 2014.
Approximately 1.6180339887
Kidder, David S., and Noah D. Oppenheim. "The Golden Ratio." The Intellectual Devotional: Revive Your Mind, Complete Your Education, and Roam Confidently with the Cultured Class. New York: Rodale, 2006. 326. Print.
Kidder, David S., and Noah D. Oppenheim. "Fibonacci." The Intellectual Devotional Biographies: Revive Your Mind, Complete Your Education, and Acquaint Yourself with the World's Greatest Personalities. New York: Rodale, 2010. 108. Print.
Fibonacci
Gardner, Martin. Fibonacci. Digital image. Wikipedia. N.p., 10 June 2010. Web. 29 Jan. 2014.
Leonardo Bonacci (aka Fibonacci) was born in Pisa in 1170. His father traveled a lot, and he grew up in what is now known as Béjaïa, Algeria. He was educated using Arabic numerals.
This series had already been known in India for 1300 years. Fibonacci was the person who introduced it into the Western world.
When he returned to Pisa, he was astounded that they were still using Roman numerals. He published Liber Abaci, which demonstrated the superiority of Arabic numbers to the traditional Roman numerals.
Fibonacci's achievements in math earned him great fame, and he was a friend of Emperor Fredrick II. He died around 1250.
The Golden Ratio
Two parts of an object are in golden proportion if the ratio of the longer part to the shorter part equals the ratio of the whole object to the longer part.
Stannered. Golden Ratio Line. Digital image. Wikipedia. N.p., 23 Mar. 2007. Web. 30 Jan. 2014.
a
b
_
=
a+b
a
___
=
1.618
Ahecht. Similar Golden Rectangles. Digital image. N.p., 26 June 2011. Web. 30 Jan. 2014.
Phi is unique because you can subtract one from it or divide one by it and get the same result.
The Parthenon
The Cathedral of Notre Dame
The Taj Mahal
The Great Pyramid of Giza
The CN Tower
Art
Meisner, Gary. "Golden Ratio in Art Composition and Design." Phi 1618 The Golden Number. N.p., 04 May 2014. Web. 06 Oct. 2014.
The Mona Lisa
Birth of Venus
Bathers at Asnières
and the Golden Ratio
Phi
If this is true, both ratios should be approximately 1.618, or phi.
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