The document discusses the Fibonacci sequence and its relationship to the golden ratio. It begins by introducing Leonardo of Pisa, who helped spread the use of the modern number system and knowledge of the Fibonacci sequence. The sequence is defined as a pattern where each number is the sum of the two preceding ones, starting with 1, 1, 2, 3, 5, etc. This sequence appears throughout nature and can be seen in spirals of shells, pinecones, and sunflowers. The ratio of consecutive Fibonacci numbers approaches the golden ratio, about 1.618, an irrational number important in art and architecture considered aesthetically pleasing. The golden ratio can also be observed in proportions of the human body.
In this presentation, we see that how golden ratio and Fibonacci series are calculated or working? and What is the problem faced by Fibonacci in Fibonacci series.
Fibonacci Sequence .
The Fibonacci Sequence is a definite pattern that can begin with either 0, 1 or 1, 1. The sequence is generated by adding the previous terms, so that 0 +1 equals 1, 1+1 equals 2, 2 + 1 equals 3, 2 + 3 equals 5, 5 + 3 equals 8, 8 + 5 equals 13, 13 + 8 equals 21, 21 + 13 equals 34, 34 + 21 equals 55, and so on. Fibonacci can be found in in every domain such as nature, art, infrastructure ,humans etc. .
In this presentation, we see that how golden ratio and Fibonacci series are calculated or working? and What is the problem faced by Fibonacci in Fibonacci series.
Fibonacci Sequence .
The Fibonacci Sequence is a definite pattern that can begin with either 0, 1 or 1, 1. The sequence is generated by adding the previous terms, so that 0 +1 equals 1, 1+1 equals 2, 2 + 1 equals 3, 2 + 3 equals 5, 5 + 3 equals 8, 8 + 5 equals 13, 13 + 8 equals 21, 21 + 13 equals 34, 34 + 21 equals 55, and so on. Fibonacci can be found in in every domain such as nature, art, infrastructure ,humans etc. .
The fibonacci sequence and the golden ratio #Scichallenge2017Miléna Szabó
#SciChallenge2017
In this presentation I would like to show how important mathematics is. It is shows up in everyday life through nature.
"In order to understand the Universe you must know the language which it is written and that is Mathematics." /Galileo Galilei/
The fibonacci sequence and the golden ratio #Scichallenge2017Miléna Szabó
#SciChallenge2017
In this presentation I would like to show how important mathematics is. It is shows up in everyday life through nature.
"In order to understand the Universe you must know the language which it is written and that is Mathematics." /Galileo Galilei/
Correlation of Fibonacci Sequence and Golden Ratio With its Applications in E...Dr. Amarjeet Singh
We have discussed in this elucidation paper about correlation of Fibonacci sequence and golden ratio with its applications in engineering and science. One of the most recurring sequences in nature is the Fibonacci sequence. As the sequence was explored, it was found out that this sequence led to the golden ratio. This study tried to apply the concept of Fibonacci and golden ratio to maximize efficiency of our live life. We consider self-similar curve like golden spiral in whose nature their beauty is much admired. The explanations show that source of Fibonacci numbers and how to exist Fibonacci numbers in the world we live. The mathematical theories of Fibonacci numbers and golden ratio gives the source of many new ideas in Mathematics, Chemistry, Civil engineering, Architecture, Automobile engineering, Philosophy, Botanic and biology, Electrical engineering, Computer science and engineering, Mechanical engineering, Communication systems, Mathematical education as well as theoretical physics and physics of high energy particles [1].
Maths in Art and Architecture Why Maths? Comenius projectGosia Garkowska
THIS EBOOK WAS PREPARED
AS A PART OF THE COMENIUS PROJECT
WHY MATHS?
by the students and the teachers from:
BERKENBOOM HUMANIORA BOVENBOUW, IN SINT-NIKLAAS ( BELGIUM)
EUREKA SECONDARY SCHOOL IN KELLS (IRELAND)
LICEO CLASSICO STATALE CRISTOFORO COLOMBO IN GENOA (ITALY)
GIMNAZJUM IM. ANNY WAZÓWNY IN GOLUB-DOBRZYŃ (POLAND)
ESCOLA SECUNDARIA COM 3.º CICLO D. MANUEL I IN BEJA (PORTUGAL)
IES ÁLVAREZ CUBERO IN PRIEGO DE CÓRDOBA (SPAIN)
5. The Fibonacci Sequence
This pattern continues and follows the rule:
xn = xn-1 + xn-2
}+
xn is term number "n"
xn-1 is the previous term (n-1)
xn-2 is the term before that (n-2)
1 1 2
3
19. What is the Golden Ratio?
The ratio between successive Fibonacci Numbers
will eventually give you the Golden Ratio:
A
B
B/A
1
1
1
1
2
2
2
3
1.5
3
5
1.666666666...
5
8
1.6
8
13
1.625
13
21
1.615384615...
...
...
...
144
233
1.618055556...
233
377
1.618025751...
20. The importance of Phi Φ
If the longer segment divided by the smaller
segment is also equal to the whole length
divided by the longer part then you will have
the golden ratio.
25. Math is Beautiful
The Golden Ratio can be applied to the
human face to determine beauty.
26. Math of Beauty Interactive
According to the Golden Ratio, Jessica
Simpson is considered beautiful!
Visit this site to participate in a fun activity:
http://www.intmath.com/numbers/math-ofbeauty.php
27. Resources
Benjamin, A. (2013). The Magic of Fibonacci Numbers. Retrieved from
http://www.youtube.com/watch?v=SjSHVDfXHQ4
Fibonacci Sequence. (2013). Math is Fun. Retrieved from
http://www.mathsisfun.com/numbers/fibonacci-sequence.html
Hart, V. (2011). Doodling in Math: Spirals, Fibonacci, and Being a Plant. Retrieved from
http://www.youtube.com/watch?v=ahXIMUkSXX0
Inspiration Green (n.d.). The Fibonacci Sequence and Nature. Retrieved from
http://www.inspirationgreen.com/fibonacci-sequence-in-nature.html
Lamb, R. (24 June 2008). "How are Fibonacci numbers expressed in nature?“ Retrieved
from http://science.howstuffworks.com/life/evolution/fibonacci-nature.htm
Number Patterns. (n.d.). Retrieved from
http://www.magicmathworks.org/exhibits/numberpatterns/index.html
Spirals and the Golden Ratio. (August 25, 2012). Retrieved from
http://www.goldennumber.net/spirals/