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Fibonacci

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by

Mohammad Hamza

on 25 November 2014

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Transcript of Fibonacci

Application
Fibonacci in Nature.
Experiment
3 indifferent flowers
Conclusion
Work
Gained Knowledge through travelling.
Rabbit Reproduction Problem
Liber Abaci also contained Fibonacci's famous problem the Rabbit Reproduction.
Biography
Fibonacci
Liber Abacci
Basic Math principles
How Does it work?
Starting with 0 and 1; the Fibonacci sequence is comprised of adding the previous two number together to create the next number in the sequence.

NOTE: In Liber Abaci, the Fibonacci sequence starts with 1 and 1.

0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
This presentation has covered the history, formula and application of the Fibonacci sequence. There was a brief history on how Leonardo Fibonacci founded the sequence. Included was how the sequence can be observed in nature and the basic formula to determine each placement in the sequence.

Also included is an experiment to view the number of petals of a flower. This experiment analyzed the number of petals on different flowers and determined if the number of petals was within the Fibonacci sequence.

Today we know Fibonacci as the greatest Mathematician of the middle ages.
Cameron, Hamza, Babar and Juan
Who was Fibonacci
Born: 1175 AD Pisa, Italy.
Completed education in North Africa
Son of Guglielmo Bonacci
Adding
Subtracting
Multiplication
Division
Algebric Equations
Root Extraction
Word Problems
Fibonacci Sequence
Agenda
Biography
Work
Rabbit Reproduciton Problem
Application
Rabbit Reproduction problem.
Fibonacci Sequence in Nature
Pinecone layers. See Figure 3
Sea Shells
Seed head Spiral
Flower Petals
Fibonacci Today
Counted the petals.
Observed the results.
Wild Rose
Result : 5 petals.
Black-Eyed Susan
Result: 14 petals.
Buttercup
Result: 5 petals.
References
Experiment
Demonstration
Conclusion
Fibonacci Spiral

"Liber Abacci"
Now let’s try to find a Fibonacci number further down the line but counting month by month might not be the most efficient way so we use Bitnet’s formula which can allow us to find the Fibonacci number more directly (See Figure 1).
1
2
3
4
5
1
2
3
4
5
Figure 1
See Figure 2.
Figure 2
Figure 3
See Figure 5.
Figure 5
See Figure 6.
Figure 6
See Figure 7
Figure 7
See Figure 8
Figure 8
See Figure 9
Figure 9
Figure 10
See Figure 10
See Figure 11
Figure 11
1
2
3
5
8
13
Arabic Number System
"Practica Geometriae"
[1] University of Surrey, “Who was Fibonacci?” 1998-2009. [Online]. Available: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibBio.html. Accessed on: November 13, 2014.
[2]School of Mathematics and Statistic, University of St Andrews, Scotland, ”Leonardo Pisano Fibonacci” 1998[online]. Available: http://www-history.mcs.st-and.ac.uk/Biographies/Fibonacci.html . Accessed on: November 19, 2014.
[3] Rutgers, “Fibonacci” 1999. [Online]. Available: http://www.math.rutgers.edu/~cherlin/History/Papers1999/oneill.html. Accessed on: November 13, 2014.
[4] Colorado State University, “Department of Mathematics” [Online]. Available: http://www.math.colostate.edu/~spriggs/m130/fibonacci.pdf. 2014 pp1 – 5.
[5] image, [Online] Available: http://www.mathsisfun.com/numbers/images/fibonacci-spiral.gif
[6] image, [Online] Available: http://1.bp.blogspot.com/_w2BYtAZdh0Y/TPJpr59HWKI/AAAAAAAAB70/PdzsEAWWVwY/s1600/pinecone4.jpg
[8] image, [Online] Available:http://www.popmath.org.uk/rpamaths/imagesrpam/sunflower3.jpg
[9] image, [Online] Available: http://s3.amazonaws.com/bandw-gallery/large/11217/Seashell.jpg?1302510831
[10] image, [Online] Available: http://jwilson.coe.uga.edu/emat6680/parveen/Fibona50.jpg
[11] image, [Online] Available: http://www.constructingtheuniverse.com/CTUclassroom/Fibonacci%20Flower%20Petals%20Numbered.JPG
[12] image, [Online] Available: http://www.terrapodcast.com/media/samples/graphics/wild%20rose%20flower.jpg
[13] image, [Online] Available: http://3.bp.blogspot.com/-B5t6PLpgric/ULxdf6tImMI/AAAAAAAADaA/XPzUVbwtfAE/s1600/Black+Eyed+Susan.jpg
[14] image, [Online] Available:http://healthyhomegardening.com/images/gardengeek/buttercup_786.jpg
[7]image.[Online]. Available: http://img.gawkerassets.com/post/8/2013/02/pinecone.jpg
Figure 4
0 --> 1
1 --> 10
0 = Baby
1 = Mature
0
1
1 0
1 0 1
1
0
1
1
0
Demonstration
Step 1: Pick a Flower.
Step 2: Count the Petals.
Result: Does it match a Fibonacci number.
Thank You
Please On your way out say thanks to Fibonacci as well.
Full transcript