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.