Need help on Maths essay, relationship between Phi and Fibonacci

In summary, a high school student is seeking help with their 4000 word maths essay on the relationship between the golden ratio and Fibonacci numbers. They have encountered a mistake and are looking for additional resources and suggestions for including Binet's formula in their essay. The student is in urgent need of assistance and is open to any amendments or advice. The target audience is the markers for their high school course.
  • #1
kenbellston
2
0
hey there! its my first post, and quite an urgent one.

i am into my last year of high school, and i am required to write a 4000 word maths essay. i chose to write on maths, because i like maths! but i am quite stucked at this stage...

i decided to writing on the mathematical relationship on golden ratio and fibonacci numbers, here is a link to my unfinished essay

http://www.fileden.com/files/2008/4/29/1888642/extended%20essay.doc

just a word file.

there is a little mistake at Pg6-7, i am still figuring out how to correct it

it will be great if you guys can take a look and see what else i can write about! i am think writing about Binet's formula, but not sure how to link it, and i need some comprehensive resources.

if you do have some nice links, pls share, i am quite desperate to get it done ASAPthanks a lot guys!

you can make amendment or change or advise on the word itself, and would be wonderful if you can email me the file, or add me on msn at <email removed>
thanks thanks thanks!
 
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  • #2
What is your target audience? How much math do they know? What is expected of the essay?
 
  • #3
hey, sorry, forgot to mention. the audience is the markers, it is a requirement of my High school course. here the marking scheme

http://www.fileden.com/files/2008/4/29/1888642/Marking%20Scheme.doc
 
Last edited by a moderator:

1. What is the relationship between Phi and Fibonacci?

The relationship between Phi and Fibonacci is that Phi, also known as the Golden Ratio, is derived from the Fibonacci sequence. The ratio between two consecutive numbers in the sequence approaches Phi as the numbers get larger. This means that the larger the numbers in the sequence, the closer their ratio is to Phi.

2. How are Phi and Fibonacci used in mathematics?

Phi and Fibonacci are used in various fields of mathematics, including geometry, number theory, and even biology. In geometry, Phi is used to create aesthetically pleasing shapes and structures, while in number theory, it is used to solve problems involving prime numbers. In biology, the Fibonacci sequence can be seen in the growth patterns of plants and animals.

3. What is the significance of Phi and Fibonacci in nature?

The presence of Phi and Fibonacci in nature is often referred to as the "golden ratio of nature." This is because many natural phenomena, such as the spiral patterns of shells and the branching of trees, follow the Fibonacci sequence and exhibit the ratio of Phi. This suggests that Phi and Fibonacci play a fundamental role in the design and organization of the natural world.

4. Can Phi and Fibonacci be found in human-made structures?

Yes, Phi and Fibonacci can be found in many human-made structures, such as architecture, art, and music. Many famous buildings and artworks, such as the Parthenon in Greece and Leonardo da Vinci's "Vitruvian Man," incorporate the Golden Ratio in their design. In music, the Fibonacci sequence is used to create harmonious and aesthetically pleasing compositions.

5. Is there a practical application for understanding the relationship between Phi and Fibonacci?

Yes, understanding the relationship between Phi and Fibonacci has various practical applications. For example, it can be used in financial markets to identify potential retracement levels, in typography and graphic design to create visually appealing layouts, and in computer algorithms to generate random numbers. Additionally, the concepts of Phi and Fibonacci can also be applied in problem-solving and critical thinking in various fields.

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