Ask an Expert: Fibonacci sequence HELP
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Fibonacci sequence HELP
Hi, I need help with the format for my project's poster board layout. My problem is that I don't have a sensible hypothesis, variables, or a materials list (I am doing my project on deriving a formula about the Fibonacci sequence). I need to know if there is a format for projects like I am doing, as Math Projects do not seem to fit the standard Science Fair reporting format. Thanks! [/url]
Re: Fibonacci sequence HELP
tanmathfan wrote:Hi, I need help with the format for my project's poster board layout. My problem is that I don't have a sensible hypothesis, variables, or a materials list (I am doing my project on deriving a formula about the Fibonacci sequence). I need to know if there is a format for projects like I am doing, as Math Projects do not seem to fit the standard Science Fair reporting format. Thanks! [/url]
Could you provide a little more detail about what and why you are doing this project? It might help us come up with a good layout.
Louise

 Former Expert
 Posts: 675
 Joined: Thu Feb 03, 2005 3:38 pm
Re: Fibonacci sequence HELP
Hi tanmathfan,
The web page:
http://www.mcs.surrey.ac.uk/Personal/R. ... 80#formula
"A formula for the nth Fibonacci number"
This page has many suggestions and includes links to three other pages:
Fibonacci Home Page, The Mathematical Magic of the Fibonacci Numbers, and The Puzzling World of the Fibonacci Numbers.
These pages may give you suggestions that may help your research. In particular, the Mathematical Magic page has lots of hypotheses.
Please excuse if you've found these pages already.
The web page:
http://www.mcs.surrey.ac.uk/Personal/R. ... 80#formula
"A formula for the nth Fibonacci number"
This page has many suggestions and includes links to three other pages:
Fibonacci Home Page, The Mathematical Magic of the Fibonacci Numbers, and The Puzzling World of the Fibonacci Numbers.
These pages may give you suggestions that may help your research. In particular, the Mathematical Magic page has lots of hypotheses.
Please excuse if you've found these pages already.
Cheers!
Dave
Dave
tanmathfan,
You are quite right: math projects have a very different format than the usual science fair project. There is nothing wrong with doing a math project (unless your teacher says you can't), you just have to go about things a bit differently.
For the layout of your board, let's start with a general overview of what a science fair board usually looks like. Here is a good example:
For a math project, you might want to consider the following, modified, layout.
The "Introduction/Statement of Purpose" section could be renamed "Motivation." In this section, you would describe the mathematical problem you are trying to solve/explored and explain why it needs to be solved/explored.
The "Background/Literature Search" section should probably keep the same name. In this section, you should summarize your research and talk about what other people have done about solving/exploring the problem.
The "Hypothesis/Engineering Goal" section could be renamed simply "Objective." In this section, you should describe exactly what you expect the be able to do. For example, you have said that you are finding a formula for the Fibonacci sequence, but how do you want your formula to work? Do you want it to generate the nth term without having to generate the first n1 terms? Or do you want it to generate a specific number of terms (like the first 300 terms of the sequence)?
The "Project Title" section is unchanged. Put your title in this section.
The "Materials, Methods, Procedures" section will also remain lasrgely unchanged. In this section (I would suggest simply calling it Methods), you should describe exactly how you went about deriving your formula.
The "Data" section should be renamed something along the lines "Proof and Examples." In this section, you should do a mathematical proof showing the validity of your formula. (Since you're dealing with a sequence, I would suggest mathematical induction as the method of proof, but this is pure personal preference.) You may also wish to show a few examples of using your formula in this section.
The "Conclusion and Discussion" section should probably be renamed "Results." In this section, you should say whether or not your objective was met (e.g. if you objective was to predict the nth term without producing all the preceding terms, were you successful?) If you achieved your objective, say so. If you did not, say so.
The "Interpretation of Data" section should probably be changed to "Implications and Applications." In this section you should discuss why anyone should care about your formula. How will it be used in real life? This should tie directly to your Motivation section.
The "Further Research" section will remain largely unchanged. In this section you will discuss what you wish to do next. (e.g. Now that you've done this project, what would you want to do if you had more time.) Do you want to improve your formula? Does your project raise any questions that need to be explored?
I hope that this helps you as you prepare your board. If you have any questions, let me know!
You are quite right: math projects have a very different format than the usual science fair project. There is nothing wrong with doing a math project (unless your teacher says you can't), you just have to go about things a bit differently.
For the layout of your board, let's start with a general overview of what a science fair board usually looks like. Here is a good example:
For a math project, you might want to consider the following, modified, layout.
The "Introduction/Statement of Purpose" section could be renamed "Motivation." In this section, you would describe the mathematical problem you are trying to solve/explored and explain why it needs to be solved/explored.
The "Background/Literature Search" section should probably keep the same name. In this section, you should summarize your research and talk about what other people have done about solving/exploring the problem.
The "Hypothesis/Engineering Goal" section could be renamed simply "Objective." In this section, you should describe exactly what you expect the be able to do. For example, you have said that you are finding a formula for the Fibonacci sequence, but how do you want your formula to work? Do you want it to generate the nth term without having to generate the first n1 terms? Or do you want it to generate a specific number of terms (like the first 300 terms of the sequence)?
The "Project Title" section is unchanged. Put your title in this section.
The "Materials, Methods, Procedures" section will also remain lasrgely unchanged. In this section (I would suggest simply calling it Methods), you should describe exactly how you went about deriving your formula.
The "Data" section should be renamed something along the lines "Proof and Examples." In this section, you should do a mathematical proof showing the validity of your formula. (Since you're dealing with a sequence, I would suggest mathematical induction as the method of proof, but this is pure personal preference.) You may also wish to show a few examples of using your formula in this section.
The "Conclusion and Discussion" section should probably be renamed "Results." In this section, you should say whether or not your objective was met (e.g. if you objective was to predict the nth term without producing all the preceding terms, were you successful?) If you achieved your objective, say so. If you did not, say so.
The "Interpretation of Data" section should probably be changed to "Implications and Applications." In this section you should discuss why anyone should care about your formula. How will it be used in real life? This should tie directly to your Motivation section.
The "Further Research" section will remain largely unchanged. In this section you will discuss what you wish to do next. (e.g. Now that you've done this project, what would you want to do if you had more time.) Do you want to improve your formula? Does your project raise any questions that need to be explored?
I hope that this helps you as you prepare your board. If you have any questions, let me know!
All the best,
Terik
Terik

 Former Expert
 Posts: 675
 Joined: Thu Feb 03, 2005 3:38 pm
Re: Fibonacci sequence HELP
Hi tanmathfan,
Adding to Terik Daly's response, another item you could put on your display board is a graph of the length in digits of Fibonacci numbers (The Fibonacci numbers themselves get quite large). Please see:
http://www.mcs.surrey.ac.uk/Personal/R. ... ?n=80#logs
Thanks.
Adding to Terik Daly's response, another item you could put on your display board is a graph of the length in digits of Fibonacci numbers (The Fibonacci numbers themselves get quite large). Please see:
http://www.mcs.surrey.ac.uk/Personal/R. ... ?n=80#logs
Thanks.
Cheers!
Dave
Dave

 Former Expert
 Posts: 675
 Joined: Thu Feb 03, 2005 3:38 pm
Re: Fibonacci sequence HELP
Sylar1234 wrote:Thank you David! Believe me or not, your link helped me too in accomplishing a project i had to do for school. Wishing you all the best!:P
Ada
Ada,
Thanks for your kind words! They make my day!!
Cheers!
Dave
Dave

 Posts: 5
 Joined: Mon Jan 21, 2008 3:22 pm
 Occupation: Student
Re: Fibonacci sequence HELP
While the above posts are highly detailed with maththemed modifications to your posterboard, remember to always stick to the rules of presentation. The University of Georgia officially presides over the science fair projects of all high school participants in my state, for example, and has highly defined rules on the naming, placement, and recording of projects. Check with your teacher for a link to the guidelines before modifying anything or risk disqualification from your local science fair!
"If you would be a real seeker after truth, it is necessary that at least once in your life you doubt, as far as possible, all things." Rene Descartes
Re: Fibonacci sequence HELP
Another simple idea to explorer is how the Fibonacci sequence relates to the Golden Ratiothe proportion found in many different pieces of art. There is a very nice and elementary connection described here: http://mathforum.org/dr.math/faq/faq.golden.ratio.html Hope this helps. Good luck!