PASCAL PYRAMID and MATHEMATICAL INDUCTION

Ask questions about projects relating to: computer science or pure mathematics (such as probability, statistics, geometry, etc...).

Moderators: MelissaB, kgudger, Ray Trent, Moderators

PASCAL PYRAMID and MATHEMATICAL INDUCTION

Postby rappyrap09 » Tue Oct 11, 2011 9:13 am

HELP!!!! i need help...

is anyone familiar with PASCAL PYRAMID AND MATHEMATICAL INDUCTION??
rappyrap09
 
Posts: 7
Joined: Tue Oct 11, 2011 7:47 am
Occupation: student: 9th grade
Project Question: math
Project Due Date: december 2011
Project Status: I am conducting my research

Re: PASCAL PYRAMID and MATHEMATICAL INDUCTION

Postby hhemken » Tue Oct 11, 2011 10:20 am

rappyrap09,

What are you looking for, specifically? Have you tried googling this:
Code: Select all
"PASCAL's PYRAMID" AND MATHEMATICAL INDUCTION


There are more than a few hits for that combination of keywords. I suggest you have a look and come back with more specific questions and what your science project might be about.
Heinz Hemken
Mentor
Science Buddies Expert Forum
hhemken
Expert
 
Posts: 260
Joined: Mon Oct 03, 2005 3:16 pm

Re: PASCAL PYRAMID and MATHEMATICAL INDUCTION

Postby rappyrap09 » Thu Oct 13, 2011 6:18 am

my project is about PASCAL PYRAMID..but, according to my professor, it can be proved by using MATHEMATICAL INDUCTION.. so i thiin the're related..please help me on this project..
rappyrap09
 
Posts: 7
Joined: Tue Oct 11, 2011 7:47 am
Occupation: student: 9th grade
Project Question: math
Project Due Date: december 2011
Project Status: I am conducting my research

Re: PASCAL PYRAMID and MATHEMATICAL INDUCTION

Postby hhemken » Thu Oct 13, 2011 10:05 am

rappyrap09,

Have you read the materials that come up on Google with the search I suggested? Print some out and discuss them with your professor. I think a one-on-one with your professor discussing specific texts you have both read will be better and faster than posting the discussion here.

Please let us know what you conclude or what additional questions you may have, though.
Heinz Hemken
Mentor
Science Buddies Expert Forum
hhemken
Expert
 
Posts: 260
Joined: Mon Oct 03, 2005 3:16 pm

Re: PASCAL PYRAMID and MATHEMATICAL INDUCTION

Postby rappyrap09 » Sat Oct 15, 2011 8:23 am

are you familiar with Pascal Triangle???if yes then you would knnow how pascal pyramid works..

i've just got questions...a formula/ae on how to get a layer without the help of its previous layers..help me..can't find it in google..

and my professor just told me that Pascal Pyramid could be proved by using mathematical induction...this one i can't do..please help..do you have any guidelines on how to prove this Pascal Pyramid...help
rappyrap09
 
Posts: 7
Joined: Tue Oct 11, 2011 7:47 am
Occupation: student: 9th grade
Project Question: math
Project Due Date: december 2011
Project Status: I am conducting my research

Re: PASCAL PYRAMID and MATHEMATICAL INDUCTION

Postby LeungWilley » Sat Oct 15, 2011 5:57 pm

Hi Rappyrap09,
Please see if this link is helpful:
http://en.wikipedia.org/wiki/Binomial_coefficient

If I understand what you are trying to do correctly, you may be using induction to prove the recurrence relation of the Pascal Pyramid. The specific are shown in the middle of the article.

Please let us know how it works out.
Good Luck!
Willey
LeungWilley
Expert
 
Posts: 10
Joined: Mon Jan 12, 2009 11:15 pm
Occupation: Field Engineer - Electrical
Project Question: n/a
Project Due Date: n/a
Project Status: Not applicable

Re: PASCAL PYRAMID and MATHEMATICAL INDUCTION

Postby Goldenzenith » Sat Oct 15, 2011 8:11 pm

Hello,

Is this for a math research paper? If so, it would be best to do what the other Experts have suggested and look into the wealth of resources provided. And don't hesitate to consult your teacher for help; you're in school to learn, remember! :)

As for Pascal's Triangle and mathematical induction, you'll need to know Pascal's Law, which is nCr = n-1Cr + n-1Cr-1. Right now, get a piece of paper and draw at least the first 3 rows of Pascal's Triangle. How can you rewrite each number as a combination? Here's a hint: the first row has 0C0, and the second row has 1C0 and 1C1.

Once you figure out why Pascal's Law makes sense, you can get to work with mathematical induction. Remember to neatly set up each step:
1) Prove that the law works for n = 1.
2) Assume that it works for n = k, where k is greater than or equal to zero.
3) Prove that it works for n = k + 1, using and beginning the proof with the assumption from step 2.

This should be all you need to get to work on your paper. If you have any questions, please ask, but remember to do your research first!
Need an idea or some inspiration?
http://www.sciencebuddies.org/science-fair-projects/project_ideas.shtml

Want to read up on awesome projects and science/math-related news?
http://www.sciencebuddies.org/blog/index.php

Enjoy! :D
-RM, Expert
Goldenzenith
Expert
 
Posts: 117
Joined: Sun Sep 11, 2011 6:14 am
Occupation: Student: 12th grade
Project Question: n/a
Project Due Date: n/a
Project Status: Not applicable

Re: PASCAL PYRAMID and MATHEMATICAL INDUCTION

Postby rappyrap09 » Thu Oct 20, 2011 5:26 am

LeungWilley, ive already seen that page..thanx anyways



Goldenzenith, yes, its a research papaer..what i need is to provve Pascal Pyramid with the use of mathematical induction..
rappyrap09
 
Posts: 7
Joined: Tue Oct 11, 2011 7:47 am
Occupation: student: 9th grade
Project Question: math
Project Due Date: december 2011
Project Status: I am conducting my research

Re: PASCAL PYRAMID and MATHEMATICAL INDUCTION

Postby Goldenzenith » Fri Oct 21, 2011 2:56 pm

My apologies; I misread what you needed to prove. In that case, tell me what you have gotten up to so far, and perhaps we can work from there!
Need an idea or some inspiration?
http://www.sciencebuddies.org/science-fair-projects/project_ideas.shtml

Want to read up on awesome projects and science/math-related news?
http://www.sciencebuddies.org/blog/index.php

Enjoy! :D
-RM, Expert
Goldenzenith
Expert
 
Posts: 117
Joined: Sun Sep 11, 2011 6:14 am
Occupation: Student: 12th grade
Project Question: n/a
Project Due Date: n/a
Project Status: Not applicable

Re: PASCAL PYRAMID and MATHEMATICAL INDUCTION

Postby rappyrap09 » Mon Jan 30, 2012 5:08 am

so far, all ive got is a formula in finding how many terms there are in a pascal pyramid..
what i need is to incorporate mathematical induction into pascal pyramid..please help..
rappyrap09
 
Posts: 7
Joined: Tue Oct 11, 2011 7:47 am
Occupation: student: 9th grade
Project Question: math
Project Due Date: december 2011
Project Status: I am conducting my research

Re: PASCAL PYRAMID and MATHEMATICAL INDUCTION

Postby Goldenzenith » Sat Feb 11, 2012 8:03 pm

Hi, rappyrap09,

The following site may be of some interest to you: http://threesixty360.wordpress.com/2009 ... rt-1-of-3/. It's not a reference site, but it does make some observations that are related to your project. Take a look!

This is probably the case, but just to confirm, are you trying to prove that the formula you found works? If so, that's something to work with! You should realize that, by proving it, you would be incorporating mathematical induction into your project on Pascal's Pyramid. Perhaps you could post the formula on here and get advice, step by step. If you don't want to do that (which is also perfectly fine), please familiarize yourself with the format of mathematical induction. You've posted many requests for help concerning induction, so I would just like to make sure that you understand what exactly it entails. Remember one of my earlier posts in this thread?

Goldenzenith wrote:As for Pascal's Triangle and mathematical induction, you'll need to know Pascal's Law, which is nCr = n-1Cr + n-1Cr-1. Right now, get a piece of paper and draw at least the first 3 rows of Pascal's Triangle. How can you rewrite each number as a combination? Here's a hint: the first row has 0C0, and the second row has 1C0 and 1C1.

Once you figure out why Pascal's Law makes sense, you can get to work with mathematical induction. Remember to neatly set up each step:
1) Prove that the law works for n = 1.
2) Assume that it works for n = k, where k is greater than or equal to zero.
3) Prove that it works for n = k + 1, using and beginning the proof with the assumption from step 2.


Although the topic of the above example is not exactly what you need (Pascal's Triangle, as opposed to something related to Pascal's Pyramid), the overall setup would be the same for the proof that you want to create. If you are confused or would like more information, this site has excellent, clear explanations, as well as a few practice problems: http://www.themathpage.com/aprecalc/mat ... uction.htm.

Once you've got mathematical induction down pat, "draft" a proof for your formula. Then look it over and see if you made any unwarranted assumptions that might make the proof invalid. If you need help with a certain step or get stuck somewhere, post your question, but make sure it's a specific one! It's a bit difficult to answer less specific ones like,

rappyrap09 wrote:my project is about PASCAL PYRAMID..but, according to my professor, it can be proved by using MATHEMATICAL INDUCTION.. so i thiin the're related..please help me on this project..


Please try to provide as many details as you can so that the Experts on Science Buddies can help you better! With that said, good luck with your project, and above all, have fun! :wink:

-RM
Need an idea or some inspiration?
http://www.sciencebuddies.org/science-fair-projects/project_ideas.shtml

Want to read up on awesome projects and science/math-related news?
http://www.sciencebuddies.org/blog/index.php

Enjoy! :D
-RM, Expert
Goldenzenith
Expert
 
Posts: 117
Joined: Sun Sep 11, 2011 6:14 am
Occupation: Student: 12th grade
Project Question: n/a
Project Due Date: n/a
Project Status: Not applicable


Return to Grades 9-12: Math and Computer Science

Who is online

Users browsing this forum: No registered users and 2 guests