IA Type I -- Stellar Number

[sweetnsimple786]

Hey, i just got the stellar number portfolio and sheet and i am really lost on how to do it, infact, even how to start it. Any suggestions and tips would be helpful. If any of you could upload or email me yours that would be greatly appreciated. Don't worry i won't plagiarize or copy any. Thank you:)

We're not here to swap IAs. What exactly are you confused about? You said you don't know how to start it. What do you think the instructions want you to do?

[holycows]

I'm a bit confused about the format of the report. Should I just format it like a lab report? do I need to write an introduction?

Thanks...

[sweetnsimple786]

Check out the links on this thread: http://www.ibsurvival.com/topic/5565-mathematics-forum-rules-the-ia/page__p__41235entry41235

I'd generally say that it can be less formal. Organize it, but it doesn't have to be very structured. Intros are nice, but they might not gain you any points. It depends on what you're saying. Even if you're talking about the topic, it might not add anything to your discussion. It really depends. I'd do my paper before doing an intro, if I did do an intro.

[holycows]

Technology is a category in my marking sheet. How can I included the use of techology in my portfolio?

Thanks...

[Angad_Amarth]

Hey, i just got the stellar number portfolio and sheet and i am really lost on how to do it, infact, even how to start it. Any suggestions and tips would be helpful. If any of you could upload or email me yours that would be greatly appreciated. Don't worry i won't plagiarize or copy any. Thank you:)

We're not here to swap IAs. What exactly are you confused about? You said you don't know how to start it. What do you think the instructions want you to do?

Hey, its not dat difficult...for da second part, as its a quadratic, u have 2 do it like this: -

1) 1st term=a(x^2) + b(x) + c

as 1st term = 1... 1=a(1^2) + b(1) + c => a+b+c=1.

thus the same way u continue for the next three terms and u'll get 3 simultaneous equations. solve them and u'll get values for a,b,c...now dat u have these values u get da general statement as a quadratic...u can validate and see dat it works...

[AV93]

Hey, thanks alot. I think i sort of get it now. If i need any help i'll get back to you'll. Thanks:)

[salutetbonsoir]

Have you heard of polynomial or quadratic sequences? The way it's been explained to me is you take the terms and find the positive difference between each consecutive term. Then you have a new list of numbers and you find the difference between each terms again, which gives a new list. Then you do the same thing again. You repeat this until you've found a list with all of the same numbers. If you get a list with all of the same numbers, then you know that there's a polynomial that will fit your sequence.

So for example

1, d+1, 2d+1, 3d+1

[take difference]

d, d, d

So that's a first degree polynomial... aka a monomial, which is what you deal with when you say a_n =a₁ + (n-1)d, where d is the difference, because when you simplify, you get a_n=dn-d+a₁

More complicated:

1, d+1, 3d+1, 6d+1

[take diff]

d, 2d, 3d

[take diff]

d, d

Since you've had to take the difference twice, it's a quadratic. If you had to take it thrice, the polynomial would be a cubic. And so on.

Does that help you?

is there a reason why it's a polynomial sequence?

some students found some general terms for the sequence without using the method of quadratic sequences.

[sweetnsimple786]

I don't know. I hadn't thought of that. Did they do it recursively? Or does 'generally' imply explicit statements?

[salutetbonsoir]

I don't know. I hadn't thought of that. Did they do it recursively? Or does 'generally' imply explicit statements?

well they did do it recursively. but from what i heard is that the quadratic method is the right way to solve it. finding a positive difference of a new list is the way to find the statement which someone told me. so why use system of equations to find the statement? or why is it called quadratic sequence?

Thank you.

[salutetbonsoir]

What does it mean by assigning different p values? Does it mean different star numbers? And if so could a five star numbers be generate like 1,11,31... and so on. Just wanted to know if I was on the right track.

yeah i think that is what they mean.

i'm also going to do a 5 vertices star.

[sweetnsimple786]

I don't know. I hadn't thought of that. Did they do it recursively? Or does 'generally' imply explicit statements?

well they did do it recursively. but from what i heard is that the quadratic method is the right way to solve it. finding a positive difference of a new list is the way to find the statement which someone told me. so why use system of equations to find the statement? or why is it called quadratic sequence?

Thank you.

I don't know what the 'right' way to solve this is. There often isn't a single right way. Explicit is typically better than recursive, but maybe IB doesn't care in this IA. I don't know.

I think it's called quadratic because there's a quadratic function... ax² + whatever. It'd be cubic if it was ax³ + whatever. That seems logical to me. And I don't know if quadratic sequence was the best term for me to use. I couldn't recall it, but now I remember that the method is called finite differences [which you can Google to see what exactly that entails].

[dood_25]

Hey everyone,

Since finishing my math portfolio, I figured I would post the images I used for everyone to have and use. Yay!

I have the images hosted here:

http://sites.google.com/site/ibstellarnumbers/home

[Tartufo]

Hi,

I have this project as well.

I've found the general statements I need, but on the sheet its to 'test the validity of the general statement' and to 'discuss the scope and limitations of the general statement'.

Does that mean that I only have to test it on more stellar figures?

Do I need proof, or is multiple tests okay?

Thanks in advance!

[mathteach]

Well, it's like star numbers which are 1,13,37,73,121,181. I have figured out the patter which is each number adds b multiples of 12. For example, 1+12=13, 13+24=37, 37+36=73 and so on. So it's not arithmetic, geometric or infinite series.

You're on the right track but wrong about it not being a series. It IS a series. It is NOT a sequence, but it is a series - one of the types you've listed. The problem is the 1 at the beginning. Think of it this way: your numbers represent a pattern of 1+Sn, not just Sn.

That's more forthcoming than I usually am.

[Tessa92]

Hey everyone

We were given a Portfolio on stellar numbers. I am so far finished but nevertheless I dont know what is meant by an informal justification. I asked my teacher about, and all he said was that it is not a prrof that your general statement works.. Woow.. helpful. Does anyone have an idea?

[Daedalus]

Hey everyone

We were given a Portfolio on stellar numbers. I am so far finished but nevertheless I dont know what is meant by an informal justification. I asked my teacher about, and all he said was that it is not a prrof that your general statement works.. Woow.. helpful. Does anyone have an idea?

As far as I can see, informal justification is explaining why something is true - perhaps proving it for certain examples - but without a formal proof. So you don't have to mathematically derive a certain statement, just show that it tends to be true.

[Tessa92]

Thanks thats really helpful! I made a table on excell where I can substitute different values to prove my statement! Thanks a lot!

I have a question in terms of the differences...

I know that when you are able to take the difference twice, the sequence is quadratic. but my teacher said i will have to explain why that is!

so can anyone tell me why the sequence MUST be quadratic

Edited April 23, 2010 by sweetnsimple786
Just use the Edit button to add more to a post =)

[hour]

I've currently got the expression I need for the 6-stellar number, but I don't know how to transfer it to other stars with different numbers of points. Can anyone point me in the right direction?

[Szoszana]

I've currently got the expression I need for the 6-stellar number, but I don't know how to transfer it to other stars with different numbers of points. Can anyone point me in the right direction?

I did it by looking for a relationship between the number 6 and the expression I had formulated for the star with 6 vertices. Then, I tested its validity by simply applying it to stellar shapes with a different number of vertices. You may want to make appropriate drawings; I found it quite helpful.

[Blue River]

I have been assigned stellar numbers portfolio for this year, which is due in one week. But I don't know how to start it? I would really need help

Thanks