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Type I -- Stellar Number


ibworking

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Hey you all!

I have to do an IA type 2 in about a weeks time. Our teacher said he had two possibilities for tasks, one of which the population growth in china one and the other one was this one. I was hoping someone could maybe send me the tasks of this one, as i already found the china one. It's just that I want to get an impression as to what that's all about, you know?

If there's anyone willing to do this, just send me a mail on my account here and ill give you my e-mail address, ok?

THANKS A LOT!

take care

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Hey you all!

I have to do an IA type 2 in about a weeks time. Our teacher said he had two possibilities for tasks, one of which the population growth in china one and the other one was this one. I was hoping someone could maybe send me the tasks of this one, as i already found the china one. It's just that I want to get an impression as to what that's all about, you know?

If there's anyone willing to do this, just send me a mail on my account here and ill give you my e-mail address, ok?

THANKS A LOT!

take care

There's a scan of the assignment sheet on the first page of this thread. :P

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I would recommend everyone who are struggling with stellar numbers to see the difference between for example S4 and S5. How many dots are added in the new "shell"? E.g. there's 13 dots in S2. In S3 there's 37, which makes the difference 24. The difference between S2 and S1 is 12. Just check this out, because I figured it out immediately.

I just had one paragraph where I wrote number of dots in the whole star, and then another paragraph where I wrote how many dots that were added for every "shell/star" (from e.g. S6 to S7).

I did it by coincidence, but I got it at once, and the general term(s) were really easy to solve after I saw the pattern(s). I hope I could help any one who's writing the Stellar Numbers-report now!

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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...

hi....i dont understand why it is a quadratic?how to find it is a(x^2) + b(x) + c?thanks

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I used calculus.

Derivatives and then integration to find the general statement. It lays out so nicely. The only problem comes when I try to prove the general statement in terms of p and n. I feel that it is too shaky. But that is what I did.

Hey!

How did you use calculus??

Could you give me a unrelated example?

Like only the method? I'm curious..

Thanks in advance

Edited by zeuble
Type 'u' fully please (you), thanks- Maha :)
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Hi, I'm new on this forum so please don't bite but...

I have a GDC and my teacher said that we must use this if we want to get good marks. But how do I use for sequences? I've almost finished but I haven't used a GDC throughout so I haven't a clue what I can do.

HELP! :P

There's a command called seq on TI GDCs. I vaguely remember being able to use it together with the sum command, something like this:

sum(seq(formula, variable, start, stop, step))

If you have catalog help it will tell you what you need to put in to get a value. You can then say what you did with your calculator, or even type what you typed in your calculator. Just indent it like I did above.

Quick Google for "TI seq" gave me this: http://tibasicdev.wikidot.com/seq-list

Edited by deissi
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This might not be the best way to explain it, but in my mind, I think of the sequences I'm familiar with. I know it's not geometric or arithemetic because there's not a common ratio or difference. It's not one of those weird arithmetic on top, geometric on bottom fraction sequences either. This is why I try to figure out if it's quadratic. I can't explain what it means for a sequence to be quadratic except for the fact that the next term is determined by a second degree polynomial, a quadratic. And you know this by using the finite differences method, although I'm not sure why that works. You could Google it. And then for how you get the coefficients of the quadratic, explain the concept of a system of equations and how you set it up.

Hey!

I too found the Formula for Tn by graphing saying it's a polynomial and testing and proving that it is quadratic.

But I want use mathematically induction to prove it, firstly do you think the IBO will think that i have cheated using a HL method.

But I found Sn by using a cubic formula, why do u suggest it's cubic instead or quadratic?

And also, when I mathematically induct it, it turns out to be false! Should I put this in and say it doesn't work for all terms??

I forgot to mention, I am using induction to try and get 2/2 in quality of work.

Thank you in advance!

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What does the part "Hence, produce a general statement, in terms of p and n, that generates the sequence of p-stellar numbers for any value of p at Sn" mean

In my understanding, it means find a formula that you can use no matter how many vertices the star has or which stage. Don't forget that p is just representing the number of vertices that the star has and that n is the subscript of the stage number.

I hope that helps!

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This might not be the best way to explain it, but in my mind, I think of the sequences I'm familiar with. I know it's not geometric or arithemetic because there's not a common ratio or difference. It's not one of those weird arithmetic on top, geometric on bottom fraction sequences either. This is why I try to figure out if it's quadratic. I can't explain what it means for a sequence to be quadratic except for the fact that the next term is determined by a second degree polynomial, a quadratic. And you know this by using the finite differences method, although I'm not sure why that works. You could Google it. And then for how you get the coefficients of the quadratic, explain the concept of a system of equations and how you set it up.

Hey!

I too found the Formula for Tn by graphing saying it's a polynomial and testing and proving that it is quadratic.

But I want use mathematically induction to prove it, firstly do you think the IBO will think that i have cheated using a HL method.

But I found Sn by using a cubic formula, why do u suggest it's cubic instead or quadratic?

And also, when I mathematically induct it, it turns out to be false! Should I put this in and say it doesn't work for all terms??

I forgot to mention, I am using induction to try and get 2/2 in quality of work.

Thank you in advance!

I'm not going to say whether it's quadratic or not (that's for you to find out :P), but I will say that it's not cubic.

Also, any formula we get really shouldn't work for all terms, logically at least. Remember were working with geometric figures.

By we I mean High School math students lol.

Edited by JoeGuff
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