IA Type I -- Stellar Number

[Ace24]

hey guys i found a general statement for the stellar numbers

Sn=6n^2-6n+1

what do u guys think?

[nametaken]

hey guys i found a general statement for the stellar numbers

Sn=6n^2-6n+1

what do u guys think?

That's good.

[ParasKumar]

Can any help me on the expressions for the 6 stellar number at stage S7

Also for the above valuse of P can some please help.

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I hope someone can help me!

I've got it down to the end, but I can't figure out how to explain the limitations... will it work with a three pointed star? I have a computer program that makes the diagram, but it won't let me make a three pointed star...

PM me your email and I will send you my diagrams and then you can edit them because I made from a program.

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hey guys i found a general statement for the stellar numbers

Sn=6n^2-6n+1

what do u guys think?

Did you get the expression for the 6 stellar number at stage S7?

Edited March 25, 2011 by Desy ♫

[dessskris]

Can any help me on the expressions for the 6 stellar number at stage S7

Also for the above valuse of P can some please help.

If you observe a pattern, just write S7 to show that pattern. For example: (a really random example)

S3=5

S4=11

S5=23

S6=47

The pattern I observe is that Sn=2*S_n-1+1

So the expression for S7 would be 2*47+1

Another example:

S3=10

S4=17

S5=26

S6=37

The pattern I observe is that Sn=n²+1

So the expression for S7 would be 7²+1

Something like that.. I hope you get it.

What are you asking for in your second question? I don't really get what you are trying to say

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my question is how doe i write this up... like what format. Our teachers aren't very helpful. I've done a type two. Do I need some sort of background for this one as with G-Force?

Yes you need a background. I posted an outline for this IA task --> http://www.ibsurvival.com/topic/8208-portfolio-type-i-stellar-numbers/page__view__findpost__p__101100

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and Sn= 6n2 - 6n+1 but how would you write it in terms of p ?

Tabulate p and expressions of Sn, you will see the pattern.

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For the general statement in terms of p and n for any stage Sn, I get **********. I understand there are probably different ways of writing this out, but is this way acceptable. Like, is it right?

Yes it is right

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I hope someone can help me!

I've got it down to the end, but I can't figure out how to explain the limitations... will it work with a three pointed star? I have a computer program that makes the diagram, but it won't let me make a three pointed star...

It should work when p=3. Sorry I can't help much on that though.

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hey guys i found a general statement for the stellar numbers

**********

what do u guys think?

yeah, it's correct

[dessskris]

At first that's what I thought, too. But the question didn't say: write an expression of S7 in terms of the previous term or in a recursive form or anything along those lines I am confused. What you said may be correct. I am not 100% sure as I didn't do this task for my IA.

Ohhh that. lol. Look, p is the number of vertices of the star and n is the...number of term? you know what that is anyway, right?

So those values you listed are Sn for 6-stellar numbers. You are asked to find Sn for p-stellar numbers. So for other stars with different number of vertices. Maybe with 5 vertices, 9 vertices, or maybe 23 vertices! (<-- my birthdate lol) You can choose your own values of p. I suggest 3-4 others if you can make it

[puddingmilk]

I've got all the general formulas and all that..but I'm just a it confused. I'm reading this here:

Triangular Numbers Table of values of n and nth term

• Triangular Numbers General Statement

• Triangular Numbers Conclusion

• Stellar Numbers Intro

• 6-Stellar Numbers Table of values of n and Sn

• 6-Stellar Numbers General Statement

• x-Stellar Numbers Table of values of n and Sn

• x-Stellar Numbers General Statement

• y-Stellar Numbers Table of values of n and Sn

• y-Stellar Numbers General Statement

• z-Stellar Numbers Table of values of n and Sn

• z-Stellar Numbers General Statement

• Stellar Numbers Table of Summary of general statements when p = 6, x, y, z

• Stellar Numbers General Statement in terms of p and n

• Stellar Numbers Informal Proof

• Stellar Numbers Scope and Limitations of the General Statement

• Stellar Numbers Conclusion

• Final Conclusion

And I don't get what Sn is exactly now? It says Table of Values of 'n and Sn'. Now I don't see the difference between them...n is always for term number and I thought Sn was stage...which is also basically the term isn't it? I plotted n against p. (p is the number of dots.)

And stellar numbers Informal Proof - basically I either solve algebraically to prove it, OR find other shapes with other vertices and show that my formula works for those too right?

[TomnTom]

I've got all the general formulas and all that..but I'm just a it confused. I'm reading this here:

Triangular Numbers Table of values of n and nth term

• Triangular Numbers General Statement

• Triangular Numbers Conclusion

• Stellar Numbers Intro

• 6-Stellar Numbers Table of values of n and Sn

• 6-Stellar Numbers General Statement

• x-Stellar Numbers Table of values of n and Sn

• x-Stellar Numbers General Statement

• y-Stellar Numbers Table of values of n and Sn

• y-Stellar Numbers General Statement

• z-Stellar Numbers Table of values of n and Sn

• z-Stellar Numbers General Statement

• Stellar Numbers Table of Summary of general statements when p = 6, x, y, z

• Stellar Numbers General Statement in terms of p and n

• Stellar Numbers Informal Proof

• Stellar Numbers Scope and Limitations of the General Statement

• Stellar Numbers Conclusion

• Final Conclusion

And I don't get what Sn is exactly now? It says Table of Values of 'n and Sn'. Now I don't see the difference between them...n is always for term number and I thought Sn was stage...which is also basically the term isn't it? I plotted n against p. (p is the number of dots.)

And stellar numbers Informal Proof - basically I either solve algebraically to prove it, OR find other shapes with other vertices and show that my formula works for those too right?

- n is the stage, Sn is the value at that stage (the number of dots). For example for triangular numbers, n=3 => Sn =6, n=5 => Sn = 15.

- For the proof, it's really difficult since different teachers grade it differently. For example, my teacher would accept using 2 different ways to find the same equation as an informal proof. However, you should not worry too much about the proof since it's only worth 1 point. If you do al the other part right you would get 19/20 which is still awesome !

[puddingmilk]

- n is the stage, Sn is the value at that stage (the number of dots). For example for triangular numbers, n=3 => Sn =6, n=5 => Sn = 15.

- For the proof, it's really difficult since different teachers grade it differently. For example, my teacher would accept using 2 different ways to find the same equation as an informal proof. However, you should not worry too much about the proof since it's only worth 1 point. If you do al the other part right you would get 19/20 which is still awesome !

Thanks!!

And one more thing - it says explain how you arrived at the general statement? According to this guideline, that would be basically a repetition/conclusion? I mean I explained already on my way to the general statement, I don't see why I have to say that after discussing scope/limitations.

[dessskris]

And one more thing - it says explain how you arrived at the general statement? According to this guideline, that would be basically a repetition/conclusion? I mean I explained already on my way to the general statement, I don't see why I have to say that after discussing scope/limitations.

Oh and p is the number of the vertices of the star. In 6-stellar numbers, p=6.

You can give the proof either way. The algebraic proof is more favourable, though.

If you have explained it, you don't need to explain it again. FYI you don't have to exactly follow the order of the questions in the task paper. They are just listing what they basically expect to see in your paper. For that part I suppose it should be okay if you explained how you arrived at the general statement before you talk about the limitations thing.

[puddingmilk]

Okay, I shall post my questions here:

for stellar numbers, should I refer 'n' as stage or term? Are they essentially the same thing?

And I don't know what's up with the curve plotting! Is it necessary?!

Basically I just solve the quadratic formula using Excel or my GDC with that STATS thing.

thanks

[dessskris]

Okay, I shall post my questions here:

for stellar numbers, should I refer 'n' as stage or term? Are they essentially the same thing?

And I don't know what's up with the curve plotting! Is it necessary?!

Basically I just solve the quadratic formula using Excel or my GDC with that STATS thing.

thanks

When you talk about n, you talk about terms...

When you talk about Sn (not the value of Sn though), you talk about stages

That is what I observed in the task paper.

And there are A LOOOTTTTTTTT of ways to come up with the general statement, and the curve plotting is one way. So it's okay if you don't do that

[timmotytimmoty]

I've found a general statement for stellar number, what you guys think?

The general form is true for every P-Stellar number’s shape and for every n^(th)stage.

P- P-Stellar numbers

Sn- Stage number

Dn- Sum number of dots of the shape

Dn=S1+2P×s(n-1)×Sn

[dessskris]

I've found a general statement for stellar number, what you guys think?

The general form is true for every P-Stellar number’s shape and for every n^(th)stage.

P- P-Stellar numbers

Sn- Stage number

Dn- Sum number of dots of the shape

Dn=S1+2P×s(n-1)×Sn

I don't get it.

You aren't supposed to come up with a new variable Dn.

You are supposed to express Sn in terms of p and n. I don't know if your expression of Dn is correct, but please bear in mind that it is not what the examiner wants to see.

I suggest putting a table of p and expressions of Sn. You will see the pattern and finally come up with an expression of Sn in terms of n very easily.

[timmotytimmoty]

You aren't supposed to come up with a new variable Dn.

You are supposed to express Sn in terms of p and n. I don't know if your expression of Dn is correct, but please bear in mind that it is not what the examiner wants to see.

Yeah, but my teacher told me that if I've explained the meanings of the terms, that would be ok!

[dessskris]

are you sure? fine then if that is what you feel like doing. can you express Dn in terms of p and n, then?

if you still have time to make some changes, I still suggest you to find the expression of Sn in terms of p and n. it's very simple actually! so give it a try

[timmotytimmoty]

are you sure? fine then if that is what you feel like doing. can you express Dn in terms of p and n, then?

if you still have time to make some changes, I still suggest you to find the expression of Sn in terms of p and n. it's very simple actually! so give it a try

Yes, I'm sure, I asked my teacher twice before I gave my work to her, and now I'm done with it! But thank you for your advice. I do appreciate it!

[puddingmilk]

Okay, you know when the second difference is constant, do you say it's a quadratic formula or equation?!!

I typed quadratic formula in google and it's all that -b+/- SQRT b^2-4ac over 2a and I want the ax^2+Bx+c so how would I call that?

Thanks

[dessskris]

Okay, you know when the second difference is constant, do you say it's a quadratic formula or equation?!!

I typed quadratic formula in google and it's all that -b+/- SQRT b^2-4ac over 2a and I want the ax^2+Bx+c so how would I call that?

Thanks

A quadratic equation

You do need to know and use these terminologies well btw

[puddingmilk]

Ok thanks again Desy!!

ME AGAIN...

Um, for the triangular numbers you can solve either the quadratic way with the 2nd differences, but there's also the other way which looks like this:

Un-U1 = Un-Un-1 + Un-1-Un-2 +....U2-U1.. (because then the difference between each term is the same as its term number, stage 2 and 3 have 3 in difference, stage 3 and 4 have 4 in difference..)

then...

Un-U1 = n+(n-1) +(n-2) +.....+2

Un= n+(n-1) + (n-2) +...+2

Un=1+2+...+(n-1)+n

then I did the trapezoid thing, base1 + last base times height divided by 2 to get the formula for triangular numbers.

BUt I don't know the proper name for this method? like finite sequence? Um, sum of an arithmetic series?? Maybe there's a bit of error in my working out but I'd just like to know what this type of thing is called in maths.

Thanks

[nametaken]

Ok thanks again Desy!!

ME AGAIN...

Um, for the triangular numbers you can solve either the quadratic way with the 2nd differences, but there's also the other way which looks like this:

Un-U1 = Un-Un-1 + Un-1-Un-2 +....U2-U1.. (because then the difference between each term is the same as its term number, stage 2 and 3 have 3 in difference, stage 3 and 4 have 4 in difference..)

then...

Un-U1 = n+(n-1) +(n-2) +.....+2

Un= n+(n-1) + (n-2) +...+2

Un=1+2+...+(n-1)+n

then I did the trapezoid thing, base1 + last base times height divided by 2 to get the formula for triangular numbers.

BUt I don't know the proper name for this method? like finite sequence? Um, sum of an arithmetic series?? Maybe there's a bit of error in my working out but I'd just like to know what this type of thing is called in maths.

Thanks

Ok, well the sum of an arithmetic series is Un=a+(n-1)d,so it can't be the sum of an arithmetic series, and is not what you'd call a 'method'. A finite sequence is simply a sequence which has a definite ending to it, e.g: 1,3,5,7,9. The sequence ends at 9. A finite sequence again, I don't believe is a 'method', it's more of a mechanism.

The formula to get triangular numbers is :

N(N + 1)

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2

I don't understand what you mean by the method. I haven't covered this, so I wouldn't really know. Sorry that I couldn't be of more help!

And finally, good luck!

Edited March 29, 2011 by nametaken