IA Type I -- Stellar Number

[gerh]

Any of you have the questions for this portfolio assingment

[Julie]

sorry... i lost mine after i turned my IA in, but I'm sure someone on here has it... I'll look around for mine...

[gerh]

We have to turn IA next week so I need the questions because I forget my paper at school.

[Julie]

I'll keep look, but I'm pretty sure I don;t have it anymoe

sorry

[dessskris]

Any of you have the questions for this portfolio assingment

It can be found in this thread

[ronali]

Hello again! Thanks juliemk, I'm definitely going to use your advice. I've got one (possibly) last question, though.

I solved for the formulas using matrices in my calculator, and right now I'm trying to create a visual representation of that process. I'm wondering whether I should write out the whole matrix each time, or if I should use the calculator's labels [A ] and . Thanks again

EDIT: I thought of another thing! Someone said in an earlier post that they included an introduction — is this necessary/what would I say if I were to write one?

Edited January 7, 2011 by ronali

[Julie]

Hello again! Thanks juliemk, I'm definitely going to use your advice. I've got one (possibly) last question, though.

I solved for the formulas using matrices in my calculator, and right now I'm trying to create a visual representation of that process. I'm wondering whether I should write out the whole matrix each time, or if I should use the calculator's labels [A ] and . Thanks again

EDIT: I thought of another thing! Someone said in an earlier post that they included an introduction — is this necessary/what would I say if I were to write one?

You can use the labels from the calculator, just state beforehand what labels A and B are, and than afterward you can continue on using just the labels. Make sure you write something like "Steps when using the GED" as a subtitle or something like that so the grader knows what you are trying to demonstrate.

YES, you must have an intro, but it is simple. It can be 1-3 sentences. You are simply stating what you are going to do. So, in very brief words, your looking for a general statement in terms of p and n. Formulate that into a sentence or two explaining what you will be doing. Our teacher gave us an example of an IA from last year or something like that, and one of the guys got a 6 instead of a 7 because he didnt have a simple intro (sucks). so get that in there

Edited January 7, 2011 by Mahuta ♥

[dessskris]

Hello again! Thanks juliemk, I'm definitely going to use your advice. I've got one (possibly) last question, though.

I solved for the formulas using matrices in my calculator, and right now I'm trying to create a visual representation of that process. I'm wondering whether I should write out the whole matrix each time, or if I should use the calculator's labels [A ] and . Thanks again

EDIT: I thought of another thing! Someone said in an earlier post that they included an introduction — is this necessary/what would I say if I were to write one?

If the matrices are augmented matrices, I'd suggest using labels A and B. Or if the matrices are just 2x2, I prefer writing out the whole matrices especially if you do a lot of calculations with those matrices.

A paragraph of introduction will do. Write what your portfolio is all about (the problem, the aim, etc).

I myself defined something in the introduction actually. It's not compulsory but I guess it will just look better..? In this IA you may want to define stellar number too.

[angelchild001]

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

Thanks...

you the do it based on if your caculation were right

[JoeG]

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

Thanks...

you the do it based on if your caculation were right

Try to use a graphing calculator for something besides rudimentary calculations. By rudimentary I mean very basic stuff, like adding and subtracting two numbers at a time (2+2 )

If you use it for matrices, or anything somewhat complex, I think it would be fine to call it a use of technology.

Also, as another use of technology, try to create diagrams USING technology/computer programs. You can take a GDC screen-shot, for example. I certainly did.

You aren't limited to this, try something creative, but don't do anything where it would harm your grade.

Just make sure it's something of significance.

Edited January 11, 2011 by JoeGuff

[niñajessica]

I'm working on the stellar numbers portfolio too. I was just wondering what it means by values of p. Does this mean the vertices??

[tiredibgirl]

Hey all the Ib maths standard students out there!

So im doing my maths investigation on stellar numbers and im completely stuck on the last general statement. I have managed to get an equation for the stellar numbers and for pentagonal numbers etc. but dont know how to put those together and include both p and n in the same equation..

Can anybody give any hints or help how to reach the final conclusion?

Help would be much appreciated:)

[dessskris]

Sorry I am getting busier with my HW since I am back to school so I can't quickly respond to you guys' questions.

---

I'm working on the stellar numbers portfolio too. I was just wondering what it means by values of p. Does this mean the vertices??

Yeah p is the number of vertices, p-stellar numbers. In 6-stellar numbers, p=6 and the stellar shape has 6 vertices

---

Hey all the Ib maths standard students out there!

So im doing my maths investigation on stellar numbers and im completely stuck on the last general statement. I have managed to get an equation for the stellar numbers and for pentagonal numbers etc. but dont know how to put those together and include both p and n in the same equation..

Can anybody give any hints or help how to reach the final conclusion?

Help would be much appreciated:)

Is that when you need to express Sn in terms of n and p?

I actually have explained this before in this thread, you know. Read the quote below:

So you have the formula of Sn in terms of n for some p-stellar numbers right?

Now you must see some similarities or patterns (I also see it, it's very obvious). Then you must produce the general statement Sn in terms of p and n.

For example (this is a really random example):

When p=1, Sn=2n+3

When p=2, Sn=3n+3

When p=3, Sn=4n+3

When p=4, Sn=5n+3

You see the pattern?

So,

Sn=(p+1)n+3

Get that?

If you still don't understand I can try to explain it a bit more clearly

[Proletariat]

If you follow the process on the question sheet, the last general statement actually ends up being the easiest to find.

Now that you've found the equation for 6-stellar numbers, simply repeat the exact same steps that you used to solve the problem, but for a different stellar number (p=5, for example.) At the end, you'll have your first equation for 6-stellar numbers and then your second for 5-stellar numbers, or whatever value for p you chose to investigate. Now compare the two equations, and see where does the two differ.

Once you've isolate that bit, you just have to equate it to an expression containing p.

[Julie]

If you follow the process on the question sheet, the last general statement actually ends up being the easiest to find.

Now that you've found the equation for 6-stellar numbers, simply repeat the exact same steps that you used to solve the problem, but for a different stellar number (p=5, for example.) At the end, you'll have your first equation for 6-stellar numbers and then your second for 5-stellar numbers, or whatever value for p you chose to investigate. Now compare the two equations, and see where does the two differ.

Once you've isolate that bit, you just have to equate it to an expression containing p.

Just wanted to add... you should probably do about 3 other values for p... so for instance: p=3, p=4, p=5. It will also help you recognize a pattern when comparing and contrasting the equations you get for them.

[CristinaV]

I decided to go the route of using quadratic equations, and it seemed to be going well with the 6-point star; however, the answer I keep getting for the general statement is when p=6, Sn=n^2 - 6n + 1 which is a wrong answer.

I noticed for the difference between the dot values of the 6-point star was a growing multiple of 12, specifically 12(n-1). when d=12. I'm not really sure how that's going to really help me thus far

anyways, what I was trying to do was to solve for a, b, and c for the 3 equations I got from the values of Sn. a + b + c = 1; 4a + 2b + c = 13; and 9a + 3b + c = 37. My logic was that solving for a, b, and c should give me the terms for my general quadratic statement.

It's all turning out wrong though, what should I do? I'm stumped.

Hey I am not doing this task but I guess I could just help...perhaps?

I decided to go the route of using quadratic equations, and it seemed to be going well with the 6-point star; however, the answer I keep getting for the general statement is when p=6, Sn=n^2 - 6n + 1 which is a wrong answer.

Did you mean using quadratic eqn to get the general statement (GS)? Well, what did you do to get it? I actually found the GS and it is very similar to yours. Hint: you are missing a coefficient

I noticed for the difference between the dot values of the 6-point star was a growing multiple of 12, specifically 12(n-1). when d=12. I'm not really sure how that's going to really help me thus far

Good that you notice that! Haha I didn't notice

So you know that:

S1=1

S2=1+12

S3=1+12+2x12

S4=1+12+2x12+3x12

Let U1=0

Let U2=12

Let U3=2x12

Let U4=3x12

And Sn=1+U1+U2+...+U(n-1)+Un

Can you find Sn in terms of n, then?

anyways, what I was trying to do was to solve for a, b, and c for the 3 equations I got from the values of Sn. a + b + c = 1; 4a + 2b + c = 13; and 9a + 3b + c = 37. My logic was that solving for a, b, and c should give me the terms for my general quadratic statement.

How did you get those equations? yeah you are correct, solving for a, b and c gives you the coefficients for your GS.

I don't know if you learn this in SL but you can solve it using matrices, do RREF. If you do learn it in SL, use your GDC to do RREF and you'll get the answer. Otherwise, solve it using other methods.

I got the same equations, so you're definitely on the right track. And I got to those by using quadratics, Desy. It's what's described in the first page of the topic/forum/whatever-this-thing-is, just taking the difference over and over again, noticing it's a quadratic equation, and plugging in the n and Sn values.

For some reason I never got the whole:

And Sn=1+U1+U2+...+U(n-1)+Un

Sn = Un + U(n-1) +...+ 1 + U1 + U2

If that's even how it's done haha

Oh well, I think that doing it with quadratics is enough.

lol and I solved those 3 equations by doing elimination. No fancy technology. Although I guess I could make my calculator do it... but I just feel like it won't bring up anything new. I don't think it would get me more use of technology points because I can easily do it myself, and because I will already have graphs with the equations and tables with the data. That's enough for a 1, and it's virtually impossible to get a 2 in use of technology because my teacher told me that you actually have to create a program that solves it hahah so that's not going to happen. I'll be ok with 1 point

[JustFine]

Well, I guess your teacher is wrong. I mean how can he/she ask of you to actually write a program that will do the stuff?? I got 20/20 for this portfolio and the only tech did was gdc and paint lol.

[JoeG]

Yeah, I didn't have to write a program for mine either, and I got a 30/30. (Well, my IB math teacher is new )

It is possible to write a program though. I could do it for the TI-84 SE, and it wouldn't be that hard.

As long as you know how to use the following, you should be able to make a basic program.

The Prompt Command

Knowing how to use the Store button

Knowing how to type an equation using variables

The Display Command

Edit: Sorry, I meant 30/30. lol.

I think that's right now. All I know is that I got a good score.

Edited January 21, 2011 by JoeGuff

[Austin Glau]

The Prompt Command

Knowing how to use the Store button

Knowing how to type an equation using variables

The Display Command

Tips:

Input "x:", p

Displays "X:" then lets user enter a number that is then stored as p.

3->x

stores x as 3

disp"....","test"

diplays "...." on first avalible line and "test" on next avaliable line. if longer than 16 chars an ellipses replaces the 16th character.

[Kayleigh.RM]

Okay, so I just got this portfolio, and Im starting on it now before I forget about it..

so I've worked through it, and I have found the general formula, but I dont really understand how we know to use the quadratic formula to solve it... I've read through the previous posts about subtracting until you get a constant difference.. but i dont see how that works in this case.. I am a little slow though, and not the best at maths, so I've probably just missed something simple thats TOTALY obvious to everyone else.. So I would really appreciate if someone could help me out?

so this is what I get:

1, 13, 37, 73, 121

and subracting gives:

12, 24, 36, 48

subracting again:

12, 24, 36

and so on...

but how does this tell us we need to use the quadratic formula?

thanks alot by the way for the previous posts, you guys are super helpful! :)

Edited January 21, 2011 by Austin Glau
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