IA Type I -- Stellar Number

[JoeG]

Hey everyone. Thanks a lot for all the resources put up here. They're really useful!

I have questions about the limitations of the statement.

Yea i came up with the general statement already and at first what i wrote for limitations was that the number of p-value has to be real integer that is greater than zero.

But then i started thinking about the geometry when p = 1 or p = 2. that seems nonsense cos i am not able to draw any diagrams with one vertex nor two..

And i searched vertex's definition in geometry is that the end point of two line segments. that means p at least has to be 3?

And if what i said was correct how do i account for it in my IA

Thanks..):

I think I said something similar to what you said. (It's been a month since I actually looked at what I said about this limitation lol)

As long as you can adequately show that p equaling one or two is a limitation, you should be fine.

To account for it, I would try to explain it, and show how it would be somewhat illogical to have a "stellar number" with certain numbers of dots.

Just be careful though. If you find something to the contrary, don't put this limitation in your IA, or modify it as you need to. I'm not saying there absolutely is, I'm only giving a warning lol.

Edited November 30, 2010 by JoeGuff

[IBomination]

I'll try to explain this quickly because I elaborate right now, so sorry.

So you have the quadratic an² +bn +c= a_n

[where n is the nth term]

Now plug in the known values. You'll have to use three "points" (n, a_n) like (x,y) because you're solving for a, b, and c. So you'll create a system of equations.

Here's a couple of them w/ your hexagonal numbers:

n=1, a_n = 1

a + b + c =1

n=2, a_n=6

4a + 2b + c=6

So continue that & solve for a, b, and c, and you'll know how to find a_n

Thanks for all your help!

I didnt really get what you were saying, but i solved it anyways.

I just have a question about portfolio expectations, apparently my teacher wants us to use "1 mm graph paper" which is extremely small to show our work, and im not sure how to graph a 6-star or a 8-star(which i used to check my general statement)

Also, is it ok if i didnt solving using your method and instead using the "quadratic Regression" function on my TI-84?

Thanks again!

Cheers!

-IBomination

[xoxomissgomez]

So I started on my project & I have found the general statement for both the triangular numbers and the stellar numbers.

What I don't understand, everything from the "Now repeat the steps above for the values of p." Everything beyond that I just blanked out. I kind of have an idea but I'm not sure at all.

If you need a copy of the sheet with all of the questions I can upload it. Just let me know. Any help is good!

Thanks!

[Kemo93]

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?

I think you have to state the obvious and say that p ( of the general statement) is equal to the number of vertices of the star. A 5 stellar number has a value of p, a 6 stellar 6 and so on

[Allen]

Does anyone here actually know how to complete the star patterns on Geogebra? I know there's a program made in Geogebra for this specific IA, but wasn't sure how it was done. Any help with this would be appreciated.

[Thisisatest]

For the star one I came up with the equation:

6n(n-1) +1

This works for all of the numbers but Im finding it hard to explain how I got it... it was sorta a lot of random thoughts in my head.

The difference between each of the terms is 12n.

The number 6 is the number of points so can be replaced with p (i think, havent tested but it makes sense)

For the basic triangle that is just (n/2)(2+(n-1))... thats simply from the equation in the textbook.

[Jackie]

@missgomez

When they say "p" they mean the number of points in the stellar pattern. The first one they give is a 6 point star and so they want you to find the equation and patterns using a 5 point or 7 point star, etc. They want you to :draw the pattern up to S4, chart it up to S6, describe any patterns, find S7 and give an equation for the other values of p you chose to do. It doesn't say to find n different p values or whatnot but two or three is a safe number.

This IA took me ages. Honestly, I think the most difficult part is drawing the stars because of how time consuming it is.

Edited December 8, 2010 by Jackie

[IBDeath17]

I'm having a lot of trouble with the star diagrams. How do you draw the Star Diagrams on Word 2003? I managed to get the sequence of numbers by counting in my head, but the drawing is excruciating!

[ultranoodles]

http://www.mediafire.com/?6pptc89ujts1d6c

This is a program to instantly make your stars, just take a screen shot and use the image. Make it so that there are 6 points and a maxed out density. Change the layers for S2, S3, etc.

Edited December 8, 2010 by ultranoodles

[IBwillkillmeD:]

Hai there! I was wondering if nebody knew how to draw the triangular dotted shapes, etc. The pentagons and whatnot on word 2007? im stuck!

[JoeG]

Hai there! I was wondering if nebody knew how to draw the triangular dotted shapes, etc. The pentagons and whatnot on word 2007? im stuck!

http://luckytoilet.wordpress.com/2010/06/30/investigations-about-star-polygons-inspired-by-someone-elses-math-homework/

Use this instead. I forgot what the other link is, but there should be a website that has all of the triangles you need, just look through the thread for it. The link I gave above generates the stars.

Edited December 12, 2010 by JoeGuff

[lulu]

How about using sigma?

For the star one I came up with the equation:

6n(n-1) +1

This works for all of the numbers but Im finding it hard to explain how I got it... it was sorta a lot of random thoughts in my head.

The difference between each of the terms is 12n.

The number 6 is the number of points so can be replaced with p (i think, havent tested but it makes sense)

For the basic triangle that is just (n/2)(2+(n-1))... thats simply from the equation in the textbook.

[ibnewbie2011]

So this is my first IB project and I have the stellar numbers one. I was just wondering if they care if we use one method for the triangular numbers but a different method for the stellar numbers. Or would they rather we use the same method throughout the whole project? Thanks in advance.

[geckofish52]

I am doing this problem in French.

What is the word for stellar in French?

[dessskris]

I am doing this problem in French.

What is the word for stellar in French?

Stellaire. Next time try google translate before asking.

[geckofish52]

I am doing this problem in French.

What is the word for stellar in French?

Stellaire. Next time try google translate before asking.

I wanted to hear from a French speaker who would know the correct term for the usage.

I suppose I can trust that's correct though.

[IzzyV]

Hey everyone!

The previous post have really help me to write my IA, but after handing in my 1st draft to my teacher he told me if I use the quadratic expression, I need to prove why the sequence is quadratic, and why I assume it, not only show that the second difference is the same.

Can anyone point me in the right direction, please.

Thanks in advance

Cheers,

[ebauer]

Alright, I have calculated all of the other functions in terms of n to find p and Sn. I also have found the relationship between p and Sn; that the stellar number is the coefficient and such. Now, how should I go about determining the general statement in terms of p and n for Sn. Is it essentially mushing the two functions for p and Sn together? Much help appreciated... thanks!!!

[JoeG]

Hey everyone!

The previous post have really help me to write my IA, but after handing in my 1st draft to my teacher he told me if I use the quadratic expression, I need to prove why the sequence is quadratic, and why I assume it, not only show that the second difference is the same.

Can anyone point me in the right direction, please.

Thanks in advance

Cheers,

I won't say much, but use systems of equations (with) matrices. I was able to do it that way.

[dessskris]

Alright, I have calculated all of the other functions in terms of n to find p and Sn. I also have found the relationship between p and Sn; that the stellar number is the coefficient and such. Now, how should I go about determining the general statement in terms of p and n for Sn. Is it essentially mushing the two functions for p and Sn together? Much help appreciated... thanks!!!

I am not doing this portfolio but I guess I could still help..

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.

Unfortunately I can't give you the answer. If you want to check with my answer, you could PM me giving your answer and I'd say yes or no well if you want to, that is..

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?

---

Hey everyone!

The previous post have really help me to write my IA, but after handing in my 1st draft to my teacher he told me if I use the quadratic expression, I need to prove why the sequence is quadratic, and why I assume it, not only show that the second difference is the same.

Can anyone point me in the right direction, please.

Thanks in advance

Cheers,

Well I don't know how much you should go into detail and how analytical your portfolio should be, but if I were to do this task, I'd explain step by step on how I get the formula of Sn instead of assuming it. But I thought SL tasks should be easier so you could just assume it? I don't know though..

I guess you could just explain how you get that quadratic equation? Or maybe you could draw it in Excel, right? Excel can give you the equation of the trendline so I think that might be enough? I don't know though..

From Mathematics HL IA criteria 2006, page 2

Criterion B: Communication

Achievement Level: 3

Descriptor: The student provides complete, coherent explanations or arguments, and communicates them clearly using appropriate forms of representation.

I hope it's the same for SL? I don't know.. You may want to check. If it's the same, you should go step by step on how you come up with the formula (I could explain it, if you want and if that criterion is the same with SL's). If it's not the same, maybe that Excel graph would be enough? The value of R² must be 1 and then it would be sure that it is the correct formula.

I don't know if it will do, though..

I hope it's quite helpful. Further questions are welcomed.