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Type I -- Stellar Number

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What does it mean by 'Discuss the scope of limitations of the general satement' does anyone know what they want us to do?

Thanks

Anyone, PLEASE!!

Edited by Charlie93

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well all you need to do is to state what are the limitations to the statement you have created. think about whether is always works or maybe there is a case when it doesn't. try thinking on the constants in the general statement. like what numbers they can be. I don't know how else am i allowed to help you...

Edited by Aboo
No text speak! - Aboo

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I got a question: What defines a shape as being stellar? Does it have to have a certain number of vertices or something? If someone could provide a site where I can read more about this, I'd be very appreciative :P

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anyone.. please help how to find the general statement of the triangular...

Look at the first couple of pages. There you can find some really good information on a method called 'finite differences' that will allow you to reach the expression. Good luck :P

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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.

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Hmm. OK - thank you. I think I've explained the second degree polynomial bit.

Do you have any idea how to justify it geometrically, though?

EDIT: Never mind, I've found the geometrical justification.

However, whole new ball game. I think this has been asked before, but what constitutes a star? Because S1 when n=1 is always equal to 1; in that case, should it work when p=1 or p=2 - is this solitary dot supposed to be counted as a "stellar shape"?

Edited by Schrödinger's Cat

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I forgot what the n and p were again, but I wouldn't count a dot as a star. I wouldn't count three or four dots as a star either, but I don't know if that's right. I would just write up a justification with the limitations as how I perceive them and hope they buy it haha

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I'm curious. How exactly do you prove THE general statement? I know this isn't part of the portfolio and I have already tested other values of p to verify the general statement and that'll provide me with all the marks I need for this portfolio. But I'm just wondering if there's a way to actually prove it.

I googled mathematical induction and I understand how it applies to things like proving a formula for the summation of numbers from 0 to n. However, I am uncertain how I may be able to apply it into proving the general statement for all values of p.

Many thanks to whoever is able to help my curious mind. (:

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See, what I did was, I looked at how the shapes were formed geometrically, and created a formula in terms of p and n as to how I could get the number of dots making up the outer shell star. Then I saw that it was related, in sequence, to the next layer (n-1) and expressed it in terms of a sequence. I worked from there, simplifying it to get the general expression.

Do you know what I mean? :no:

Also - isn't justifying it a big part of the portfolio? It is for our class at least...

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the equation pn2+pn+1 works for every number, except 1,2,3 because only by 3 dots you can not draw a stellar, that was the only limitation ı could find.

ıf there is someone who got the g-force tolerance portfolio and have an idea, please give me a simple information about that portfolio, because ı am quiet confused.thanks

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Hey guys, I'm new here. I'm doing the Math Port for Stellar Numbers, and I know all the equations and answers already. What I was wondering is whether anybody knows any programs that can be used to re-create the diagrams used in the question. I was going to use that for my proofs.

Thanks in advance.

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Please check this topic - http://www.ibsurvival.com/topic/8208-math-portfolio-stellar-numbers/ ; at one point, one of the members posts a link to a website on which you can find most - if not all - of the diagrams needed for the maths portfolio. In the topic you may also find a program with which you can draw the diagrams, and someone I think actually posted some images they used in their portfolio.

Hope that helps. Good luck!

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[i assumed c = 0 because of what you had done earlier, but you'd need to plug in n=3 or any other number to find c].

Hey, I don't understand why you assume c=0?

If I don't assume that, then I get 0.5n^2 - 0.5n +1 = Sn but that doesn't seem to be correct when I sub in values.

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Here's a blog post with a downloadable program at the bottom that lets you automatically create all sorts of stars for this project (if it ever gets assigned again):

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

Screenshot:

oIdBd.gif

HELLO! :) sorry to bother but i cant copy and paste the produced image from the java program. any ideas? >< thanks!!!

edit. ohhh have to take a screen shot and crop it.... thanks for the super useful program btw :o

Edited by winston

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