IA Type I -- Stellar Number

[Ambition]

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:

that is so bloody awesome

[Buttersbee]

Hi, I'm doing the maths portfolio on stellar numbers and whilst I'm not stuck on the maths side of things I am stuck on what it is asking me to do.

'Consider stellar (star) shapes with p vertices, leading to p-stellar numbers. The first four representations for a star with six vertices are shown in the four stages S1 – S4 below. The 6 stellar number at each stage is the total number of dots in the diagram.'

Find an expression for the 6-stellar number at stage S7 .

Find a general statement for the 6-stellar number at stage Sn in terms of n.

Now repeat the steps above for other values of p.

Hence, produce the general statement, in terms of p and n, that generates the sequence of p-stellar numbers for any value of p at stage Sn .

I have already made a general statement for the stellar numbers, but what does it mean find an expression a stage S7? By expression does it mean answer? Otherwise why would the question about the general statement be below the question about finding an expression?

Also when it askes me to repeat the steps for values of p does it mean the vertices? And I don't entirely understand what it means when it says p-stellar numbers.

[theloserwins]

It's interesting that i didn't find "Find an expression for the 6-stellar number at stage S7 ." in my IA.

Maybe I made a mistake.

Incase you don't know what stage 7 means...

Stage number equals to n.

Therefore...

S(1) = Stage 1

S(2) = Stage 2

S(7) = Stage 7

I don't know what exactly they are looking for in the Stage 7 expression, so I cannot answer you.

p-stellar numbers... The one you are working with in the earlier part

Has 6 vertices = 6-stellar = p is 6

You should go to This post, coz it's very helpful.

For your convenience, there are also two useful links.

Stellar Number Images

A Useful Tool and Guide in Creating Your Own Stellar Shape

Edited August 20, 2010 by theloserwins

[Buttersbee]

Ah Ok. Thanks. But I'm still not sure as to what it means for 'find an expression for the 6-stellar number at stage 7'. Surely I'm doing something similar to that in the step below when I find the general statement. So why ask me to find an expression for the stage 7 expression first?

[theloserwins]

I'm guessing that they want you to deduce the pattern before coming up with the general statement?

Ie.

S(1) + 12 = S(2)

S(2) + 12 = S(3) and so on...

[maomomi]

Hey everyone.

I've done my general statement.

I am just asking, what defines a stellar number?

My teacher say that you have a 4-star number? How about 3(which would look like a triangle)?

This would greatly help in my limitation, because I dont know which values don't work. Obviously, (sn) increases infinitely as p increases...

Also, when it asks me to "test the validity of the general statement", what do I do?

[selma van burren]

hey guys I was finding all ways for an answer in this question but what is most confusing is finding d.. If there is d than it is easy to discover the answer... any help

Hi, I'm doing the maths portfolio on stellar numbers and whilst I'm not stuck on the maths side of things I am stuck on what it is asking me to do.

'Consider stellar (star) shapes with p vertices, leading to p-stellar numbers. The first four representations for a star with six vertices are shown in the four stages S1 – S4 below. The 6 stellar number at each stage is the total number of dots in the diagram.'

Find an expression for the 6-stellar number at stage S7 .

Find a general statement for the 6-stellar number at stage Sn in terms of n.

Now repeat the steps above for other values of p.

Hence, produce the general statement, in terms of p and n, that generates the sequence of p-stellar numbers for any value of p at stage Sn .

I have already made a general statement for the stellar numbers, but what does it mean find an expression a stage S7? By expression does it mean answer? Otherwise why would the question about the general statement be below the question about finding an expression?

Also when it askes me to repeat the steps for values of p does it mean the vertices? And I don't entirely understand what it means when it says p-stellar numbers.

[Th-3n]

how to draw 7-stellar on the labtop? which technology can we use?

[Th-3n]

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:

could u teel me where can we find this picture on the internet?

Thanks.

[xlaugh16]

Hey, I got this assignment today, the stellar numbers one. I have been sitting at my desk for literally 3 hours and am completely stuck! The first one.. with the triangles.. like how do you go about getting a formula for it?

I started with trying out random formulas to get the first number and once I got it to work for that would attempt to use it on the other points we got. However, I am failing miserably at it. I got one formula that gets the answer you need, but if you were further down the road when n=100 for example I wouldn't be able to get u_n.

I understand that you can't give me the answer, but I read through the pages and am not getting the explanations, so any help would really be appreciated! We have until Friday midnight Western Europe time to finish it!

[Buttersbee]

The thing that I am having trouble with is finding the scope and limitations. I have done all the rest. Can anyone tell me how I can go about in solving scope and limitations?

[Rebel]

due tomorrow... how long is this Ia should be?

[AdamV]

Okay - I'm doing this paper (Amen that I found this page because I am LOST)

Loads of you guys keep saying they managed to find the triangular equation. Well I'm so lame - I've been on this for two hours now and I'm just stuck.

I managed to find an equation;

nx = n(x-1) + x

But that only works if you know the previous term of the series. So I wrote all down and explained how it wasn't valid and said I would research the internet; and all I'm finding online is ...

Tn = (n + 1)

2

I don't know what that means. What's T? What's n? And why isn't there a dividing line between the n+1 and the 2?

Thx

[Naiya]

hi everyone,

i think this is kind of a stupid question

bt what does it mean when they say "find the expresseion for 6-stellar number at stage 7"

i found the general statement for 6-stellar number which is a quadratic equation....so it is telling to write the number of dots at 7th stage..like 1st stage the number of dot is 1, 2nd it is 13,......so in 7th it will be....(i know the number of dots bt since we are not allowed to give direct answer). or is it telling to subtitute n as 7 in the general statement found for 6 stellar number and leave it???

[mjn46]

Okay - I'm doing this paper (Amen that I found this page because I am LOST)

Loads of you guys keep saying they managed to find the triangular equation. Well I'm so lame - I've been on this for two hours now and I'm just stuck.

I managed to find an equation;

nx = n(x-1) + x

But that only works if you know the previous term of the series. So I wrote all down and explained how it wasn't valid and said I would research the internet; and all I'm finding online is ...

Tn = (n + 1)

2

I don't know what that means. What's T? What's n? And why isn't there a dividing line between the n+1 and the 2?

Thx

well,

since the second difference of the sequence is 1 and you know the rule is, if if the second difference is 2 then the equation starts with n², the triangular number sequence will obviously be n²/2,

for simplicity, multiply your triangular number sequence times two, and it will now be (2, 6, 12, 20...etc) and start of from there. your general statement must start with

n². Because it is a quadratic sequence, the formula should look sort of like this:

an²+bn+c. to find b and c try making it an equation, meaning try a value of n, say 3.

3²+(space) = 12

12-9= 3

and if you try it with different values of n, you will realize there is a pattern.

did it make any sense?

[Chloe Nicole :)]

im stuck with finding an expression for the 6-stellar number at stage S7 .

and finding a general statement for the 6-stellar number at stage Sn in terms of n.

Any help pleeeaseee would be great

[onejpu2]

I'm confused on the difference between "Find an expression for the 6-stellar number at stage S7" and "Find a general statement for the 6-stellar number at stage Sn in terms of n" Aren't they the same? Do they want you to find S7 using the general statement? Any help is much appreciated...

[LaFin]

The formula of biggest star is 12n+1 and the sum's equation is Σn.12 +1 (sigma is the symbol of addition)

Try these equation and you will find out that they're correct.

Edited September 12, 2010 by LaFin

[Awesome Sauce]

what would be a good way of "testing the validity of the general statement"? i'm referring now to the final statement in terms of p and n.

and what would be an effective way of explaining "how you arrived at the general statement"? would it be enough to just say that you got pretty much the same general statement for other p-stellar number sequences?

my IA is due in 2 days. please reply soon!!

[LaFin]

Both of the sequences have a common side which is n

you can also use kn+p as a kind of formula. About genereal statement you just need to say that i count the points in the sequences and it has a formula "kn+p".