IA Type I -- Stellar Number

[CelticPride]

guys how did u get to the general statement in the 1st set of triangles? i dont get it

You know if your not lazy and actually read through the thread, you can find great help for the IA?

Hey, my only problem is the proving my general statement part. How do I prove it? Just show how I got it and just apply my general statement on different stellar numbers?? Or is there a better way to prove it?

[JoeG]

guys how did u get to the general statement in the 1st set of triangles? i dont get it

You know if your not lazy and actually read through the thread, you can find great help for the IA?

Hey, my only problem is the proving my general statement part. How do I prove it? Just show how I got it and just apply my general statement on different stellar numbers?? Or is there a better way to prove it?

Remember that stellar numbers are geometric figures (in other words use pictures), then do the math out in your formula to prove that it works. Your teacher/external moderator may be super-sarcastic that day and say and say 42? 42 what? FAIL!! So just make sure to add a sentence or two explanation with your work.

Good luck. As always, ask someone else to make sure what I'm saying isn't absolutely crazy lol.

[CelticPride]

guys how did u get to the general statement in the 1st set of triangles? i dont get it

You know if your not lazy and actually read through the thread, you can find great help for the IA?

Hey, my only problem is the proving my general statement part. How do I prove it? Just show how I got it and just apply my general statement on different stellar numbers?? Or is there a better way to prove it?

Remember that stellar numbers are geometric figures (in other words use pictures), then do the math out in your formula to prove that it works. Your teacher/external moderator may be super-sarcastic that day and say and say 42? 42 what? FAIL!! So just make sure to add a sentence or two explanation with your work.

Good luck. As always, ask someone else to make sure what I'm saying isn't absolutely crazy lol.

haha that part made me laugh. Thanks for the help. appreciate it.

[IB senior girl 99]

Hi, i am currently in IB math SL and am rather confused about how to start the stella numbers portfolio. i have the formula for the 6-stellar number at stage s^7, and a general statement. I just don't understand how to incorporate graphs, how to test the valididty, or discuss the scope of limitations ect.

Any help would be GREATLY apppreciated.

thank you

[chuck1norris1]

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

What, my equation worked for when p=3

[JoeG]

Hi, i am currently in IB math SL and am rather confused about how to start the stella numbers portfolio. i have the formula for the 6-stellar number at stage s^7, and a general statement. I just don't understand how to incorporate graphs, how to test the valididty, or discuss the scope of limitations ect.

Any help would be GREATLY apppreciated.

thank you

There's already another thread for this on the board, it should answer most of the questions you have, just hunt for them in there.

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

This program is really great, I actually used it in mine. It should give you a pictures for a whole bunch of p-stellar numbers at stage Sn lol.

For discussing scope and limitations, is BASICALLY a domain range issue, mixed in with some logic. For example, you can't have a negative number of points, or 0.3333 points, can you ? To test the validity, remember that the formula represents the number of dots in a GEOMETRIC figure, so try to incorporate pictures. You can always do more than I say, and I actually recommend that.

[freakingnameless]

I'm sorry to go OT now, I am just wondering what programme you are planning to use when typing up the task? My maths teacher are suggesting excel but there most be a more suitable programme for stellar numbers?

[JoeG]

You can use any program you want to type it up.

I found incorporating the charts from Excel ----> Word was painful, so I just made all of my charts in Word lol.

You can also just copy/paste pictures from the programs used to generate stellar numbers into Word.

If you want the programs, look around this tread, they're mentioned alot.

Good luck.

[WillDance4Marks]

Hi! im soo glad i found this website. Im completely stuck with the second part. All i know is that it increases by the next multiple of 12 but i dont know how to put that into a general statement and i hav no idea how to even put the number of vertices into the statement. Can someone please help? Thanks.

Edited November 19, 2010 by Mahuta ♥
No text speak please. :)

[firedemon777]

What methods are there to prove the general statement? I can't figure out how to do it because there are two variables. Also, is there a method to derive the general statement without using finite differences?

[IBjunior2012]

Hi, i am currently in IB math SL and am rather confused about how to start the stella numbers portfolio. i have the formula for the 6-stellar number at stage s^7, and a general statement. I just don't understand how to incorporate graphs, how to test the valididty, or discuss the scope of limitations ect.

Any help would be GREATLY apppreciated.

thank you

There's already another thread for this on the board, it should answer most of the questions you have, just hunt for them in there.

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

This program is really great, I actually used it in mine. It should give you a pictures for a whole bunch of p-stellar numbers at stage Sn lol.

For discussing scope and limitations, is BASICALLY a domain range issue, mixed in with some logic. For example, you can't have a negative number of points, or 0.3333 points, can you ? To test the validity, remember that the formula represents the number of dots in a GEOMETRIC figure, so try to incorporate pictures. You can always do more than I say, and I actually recommend that.

what does it mean by "describe the scope"? I am so close to being finished completely but im stuck as this second to last section. any help?

[Ray]

I used calculus.

Derivatives and then integration to find the general statement. It lays out so nicely. The only problem comes when I try to prove the general statement in terms of p and n. I feel that it is too shaky. But that is what I did.

Hey!

How did you use calculus??

Could you give me a unrelated example?

Like only the method? I'm curious..

Thanks in advance

To use calculus in this, the concept is that the second finite difference, from your sequence/series is your second derivative. then integrate the difference twice (becasue is quandratic) to find your expression.

[Amelia Lloyd-Pratt]

What kind of things would you include in the introduction for the Stellar Numbers portfolio piece??

[IB senior girl 99]

Hi, i am currently in IB math SL and am rather confused about how to start the stella numbers portfolio. i have the formula for the 6-stellar number at stage s^7, and a general statement. I just don't understand how to incorporate graphs, how to test the valididty, or discuss the scope of limitations ect.

Any help would be GREATLY apppreciated.

thank you

There's already another thread for this on the board, it should answer most of the questions you have, just hunt for them in there.

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

This program is really great, I actually used it in mine. It should give you a pictures for a whole bunch of p-stellar numbers at stage Sn lol.

For discussing scope and limitations, is BASICALLY a domain range issue, mixed in with some logic. For example, you can't have a negative number of points, or 0.3333 points, can you ? To test the validity, remember that the formula represents the number of dots in a GEOMETRIC figure, so try to incorporate pictures. You can always do more than I say, and I actually recommend that.

what does it mean by "describe the scope"? I am so close to being finished completely but im stuck as this second to last section. any help?

Describe the scope means simply, talk about what values the general stement works for. If you found any values which it doesnt work for, list them. It does not work for negative values, so start with that. for example "the general statement [ ] is valid for all positive values geater than zero, but not negative values

Hi! i just wanted to tell everyone who posted things on here thank you so much, it was all very helpful. Now my masterpiece of a portfolio is done! good luck to those of you who are still working on yours, and i hope you all have a great thanksgiving

[Becky*]

What does it mean when it says, "Discuss the scope or limitations of the general statement"?

Talk about why having negative numbers won't work and also decimals. They are physically impossible in a sequence that makes up a star hence you could not explore them in your investigation. As you are asking about scope and limitation, have you sorted out the quadratic formula? All I have is a recursive formula and I don't really know how to work out the quadratic one that works for all of the stellar numbers of p-vertices. Help please x

In desperate need of help with all this. I can't seem to find a quadratice formula. I have the recursive one but I can't seem to find a way to the overall quadratic resolution. Can anyone point me in the right direction? x

[zeuble]

What does it mean when it says, "Discuss the scope or limitations of the general statement"?

Talk about why having negative numbers won't work and also decimals. They are physically impossible in a sequence that makes up a star hence you could not explore them in your investigation. As you are asking about scope and limitation, have you sorted out the quadratic formula? All I have is a recursive formula and I don't really know how to work out the quadratic one that works for all of the stellar numbers of p-vertices. Help please x

In desperate need of help with all this. I can't seem to find a quadratice formula. I have the recursive one but I can't seem to find a way to the overall quadratic resolution. Can anyone point me in the right direction? x

Hey! I used two different methods,

One- finding the recursive formula through quadratic which was easy

Two- finding the quadratic through recursive which is your problem. I recommend that unless you are really strong in maths (I mean HL standard) you do not do it manually but instead use "technology" like I used. I used wolfram alpha which I recommend

Type in: f(n)=f(n-1)+ {WHATEVER YOUR FACTOR IS}, f(1)=1, f(2)=13, f(3)=37, f(4)=73

and it will give you your answer! You will earn marks for technology while fulfiling your method. I hope it works!

Good luck!

[strawberrycheesecake]

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..):

[Gee94]

Does anyone know where I can get some 10-Stellar shapes and 12-stellar shapes online, so that i don't have to draw them out?

[JoeG]

Does anyone know where I can get some 10-Stellar shapes and 12-stellar shapes online, so that i don't have to draw them out?

There are two excellent links that are mentioned many times in this thread. One of them is http://luckytoilet.wordpress.com/2010/06/30/investigations-about-star-polygons-inspired-by-someone-elses-math-homework/

The download link should be near the bottom.

I don't remember the other one, but I know it has been mentioned before.

Good luck.

[Guest ramonimacaroni]

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

this helped me figure out my paper a LOT (i'm mathematically challenged haha). thanks so much!!