Math Stellar numbers IB portfolio

[ihumayun]

Homework Statement

Its a series of triangles, the data table being
n-#
1-1
2-3
3-6
4-10
5-15

I need a general equation in terms of n.

Homework Equations

The Attempt at a Solution

I can't really find anything. The solution has to be non-recursive, and i can find a bunch of patterns, but all of them rely on the term before and after.
AAAAAAAAAAAAAAAAAH.

 

[HallsofIvy]

your numbers are 1, 3= 1+ 2, 6= 1+ 2+ 3, 10= 1+ 2+ 3+ 4+ 5, etc.

In particular, the "nth" number is $F(n)= 1+ 2+ 3+ \cdot\cdot\cdot+ (n-2)+ (n-1)+ n$

To get a "closed form" formula for that note that F(n) is also given by
$F(n)= n+ (n-1)+ (n-2)+ \cdot\cdot\cdot+ 3+ 2+ 1$

Write those together:
$F(n)= 1+ 2+ 3+ \cdot\cdot\cdot+ (n-2)+ (n-1)+ n$
$F(n)= n+ (n-1)+(n-2)+ \cdot\cdot\cdot+ 3+ 2+ 1$

Do you see that if you add those together, each vertical sum is n+1? And that you have n such sums?

 

[ihumayun]

Ohhhhhohoh.
n(n+1)/2. I get it now. Thank you for your help! I also realized this could be derived by looking at the triangles as half a square, and since the number of dots in a square in n^2, The number in a triangle is (n^2)/2, + n/2 to account for the dots that are cut in half when the square is halved.

Thanks again!

 

[IB2011]

hey listen I'm doing the same portfolio. how did u draw the star diagrams?

 

[Lilkidgohome]

@IB2011 It's tedious work--however if you're willing to put forth the effort, Microsoft Word 2003/2007 will get the job done. Simply click on the "Insert" tab and then click on "Shapes". It took me about two hours to create those meddlesome stars. :/

 

[despneedshelp]

Hey does anyone know the scope and limitations of the general statement?..I don't really get how to explain it . would really appreciate the help !

 

[sethammons]

Re: How to draw stellar numbers:
While GeoGebra or any graphics program can help you to draw them, it helps to know HOW to draw them. Here is a video guide: http://www.youtube.com/watch?v=1S2B9weD3Yw"

 

[Darwin Monkey]

@ seth
GeoGebra is a great program to make these figures, mind you it will take a while to create them but they will turn out very nicely.
p.s. The rotate tool is extremely useful.

 

[Mentallic]

@ seth
GeoGebra is a great program to make these figures, mind you it will take a while to create them but they will turn out very nicely.
p.s. The rotate tool is extremely useful.

You're replying to a person that posted nearly a year ago. He's long gone.