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Math Stellar numbers IB portfolio

  • Thread starter ihumayun
  • Start date
  • #1
12
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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 cant 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.
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,833
955
your numbers are 1, 3= 1+ 2, 6= 1+ 2+ 3, 10= 1+ 2+ 3+ 4+ 5, etc.

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

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

Write those together:
[itex]F(n)= 1+ 2+ 3+ \cdot\cdot\cdot+ (n-2)+ (n-1)+ n[/itex]
[itex]F(n)= n+ (n-1)+(n-2)+ \cdot\cdot\cdot+ 3+ 2+ 1[/itex]

Do you see that if you add those together, each vertical sum is n+1? And that you have n such sums?
 
  • #3
12
0
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!
 
  • #4
1
0
hey listen i'm doing the same portfolio. how did u draw the star diagrams?
 
  • #5
@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. :/
 
  • #6
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 !
 
  • #7
Last edited by a moderator:
  • #8
@ 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.
 
  • #9
Mentallic
Homework Helper
3,798
94
@ 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.
 

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