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Math Stellar numbers IB portfolio

  1. Mar 8, 2010 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations



    3. 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.
     
  2. jcsd
  3. Mar 9, 2010 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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?
     
  4. Mar 10, 2010 #3
    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!
     
  5. Nov 10, 2010 #4
    hey listen i'm doing the same portfolio. how did u draw the star diagrams?
     
  6. Nov 19, 2010 #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. :/
     
  7. Feb 3, 2011 #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 !
     
  8. Feb 18, 2011 #7
    Last edited by a moderator: Apr 25, 2017
  9. Dec 19, 2011 #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.
     
  10. Dec 20, 2011 #9

    Mentallic

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    Homework Helper

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