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General function in 2 variables

  1. Mar 26, 2012 #1
    1. The problem statement, all variables and given/known data
    I need to get a general function in 2 variables f(m,n).
    The task is to find a general function f(m,n) with these terms:
    The function has to be periodic.
    The function has to include those blue and red points in each example.
    The value of the function has to be f(m,n) =1 ONLY in blue points, and the value of the function has to be f(m,n)=0 ONLY in red points.

    The look of the function isn't important as long as it complies with previous terms.



    2. Relevant equations
    You can see a graphicon with charasteristic points:
    In the first example m=2 (m is period).
    attachment.php?attachmentid=45533&stc=1&d=1332771899.png
    In the next example m=3:
    attachment.php?attachmentid=45534&stc=1&d=1332771923.png
    For m=4:
    attachment.php?attachmentid=45535&stc=1&d=1332771923.png
    and so on.




    3. The attempt at a solution
    In first example (for m=2) I used functions: sin and absolute, but for all other m,
    it is not possible with only those functions, I also tried use the Fourier series but I dont have so
    much knowledge in mathematics to built a such function.
    Does somebody know how to do it?
     

    Attached Files:

    • m2.png
      m2.png
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    • m3.png
      m3.png
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    • m4.png
      m4.png
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    Last edited: Mar 26, 2012
  2. jcsd
  3. Mar 26, 2012 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    What have you done so far? You must show some work and exhibit some effort before receiving help in this Forum.

    RGV
     
  4. Mar 27, 2012 #3
    I tried and wrote about it above in previous post.
     
  5. Mar 27, 2012 #4

    Ray Vickson

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    Science Advisor
    Homework Helper

    Your previous post did not show any work; it just said you had tried some things, but did not show exactly what you did.

    RGV
     
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