Venn diagram

Discussion in 'Scientific Statistics Math' started by Rod, Oct 9, 2011.

  1. Rod

    Rod Guest

    I want to draw a Venn diagram in which 3 'circles' overlap. The snag is I
    want the areas to be proportional to the numbers they represent.
    I guess at least one of the 'circles' will be an ellipse, but how to choose
    the relative position of the circles so the intersection areas are correct.
    I have found a JavaApp which draws such area-correct diagrams by using
    irregular pentagons, but the results are not pretty.

    Does anyone know of a solution or a website does it all?

    Not even sure that ellipse + 2 circles will always suffice. An ellipse does
    gives me an extra 2 degrees of freedom and I only need one. So I would use
    the other up by making the ellipse's eccentricity as small as possible.

    many thanks
     
    Rod, Oct 9, 2011
    #1
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  2. So 2 circles by themselves gives you 3 degrees of freedom (each radius
    independently, plus distance between them). Adding another circle would
    achieve only an additional 3 degrees of freedom (1 radius + 2
    distances), and 6 overall, where you need 7. If that last circle were an
    ellipse, you'd get 5 additional degrees (2 radii, 2 distances, and 1
    rotation) so ellipse + 2 circles should allow you to do what you want.

    The actual math is, off the top of my head, annoying. With pencil and
    paper, solving the case of two circles requires only one trigonometric
    integral; if you add an ellipse on top of that, you're probably going to
    get some nasty formulas to have to solve, possibly even an elliptic
    integral.
     
    Joshua Cranmer, Oct 9, 2011
    #2
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  3. Venn diagrams represent sets, not numbers. There is no significance to
    the areas of the overlapping sections.

    --
    Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

    Unsolicited bulk E-mail subject to legal action. I reserve the
    right to publicly post or ridicule any abusive E-mail. Reply to
    domain Patriot dot net user shmuel+news to contact me. Do not
    reply to
     
    Shmuel (Seymour J.) Metz, Oct 9, 2011
    #3
  4. Rod

    Rod Guest



    OK, my graphical representation which are similar to Euler diagrams.
    happy
     
    Rod, Oct 10, 2011
    #4
  5. Rod

    Art Kendall Guest

    when I Googled "software euler diagrams" I obtained many hits.

    I only glanced at a few. From a perception approach. It seems that these
    would have the same problem that pie charts do. People in general are
    not good at comparing areas. People do best at comparing horizontal
    distances with a common reference. IMHO This is due to our eyes being
    separated horizontally.

    Can you think of a way to have the comparisons be of horizontal lines
    with a common reference line?

    There was a very interesting example in a recent AMSTAT NEWS (September
    2011, #411, pp. 28 - 30 that showed sets of horizontal bar charts but
    there was a reference line part way across. (I would find it easier to
    read if there were a more vertical separation between the sets of values
    of the IV's. YMMV)


    Art Kendall
    Social Research Consultants
     
    Art Kendall, Oct 10, 2011
    #5
  6. Rod

    Rod Guest

    I didn't know that. I shall keep that in mind, thanks.
     
    Rod, Oct 10, 2011
    #6
  7. Rod

    Art Kendall Guest

    You're welcome.

    Art

     
    Art Kendall, Oct 10, 2011
    #7
  8. Rod

    JEmebius Guest


    VENN DIAGRAMS FOR FINITE SETS - AREAS PROPORTIONAL TO NUMBERS OF ELEMENTS

    Such Venn diagrams are possible, at least for unions and intersections of two through six sets.
    Just use a square or a hexagonal grid to represent the elements. Take care that the elements of the
    diverse intersection sets are represented by adjacent points in the grid.

    Consider for instance three finite sets: A, B, C and their unions and intersections.
    Start with drawing G = A i B i C, the intersection of A, B and C. Then add the elements which extend
    G to D = A i B, E = B i C, F = C i A. Next, add the remaining elements of A, B, C which are not in
    any of the other two sets. Finally, draw boundary lines in-between the points representing the sets
    A through G. Done! Forget exact circles and ellipses.

    Disclaimer: I did not yet try this.

    Maybe the almost-periodic quasi-crystalline tenfold-symmetric Penrose grid will be helpful in
    diagramming seven through ten sets; am too lazy to try this right now.

    Good luck: Johan E. Mebius
     
    JEmebius, Oct 10, 2011
    #8
  9. Rod

    Matt Guest


    I detect an extraordinary level of creativity in you.
     
    Matt, Oct 23, 2011
    #9
  10. Rod

    porky_pig_jr Guest

    Well, the fact is that Venn diagrams are commonly used to look at the
    unions and intersections of several sets so to make some statement
    about them. Are you trying to be ironical with that "I detect an
    extraordinary level of creativity in you" crap? Well, you at yourself
    first and you idea to use Venn diagrams to represent numbers first.

    PPJ.
     
    porky_pig_jr, Oct 23, 2011
    #10
  11. Why thank you. My comment, however, didn't require any creativity,
    just an understanding of what a Venn diagram is and the ability to
    distinguish between "Euler" and "Venn".

    --
    Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

    Unsolicited bulk E-mail subject to legal action. I reserve the
    right to publicly post or ridicule any abusive E-mail. Reply to
    domain Patriot dot net user shmuel+news to contact me. Do not
    reply to
     
    Shmuel (Seymour J.) Metz, Oct 24, 2011
    #11
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