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Thread: Venn Diagram

  1. Jun 11th, 2003, 05:13 PM #1
    bugzpodder
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    Venn Diagram

    using circles, can you draw a Venn Diagram of order 4?
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  2. Jun 11th, 2003, 06:35 PM #2
    Guv
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    I do not think so. Combinations(4, 2) = 6, which looks like a problem. If it can be done, the diagram is not likely to be symmetric like the order 3 diagram.
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  3. Jun 12th, 2003, 05:20 AM #3
    sql_lall
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    Talking No

    No, i'm pretty sure u can't
    Consider the normal 3-circle thing. now, look at only the union parts (A&B, A&C, B&C, A&B&C). You get some flower-thing, with three petals.
    Consider two of the petals (A&B, and A&C). If D completely covered one of them, then there would be no (A&B&!C&!D) or (A&C&!B&!D) part left.
    => some parts of these two petals must not be within D, some also must be.
    However, this means that both:
    a) D covers some of B&C which A doesn't
    b) D must have a smaller radius than A

    combining the two, you get that there is no section of D that is by itself. (I think)

    => impossible

    Also, # of sections actually = 2^4=16, with each circle in 8 sections
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  4. Jun 12th, 2003, 06:45 AM #4
    twanvl
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    A venn diagram with four circles is imposible in 2D, but it can be done in 3D.

    Hypothesis: max possible venn diagram size = dimension+1
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  6. Jun 12th, 2003, 07:13 AM #5
    bugzpodder
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    interesting hypothesis...
    Massey RuleZ! ^-^__Cheers!__^-^ Massey RuleZ!


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    The probability that a random rational number has an even denominator is 1/3 (Salamin and Gosper 1972)? This result is independently verified by me (2002)!
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