wuzzy wrote:
>
> Is it possible to draw a venn diagram with more than 3 vars?
> I've tried and it seems impossible to me:
It cannot be done with equal circles; I'm not sure about circles of
mixed sizes. Ellipses can go to at least 4 (use 2 pairs of long skinny
ones in a "plaid") and possibly higher.
Convex sets work for an arbitrary number of variables. The standard
example, not due to me, works as follows.
Divide a circle into 2^n sectors, and add a "bump" to any subset
of these sectors so as not to destroy convexity. This may be
conveniently done by extending tangent lines from the corners of each
sector. Clearly any of the 2^(2^n) subsets of vertices may be so "pushed
out" [see attached gif]
Now starting with n superimposed circles, push out vertices 1,3,5,...
on circle 1; 1,2,5,6,... on circle 2; and so forth. On circle n, push
out exactly the ponts whose nth binary digit is 1. The final result
will be a Venn diagram.
There may be some result saying that a Venn diagram with the ratio of
the largest region to the smallest less than A cannot have more than
n(A) variables. Or (more likely) it's true but not yet proved. Research
project, anybody?
-Robert Dawson
.
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