I have read some of the venn diagram e-mails recently. If we restrict the
sets to be represented by (perfect) circles only, it may happen that for
certain situations the circle-only venn diagram does not exist.
For 2 sets, the circle-version venn diagram always exists. First you draw 2
circles, with areas equal to the 2 given sets. Then you adjust the distance
(between the 2 origins) and soon or later the common area will be equal to
the proper intersection. And that's it.
For 3 sets, you can do the same thing pairwise. First you do 2 sets, say A a
nd B, as before.
Then you do A and C. Here C is along SOME direction on the plane. Adjust C
so that the common area between A, C is equal to the prpper intersection.
Finally, consider the set C',
and we do the same for B and C', and B and C' is along some direction on
the plane. In this construction, we let C and C' have same area, and B
intersection C' have the same area as
the intersection between B and C.
For the the 3-circle venn diagram to exist, we need C and C' coincide. This
means
distance(A,C)=distance(B,C'), and C=C'
There are only 2 points (at most) on the plane that satisfies the above
condition. But if
C exists, then the common part of A, B and C is fixed --- i.e., not free.
This means for certain
A, B and C (with all 8 areas pre-determined), the proper circle-based venn
diagram does not exist.
Min-Te Chao
----- Original Message -----
From: "Tom Johnson" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Saturday, August 18, 2001 2:26 AM
Subject: Re: Venn diagram program?
>
> > > Yes, I am using Powerpoint now. It's harder than it sounds, because
> > > one must calculate the radius' that give appropriately scaled circle
> > > areas; and one can only guess how close to move the circles to give
> > > the correct overlap area.
> > >
> >
>
> I use rectangular areas in Power Point. That make it easy to get
> the proportions you want. It of course does not help with the
> problem of observers incorrectly perceiving relative sizes.
> Therefore, if the relative size is important, I label the parts.
>
> TJ
>
> >
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>
> Tom Johnson
> [EMAIL PROTECTED]
> tel: (919) 515 4620
> fax: (919) 515 1824
> Box 8109
> 4336 Nelson Hall
> North Carolina State University
> Raleigh, NC 27695-8109
>
>
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