# Venn diagram

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

1. ### RodGuest

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

2. ### Joshua CranmerGuest

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

3. ### Shmuel (Seymour J.) MetzGuest

Venn diagrams represent sets, not numbers. There is no significance to
the areas of the overlapping sections.

--
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Shmuel (Seymour J.) Metz, Oct 9, 2011
4. ### RodGuest

OK, my graphical representation which are similar to Euler diagrams.
happy

Rod, Oct 10, 2011
5. ### Art KendallGuest

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
6. ### RodGuest

I didn't know that. I shall keep that in mind, thanks.

Rod, Oct 10, 2011
7. ### Art KendallGuest

You're welcome.

Art

Art Kendall, Oct 10, 2011
8. ### JEmebiusGuest

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
9. ### MattGuest

I detect an extraordinary level of creativity in you.

Matt, Oct 23, 2011
10. ### porky_pig_jrGuest

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
11. ### Shmuel (Seymour J.) MetzGuest

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>

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