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When we draw a Venn diagram, we use circle to represent a Set. We can use any closed plane figure but most of the time it is a circle. Why? are there any specialty about that?

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Tradition? I've also seen boxes (i.e. squares) used, BTW. And I draw more oval-like shapes. So I wouldn't even agree it's always a circle.... –  Henno Brandsma Jun 27 at 16:59
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Note the circle itself is a set of points in the plane, so you are using a set to represent a set. Prof JF Adams made the point in one of my very first undergraduate lectures, and I've remembered it ever since - "grown up" maths was going to be very different from what went before. –  Mark Bennet Jun 27 at 17:06
    
I don't like to draw things very much, but I often prefer to use squares. –  Asaf Karagila Jun 27 at 17:49

2 Answers 2

up vote 9 down vote accepted

Circles are easy to draw and conceptually very nice. There is no requirement for anything other than a circle for Venn diagrams with $n \le 3$ classes. Also, the boundaries of two circles intersect each other at not more than two places, which is an important aspect that has connections to some deeper results in mathematics, such as the Jordan Curve Theorem.

However, when you get to $n \ge 4$, you can no longer draw (symmetric) Venn diagrams with circles. $n=4$ requires ellipses, and for prime $n \ge 5$, the shapes get more and more complicated!

If you'd like to read more, this answer covers more details.

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Look at this noncircle Venn Diagram:

Venn Diagram

Source : http://www.learnnc.org/lp/media/authors/walbert/venn/venn-edwards-food.png

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Obviously wrong. Jello salad is listed in the "foods" category. –  Arkamis Jun 27 at 17:08
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YUP! That's a good counter-example, therefore this is NOT a Venn Diagram. Caught me! –  Squirtle Jun 27 at 17:09
    
lowfat yogurt is in the "LOW FAT" category. How surprising. Also reminds me of the seinfeld episode with the low fat yogurt :) –  Cruncher Jun 27 at 20:52

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