Date: Sat, 3 Dec 2005 18:08:08 -0500 (EST)

From: baloglou@Oswego.EDU

To: ------------------------

Subject: Re: Question



Will you be mad at me if I tell you that it IS possible to get 16 regions?


[It IS possible, but, of course, the 16th region is the one that belongs

to none of the four sets, it's the 'outside'; so the trick is to get 15

'non-trivial' regions out of four 'eggs' intersecting each other -- which

can be done, except that I (for example) actually get 19 regions, 4 of

which are redundant (due to the fact that, in my example always, B, C,

B-cross-C, and C-cross-D are represented by two regions each)!]


...Yes, it takes some effort to achieve this, even for me, but it is

within reasonable limits of difficulty, and it requires no special

knowledge or background of any kind -- you may in fact assign this problem

to YOUR students a few years down the road! :-) Plus, you can always do

the problem without using any Venn diagrams, it might even be easier that

way :-))


GB



> For question one on the homework sheet.... Previously I was told that

> there are supposed to be 16 regions in a four circle venn diagram but

> everytime i draw it i can only come up with 13 so am I drawing it

> correctly if there are only 13 regions? Thanks!

>

> Shana

>

>




Postscript: Shana had a point -- it can be done with ellipses, yes, but not with circles!