Some R & R (Research and Recreation)

Other Stuff

Jim Hoffman and I played with symmetric Venn diagrams for awhile, trying to find one for N=11. ("Nonsimple" ones have recently been discovered by Peter Hamburger, et al.) (See the Symmetric Venn Diagrams page, part of the Venn Diagrams Survey maintained by Frank Ruskey, in the Electronic Journal of Combinatorics.) We didn't succeed, but had a lot of fun. A prettier version of my graphic ("ice cream cone curves") mentioned in the above page can be found HERE. A really ugly version (actually the same one) is HERE. And then there is THIS!

While we were playing around, we convexified a 7-symmetric Venn diagram using the Geometer's Sketchpad. (Click Here for a GSP file. A reasonable printout takes 6 pages. It needs to be pretty big to even begin to see what is going on because each of the 7 pieces is a convex polygon with 37 sides.) Not all 7-symmetric Venn diagrams can be convexified. For such an example, see Figure 5 in Branko Grunbaum's article, "Venn Diagrams II," Geombinatorics, 2, no. 2 (Oct. 1992), 25–32.