The Search for Simple Symmetric Venn Diagrams

Abstract:

• Appears in Notices of the American Mathematical Society, December 2006, pages 1304-1311.
• Here is a link to the article on the AMS site.
• The cover (pdf)
• About the cover (pdf)
• ERROR: The is a problem with the way that Figure 5 is drawn. The final result is a Venn diagram with the required properties, but the curve colouring is inconsistent with the bit patterns. In Figure 5b on the rightmost inner circle, the colors should be red-black-gold top-to-bottom (instead of gold-red-black as they are now). Then this color change needs to be carried out consistently in Figures 5c, 5d and 6b. Below are the corrected figures:
  • Figure 5b.
  • Figure 5c.
  • Figure 5d.
  • Figure 6b.
• In case you have trouble downloading the article from the AMS site: fea-wagon.pdf.
• For more on Venn diagrams, check out the Survey of Venn Diagrams, Dynamic Survey #5 at the Electronic Journal of Combinatorics.
• Selected citations:
  • Stan Wagon and Peter Webb, Venn symmetry and prime numbers: a seductive proof revisited, American Mathematical Monthly, Vol. 115, No. 7 (Aug. - Sep., 2008), pp. 645-648.
  • Patricia Hersh and Anne Schilling, Symmetric chain decomposition for cyclic quotients of Boolean algebras and relation to cyclic crystals, International Mathematics Research Notices (IMRN), Volume 2013, Issue 2, pp. 463-473.
  • Timothy T. Eaton, Science-based decision-making on complex issues: Marcellus shale gas hydrofracking and New York City water supply, Science of The Total Environment, Volumes 461-462, 1 September 2013, Pages 158-169.
  • Parmar, V., Di Rocco, D., Sopouch, M., and Albertini, P., Multi-Physics Simulation Model for Noise and Vibration Effects in Hybrid Vehicle Powertrain, SAE Technical Paper 2014-01-2093, 2014, doi:10.4271/2014-01-2093.