Proposal: Symmetry of Crop Circles

Topic:

I wish to explore the symmetry of crop circles by employing the accepted classification scheme for planar symmetry groups. Recognizing that all crop circle designs are planar and ‘revolve’ around a center, point group and, to a lesser extent, wallpaper group symmetry will most likely be involved.

Throughout this study, I wish to delve deeper into rotational and reflectional Euclidean plane isometry theory and explore the ways planar symmetry is classified. In doing so, I hope to gain a better understanding of the ‘language’ of symmetry and perhaps attempt to use this language to decipher some meaning from the crop circle phenomenon.


References:

Web-sites on symmetry classification:

• http://en.wikipedia.org/wiki/Euclidean_plane_isometry
• http://en.wikipedia.org/wiki/Reflection_symmetry
• http://en.wikipedia.org/wiki/Rotational_symmetry
• http://en.wikipedia.org/wiki/Symmetry_group
• http://en.wikipedia.org/wiki/Point_group
• http://en.wikipedia.org/wiki/Cyclic_group
• http://en.wikipedia.org/wiki/Dihedral_group
• http://en.wikipedia.org/wiki/Wallpaper_group
• Derivation and Classification of Groups: http://www.xahlee.org/Wallpaper_dir/c4_Derivation.html

• Tables and illustrations of the 17 wallpaper groups: http://www.xahlee.org/Wallpaper_dir/c5_17WallpaperGroups.html

• http://en.wikipedia.org/wiki/Orbifold_notation
• Field Guide to Orbifolds: http://www.geom.uiuc.edu/docs/doyle/mpls/handouts/node39.html

• http://en.wikipedia.org/wiki/List_of_planar_symmetry_groups
  

Potential books:

• Alexander, S. Crop Circles: Signs, Wonders and Mysteries. Chartwell Books, 2006.
• ISBN: 0785820698
• Burn, R. P. Groups, a path to geometry. New York: Oxford University Press, 1985.
• ISBN: 0521300371
• Location: Daley Library - Math Collection/2d floor south - Books
• Call Number: QA171 .B93 1985
• Butler, Philip H. Point group symmetry applications: methods and tables. New York: Plenum Press, 1981.
• ISBN: 0306405237
• Location: Science Library/3500 SES
• Call Number: QD911 .B89
• Yale, Paul B. Geometry and symmetry. San Francisco: Holden-Day, 1968.
• Location: Daley Library - Math Collection/2d floor south - Books
• Call Number: QA477 .Y3

Crop Circle reconstructions using simple geometry:

• http://www.zefdamen.nl/CropCircles/en/Crop_circles_en.htm

High-quality photos of crop circles:

• http://www.temporarytemples.co.uk/