Joshua wrote: << http://www.sciencemuseum.org.uk/images/I046/10314758.aspx Nice photo, nice piece of glass, and some nice humor: "It consists of three Klein bottles, one inside another." LOL!
Interesting. (Of course to a topologist a "real" Klein bottle is a surface that can't be modeled in 3-space without self-intersection, but be that as it may.) They kinda fail to be nested along the thin tubes that curve away from the "small ends" of the bottles and re-enter along the sides. *****>>>>>So, suppose you made this standard picture of a Klein bottle in 3-space out of a 5-ply sheeting, where plies 1,3,5 are glass and plies 2,4 are some volatile solid that sublimates shortly after the model is completed. (Something like taking three stacked strips of paper and going through the usual construction of a Moebius band with them.) QUESTION: When this model is completed, what do you have, topologically? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele