AlgTop6a: Non-orientable surfaces--the Mobius band
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Uploaded by njwildberger on Aug 3, 2010
A surface is non-orientable if there is no consistent notion of right handed versus left handed on it. The simplest example is the Mobius band, a twisted strip with one side, and one edge. An important deformation gives what we call a crosscap.
This is the first video of the sixth lecture in this beginner's course on Algebraic Topology, given by Assoc Prof N J Wildberger of the School of Mathematics and Statistics at UNSW.
NOTE: This entire series is now available in the full (hour long lectures), also at this channel under the playlist AlgTop (full lectures):
http://www.youtube.com/playlist?list=PL6763F57A61FE6FE8&feature=view_all
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Uploader Comments (njwildberger)
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The lectures are very good. Is it possible to do lectures on Group Theory?
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спасибо было интересно.
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Experimenting with a paper Moebius band I learned something interesting. I drew X and Y axes along the "lower" edge at regular intervals until I was back at the starting point. The last and first drawings matched exactly and were not inverted as I had expected. But... since the paper is a bit transparent I noticed that the drawings on the "other" side had the Y axis inverted! Mathematically there is no "other" side so I was watching non-orientability in action!
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According to wikipedia : "closed surface is a surface that is compact and without boundary."
02:25 Closed surface with boundary.
Something's wrong here :|
mafLT 7 months ago
@mafLT Nothing is particularly wrong here. A "closed surface with boundary" is not a special case of a "closed surface", though I admit the terminology might suggest so.
njwildberger 7 months ago