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Is the Projective Plane Hat Crazy Enough?

Do I have the craziest hat on YouTube? This is a response to Sarahendipity's Crazy Hat Contest!: http://www.youtube.com/watc... This hat is so crazy it's four-dimensional (in theory)! The letteri...  
 
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ha14mu (2 months ago) Show Hide
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This is awesome!!! I want one such hat...
hiswayornoway (11 months ago) Show Hide
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Well, I clicked on this video expecting a hat that somehow protected people from attacking aeroplanes, so at first I was slightly disappointed.

However, the real thing turned out to be even better (although not for people under aeroplane attack). Very cool hat. You're very clever.

Hasn't it got five dimensions, though, because presumably it exists in time as well as space?
matedu (1 year ago) Show Hide
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Nice Hat =S
phil10300 (1 year ago) Show Hide
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It definitely IS the crasiest hat!
DILLIGAF333 (1 year ago) Show Hide
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So it's like a Mobius Strip on steroids?
TheMathGuy (1 year ago) Show Hide
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Something like that--yes! You can get a Klein Bottle by joining two Mobius Strips along their edges, or a Projective Plane by joining a single Mobius Strip to a disc. Though you won't be able to finish the process in 3-dimensional space. You'll need a 4th dimension to make it truly work (or 'cheat' by passing the surface through itself, which is what the hat does, since it obviously can't actually be 4-dimensional!)
Madseason3 (1 year ago) Show Hide
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wuts song name?
inpenev (1 year ago) Show Hide
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Nice presentation, congratulations!
But would you tell me something about the music used in this clip (title of the piece, composer, etc.)?
GentleSavage1 (1 year ago) Show Hide
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It's Carl Orff's Carmina Burana, in particular, the introduction "O Fortuna"
inpenev (1 year ago) Show Hide
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Thank you! :)

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