In my opinion the most awesome and funny exercise I recieved so far was in art. We listened a short lecture about the Möbius strip (a thingy which has no distinction between upside and downside face and only one edge but forming a ringlike object will transform your brain into some similar structure if you really try to understand it). The task was to take the Möbius strip and to think it one step farther and get some not yet known use, object or generel piece of art.
The Möbius strip beeing a two dimensional object that can only excist in three dimension as it twist in a way that is impossible in only two dimensions has a three dimensional counterpart the Klein bottle, which is basically a volume that is twisted in the fourth dimension to recieve an object that has no distinguishable in- or outside. To be able to understand that horrible wiggly thing you need to project it into three dimensional space where it can only be displayed with a selfintersection (in the fourth dimension it won't intersect).
Me and a fellow student did a quick brainstorm (I will write something about that subject soon as it is a very productive method of gathering and improving ideas) and produced a whole lot of ideas ranging from Möbius texts that end where they start, but twisted over Möbius videos wher the camera follows a Möbius strip to a Möbius projection of a closed ring-street section. We decided to go for a fourth option and went to lunch.
While eating we stumbled over a much greater idea than the ones we had before and decided to taylor a Klein pullover. The plan was to sew the collar of a T-shirt to the sleeve of a pullover and sew the seems of the T-shirt to the corresponding ones of the pullover to create a self intersecting projection of a four dimensional Klein pullover. We hurried out to the city as we only got five ours to submission and bought sewing stuff, a pullover and a T-shirt (thanking c&a for their cheap fashion). After a lots of sewing, tayloring and logofaking we came up with a brand new fashion label "wear Klein" which was painted on the backside of the pullover. After a hastly done fotoshooting we ran for our submission. Unfortunatly two other fellow students have had exactly the same train of though as we had and presented a Klein jacket (not as nicley taylored as we did though, only pulling one sleeve through the collar and sticking it into the other one). Finally the photos of me wearing Klein on the catwalk:
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