One of the coolest things in Mathematics to me is the Möbius Strip. The Möbius Strip is a 2 dimensional strip of paper that holds both 2 and 3 dimensional properties. Cut a strip of paper, fold it once, connect it back to itself. Start one point on the strip and trace along the strip and you will traverse every side of the mobius ring including the inside AND outside....while still ending up at the end...in a sense, while it is a 3 dimensional object, its surface is a 2 dimensional non-orientable topological surface (much like the widely loved nerd referenced and worshiped Klein Bottle).
The Möbius Strip was actually mentioned in my previous blog by the authors video as an example of 2/3 dimensional manipulation.
The Klein bottle is something I cannot even begin to explain...however I will try...Topology is a field of mathematics that makes sense to few...and those are the ones that tend to be insane. Klein bottles do however hold many cool geometric properties. Essentially, in lamen terms, a Klein bottle is a bottle created by the combining of two Möbius Strips. This is what you end up with...a bottle which only has one side, and amazingly CONTAINS ITSELF and whos INSIDE IS ITS OUTSIDE....ponder that one for a while...
But although it's a 2-D manifold, it can only exist in 4-dimensions...yeah...crazy...and freaking Mathematically AWESOME...I have an Klein Bottle coffee mug that I use often and its sweet...I have no idea how it works and never will...but I have the pleasure of taking it into math classes and looking smart while at the same time boasting my ability to hold coffee in a 1 sided 2/3/4 dimensional object....sweet!
3 comments:
For further proof of Klein bottle awesomeness, see Futurama, s03 e12, "The Route of All Evil" and gaze upon Klein's Beer
The Mobius strip has always interested me as well. But that Klein thing, I would need a bit more explaining to grasp that. I kind of get it, kind of don't. So this blogger thing, do you add friends like a xanga or anything? I am not seeing a place to so I am assuming you don't. Just trying to get the logistics of this thing. Either way, I added your blog to my google reader so it should update me to when you post. Isn't google great!
Sweet! Its good to know that you are reading google reader. Its a fantastic Tool!
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