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Knot theory is a branch of topology inspired by observations, as the name suggests, of common knots. But progress in the field does not depend exclusively on experiments with twine. Knot theory concerns itself with abstract properties of theoretical knots — the spatial arrangements that in principle could be assumed by a loop of string.
When mathematical topologists consider knots and other entanglements such as links and braids, they describe how the knot is positioned in the space around it, called the ambient space. If the knot is moved smoothly to a different position in the ambient space, then the knot is considered to be unchanged, and if one knot can be moved smoothly to coincide with another knot, the two knots are called "equivalent".
In mathematical language, knots are embeddings of the circle in three-dimensional space. A mathematical knot thus resembles an ordinary knot with its ends spliced. The topological theory of knots investigates such questions as whether two knots can be smoothly moved to match one another, without opening the splice. The question of untying an ordinary knot has to do with unwedging tangles of rope pulled tight, but this concept plays at best a minor role in the mathematical theory. A knot can be untied in the topological sense if and only if it can be smoothly moved through the ambient space until it assumes the shape of a circle. If this can be done, the knot is called the unknot.
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@Calitheman segway cops got me a couple years back makin that left from K onto 14th @ rush hour.. i was HOT
OnlyNateDizzle (Nate Dizzle) Wed, 16 Dec 2009 19:19:48 -0000
@Calitheman segway cops got me a couple years back makin that left from K onto 14th @ rush hour.. i was HOT
@DJDTRAIN_ k was ergens anders mt me hoofd =p
Supadupacute (Saffira Comvalius) Wed, 16 Dec 2009 19:19:45 -0000
@DJDTRAIN_ k was ergens anders mt me hoofd =p
Ke hatinya @pipit_ aja d aw2 RT @nissaniniss: Yaudah k udik aja sonooo..hihii.:D
ecantiiiikk (Rhezza Setyoputra ) Wed, 16 Dec 2009 19:17:51 -0000
Ke hatinya @pipit_ aja d aw2 RT @nissaniniss: Yaudah k udik aja sonooo..hihii.:D
RT @Teal_2_FLY: Driving down 285 on this loud pack before I go to work.<---Nigga they gon fire yo butt,lol!!!! J/K
CoCoChanel00 (Chanel Jordan) Wed, 16 Dec 2009 19:07:45 -0000
RT @Teal_2_FLY: Driving down 285 on this loud pack before I go to work.<---Nigga they gon fire yo butt,lol!!!! J/K
viendo el video de bad romance en mtv.. k loquera guaaay
gabinha_dice (Gabriela A.) Wed, 16 Dec 2009 19:07:10 -0000
viendo el video de bad romance en mtv.. k loquera guaaay
@lizelleb I guess some Twi fans were upset that R had a photo shoot with EDR. They told Laimey that K was R one true love, she said K could
Poohbear0429 (Poohbear0429) Wed, 16 Dec 2009 19:07:09 -0000
@lizelleb I guess some Twi fans were upset that R had a photo shoot with EDR. They told Laimey that K was R one true love, she said K could
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