stretch and tie in a knot

This knot in my extension cord occurred inadvertently and thus I assumed with the highest likelihood it could be undone with a single pass through a cable end through a loop or loops with the loops arranged so only a single pass is required.  You would think this because once the cord is knotted it is hard to get another knotting function to occur on an existing knot.  The most likely scenario being a knot occuring due to an incorrect uncoiling.  Carefully looking at it I found this was true and verified it by doing just that.  The fact it looks like a pretzel dazzles a bit.  By the way the left side is the short end. To the right is the 25 foot long extension.

 

Initial solution

As with the above photo the left side exit strand is the short strand to be passed through in whatever method we can find.  

Stretch out the knot to get the second state shown in the second photo. Pass the left hand strand through the loop on the left.  You are left with a twisted loop that is no longer knotted. 

 

 

 

Schematic illustration of the simplified model for knot formation. Because of its stiffness, the string tends to coil in the box, as seen in Fig. 1, causing a number of parallel string segments to lie parallel adjacent the end segment. As discussed in the text, we model knots as forming due to a random series of braid moves of the end segment among the adjacent segments (diagrams at bottom). The overall connectivity of the segments is indicated by the dashed line.

Categories: Math

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