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March 14, 2020

Further clarification on the proof of the handedness of the trefoil

Filed under: clarification of demonstration — Rob @ 11:39 pm

March 10, 2020

Sketch of proof that the trefoil is unequal to it’s mirror image.

Filed under: clarification of demonstration — Rob @ 8:28 am
The top diagram shows that the reduced diagram of the trefoil must take the shape that it does as well as being knotted through the use of tricolorability as shown in the previous entry. The doublets a(1)r(1), b(1)s(1),,, etc. are shown as a(1), a(2), etc. and have the same cyclic order as from when the knot diagram is first reduced. If I don’t consider knot direction then either the left hand or the right hand trefoil can be reformed but if I give the knot a direction then only the original handedness can be recovered.

March 5, 2020

Other diagrams of the Trefoil-Coloring

Filed under: clarification of demonstration — Rob @ 5:13 am
This work is sketching the level where I can apply coloring to any diagram of the Trefoil after having gone through the Reidemeister Moves. I can have a reduced diagram through the use of an undoing move applied after only S1,S2,S3 the counterparts of the Reidemeister moves are applied to a diagram.

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