KNOT THEORY 101
Cocalc + Sage Worksheet
MAKO 2018
Trefoil
A continuous function whose range is the trefoil knot:
given by
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Trefoil, again
given by
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Figure-Eight Knot
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Torus Knot T(2,3) = Trefoil
2 times around long way, 3 times around short way.
2 triangles.
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Torus Knot T(3,2) = Trefoil
3 times around long way, 2 times around short way.
T(3, 2) = T(2, 3).
3 footballs
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Torus Knot T(3,4)
3 times around long way, 4 times around short way.
Knot 819, the first nonalternating prime knot.
3 squares.
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Torus Knot T(4,3)
3 times around long way, 4 times around short way.
Same as T(3,4)
4 triangles.
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T(11,12), crossing number 120
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1-Twist Moebius Strip
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2-Twist Moebius Strip
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3-Twist Moebius Strip
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Torus Knot T(2,3) again, with Moebius Strip
Same, with a torus
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Torus Knot T(2,5) on a 5-Twist Moebius Strip
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Torus Knot T(2,11) with an 11-Twist Moebius Strip
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