3 1 Further Notes and Views: Difference between revisions

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text = Trefoil depicted in non-threefold form
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text = Thurston's Trefoil - Figure Eight Trick [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/TrefoilFigureEight/index.html]|
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text = The NeverEnding Story logo is a connected sum of two trefoils. [http://www.thealmightyguru.com/Reviews/NeverendingStory/NeverendingStory.html]|
text = The NeverEnding Story logo is a connected sum of two trefoils. [http://www.thealmightyguru.com/Reviews/NeverendingStory/NeverendingStory.html]|
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Revision as of 04:37, 25 March 2010

The trefoil is perhaps the easiest knot to find in "nature", and is topologically equivalent to the interlaced form of the common Christian and pagan "triquetra" symbol [12]:

Logo of Caixa Geral de Depositos, Lisboa [1]
A knot consists of two harts in Kolam [2]
A basic form of the interlaced Triquetra; as a Christian symbol, it refers to the Trinity
3D depiction
Further images...
Ribbons (straight lines and 2/3 circles)
Ribbons (circular arcs)
Tightly-knotted form
Celtic
A Knotted Box [3]
A trefoil near the Hollander York Gallery [4]
A Knotted Pencil [5]
File:Image:Trefoil-non-3-symm.png
Trefoil depicted in non-threefold form
Banco Do Brasil [6]
A hagfish tying itself in a knot to escape capture. [7]
One version of the Germanic "Valknut" symbol
A Kenyan Stone [8]
Square depiction
In the form of an architectural trefoil
Polar equation curve.
Mike Hutchings' Rope Trick [9]
The NeverEnding Story logo is a connected sum of two trefoils. [10]
Thurston's Trefoil - Figure Eight Trick [11]

Non-prime (compound) versions

  • Two trefoils (single-closed-loop version of the "granny knot" of practical knot-tying).

    Two trefoils (single-closed-loop version of the "granny knot" of practical knot-tying).

  • Two trefoils (single-closed-loop version of the "square knot" of practical knot-tying)

    Two trefoils (single-closed-loop version of the "square knot" of practical knot-tying)

  • 3D square knot

    3D square knot

  • Three trefoils (symmetrical).

    Three trefoils (symmetrical).

  • Four trefoils (Celtic or pseudo-Celtic decorative knot which fits in square)

    Four trefoils (Celtic or pseudo-Celtic decorative knot which fits in square)

  • Three trefoils along a closed loop which itself is knotted as a trefoil.

    Three trefoils along a closed loop which itself is knotted as a trefoil.

For a configuration of two trefoils along a closed loop which is prime, see 10_120.


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