3 1 Further Notes and Views: Difference between revisions

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image = Trefoil-triquetra-circular-arcs-around-triangle.png |
image = Trefoil-triquetra-circular-arcs-around-triangle.png |
text = Ribbons (straight lines and 2/3 circles)|
text = Trefoil/triquetra without outside corners (made from straight lines and 240° circular arcs)|
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image = Triquetra-Vesica.png |
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text = Triquetra made from circular arc ribbons|
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image = RopeTrick_160.jpg |
image = RopeTrick_160.jpg |
text = Mike Hutchings' Rope Trick [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/RopeTrick/index.html]|
text = Mike Hutchings' Rope Trick [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/RopeTrick/index.html]|
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Revision as of 18:54, 27 May 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...
Trefoil/triquetra without outside corners (made from straight lines and 240° circular arcs)
Triquetra made from circular arc ribbons
Tightly-knotted form
Celtic
A Knotted Box [3]
A trefoil near the Hollander York Gallery [4]
A Knotted Pencil [5]
Trefoil depicted in non-threefold form
3D depiction in non-threefold form
A hagfish tying itself in a knot to escape capture. [6]
One version of the Germanic "Valknut" symbol
A Kenyan Stone [7]
Square depiction
In the form of an architectural trefoil
Polar equation curve.
Alternate Valknut depiction
Mike Hutchings' Rope Trick [8]
Banco Do Brasil [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 configurations of two trefoils along a closed loop which are prime, see 8_15 and 10_120. For a configuration of three trefoils along a closed loop which is prime, see K13a248. For a prime link consisting of two joined trefoils, see L10a108.


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