3 1 Further Notes and Views: Difference between revisions

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===Non-prime (compound) versions===
===Non-prime (compound) versions===
<gallery>
<gallery>
⚫
Image:Square-knot-6-crossings.png|Two trefoils (single-closed-loop version of the "square knot" of practical knot-tying)
Image:Granny-knot-6-crossings.png|Two trefoils (single-closed-loop version of the "granny knot" of practical knot-tying).
Image:Granny-knot-6-crossings.png|Two trefoils (single-closed-loop version of the "granny knot" of practical knot-tying).
⚫
Image:Square-knot-6-crossings.png|Two trefoils (single-closed-loop version of the "square knot" of practical knot-tying)
Image:Blue Square Knot.png|3D square knot
Image:3trefoil-9crossings.gif|Three trefoils (symmetrical).
Image:3trefoil-9crossings.gif|Three trefoils (symmetrical).
Image:Celtic-knot-insquare-green-transparentbg.png|Four trefoils (Celtic or pseudo-Celtic decorative knot which fits in square)
Image:Celtic-knot-insquare-green-transparentbg.png|Four trefoils (Celtic or pseudo-Celtic decorative knot which fits in square)

Revision as of 01:28, 23 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]
Thurston's Trefoil - Figure Eight Trick [6]
Banco Do Brasil [7]
A hagfish tying itself in a knot to escape capture. [8]
One version of the Germanic "Valknut" symbol
A Kenyan Stone [9]
Square depiction
In the form of an architectural trefoil
Polar equation curve.
Mike Hutchings' Rope Trick [10]
The NeverEnding Story logo is a connected sum of two trefoils. [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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