It’s An Illusion, Part 8 – An Endless Knot

Trefoil Knot, right-handed

Trefoil Knot, Right-handed.

There are sailors’ knots and outdoorsmen’s knots, and knots with all kinds of practical uses.  This knot is different.  The trefoil knot is a mathematician’s knot – it can be explained by mathematical theory, it has no ends and it cannot be undone.

There are lots of interesting things about this knot.  It is called Trefoil because it has three crossings.  It can be made so that it is right- or left-handed; the illustration above is of a right-handed knot.  Like the Moebius strip, it is continuous.

You can make even one using a technique similar to the one used to create a Moebius Strip.  Except that in this case you cut your strip and give it three half twists before connecting end to end.  Cutting along the middle of that strip creates a longer strip that crosses itself three times and creates three loops – your own trefoil knot.  Though you may find it takes some manipulation to get it to look as neat as the illustrations!

The idea of this knot without ends intrigued Escher, so he played with showing what the knot that mathematicians described would look like if it was created using different materials.

In Knots, we see what Escher imagined.  He gave his knots different textures and made them look as if they were made from different materials.  The textures and shadings he used draw the eye into trying to follow the shapes, as the brain tries to make sense of what it is seeing.  But of course his knots are not real; they are another illusion.

Images:

M. C. Escher,  Knots.

Picture of right-handed Trefoil Knot by David J. Fred, shared under Creative Commons Attribute/Share Alike license.

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