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## 'Drawing Celtic Knots' printed from http://nrich.maths.org/

Celtic knots are graphical representations of knots used for
decoration by the ancient Celts. Here is a picture of an
illuminated letter from a manuscript, showing intricate overlapping
knots:

How about trying to draw some simple Celtic knots of your own?
Watch the two videos, which show two different methods for drawing
the same knot:

#### Alison's Video

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#### Charlie's Video

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Here are some images of completed knots. They have been coloured in
so you can follow the different "ribbons" that make up the knot
(click to enlarge):

You may find it useful to print off some of these grids (

Word,

pdf) to draw onto.

Alternatively, it is fairly simple to create your own grids by
drawing faint diagonal lines on squared or square dotty paper. The
straight lines needed to create the knots all go through the
midpoints of the sides of the squares:

While you are drawing the Celtic knots, you may think of
mathematical questions to ask.

Here are some questions that occured to us:

Try drawing some knots on square grids. What do you notice about
the number of ribbons needed to create square knots? Can you
explain your findings?

For rectangular knots, can you explain how the knot size
determines the number of ribbons?

Is it possible to draw a rectangular Celtic knot without rotational
symmetry?

Can you explain how the knot size determines the number of
overlaps?

Send us your findings, and pictures of your knots.