Celtic Knotwork - knotwork panel I.

in WORLD OF XPILAR17 days ago

8.jpg

Hi friends!

In the first knot that we drew previously (https://steemit.com/hive-185836/@jorgevandeperre/celtic-knotwork-basic-principles-i), we can see that with a 4 x 4 grid of squares, we have drawn a Celtic knot and we can conclude that this is the minimum number of squares necessary to do so. We can also see that the result is a pair of independent loops that intertwine.
If we try to establish a mathematical connection, we can see that there is a common factor in the relationship between the number of horizontal and vertical boxes, this factor is 2.

image.png

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Now, to draw the first Celtic knot panel, we'll make a 16 x 8 grid, as shown below.
Remember that to draw one knot we need a grid with 4 x 4 squares. In this case (16 x 8 grid), we have the equivalent of 8 knots.
1.jpg

First, we draw the patterns around the external boxes of the grid, in the same way that we have done in previous posts.
2.jpg

Then, we draw the interior lines as shown next, taking care to maintain the interlacing (one above, then below).
3.jpg

Once the sketch is finished, we proceed to draw, with a broader stroke, all the lines of the panel.
4.jpg

At this stage, we outline the strokes with black to reveal the interlacing.
5.jpg

We see that this panel, being made up of 16 x 8 squares, has common factors 2 and 4, so we should expect that the design will give us more than one endless loop.
8.jpg

Here, in the two next images, we have the loops, there are 4 independent loops, as you'll see if you follow the tour of them.
untitled.jpg
untitled2.jpg

As you may have seen, this analysis once again reminds us of the close relationship between mathematics and art, and
although we do not have a mathematical formula to back us up, we could affirm that when there is a common factor for the number of horizontal and vertical boxes in the grid, we'll obtain separate loops that intertwine.
Later we will continue looking at other examples to check if this premise is met.

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I wish you a very nice day!

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