Celtic Knotwork - knotwork panel III

Hi friends!

Designing a Celtic knot and determining whether it will generate a single line or several depends largely on the skill of the designer and the creative decisions made during the drawing process. There is no single mathematical formula for this purpose, as the design of Celtic knots is more a matter of art and design than pure mathematics. However, geometric and mathematical concepts can be useful in understanding the structure of these designs.
Thus, trying to empirically find some numerical relationship that helps us anticipate in a certain way what the result of interlacing could be, maybe could not be out of place.
Maybe, if we try to establish a numerical relationship between the number of patterns and the final result of interlacing instead of counting the number of grid cells, can establish some rules.
Let's see...

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7 arcs by row and 3 arcs by column haven't a common factor... the result could be a single endless line.

Drawing again the knotwork, but now with a wider stroke.

Knotwork of 7 arcs by 3 arcs, the result is a single interlaced endless line, (numbers with no common factor).

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In this knotwork of 7 arcs by 4 arcs the result is a single endless, (numbers with no common factor).

Knotwork of 8 arcs by 4 arcs, the result is the interweaving of more than one endless loop, (numbers with common factors: 2 and 4).

3 arcs by 2 arcs, the result is a single endless, (numbers with no common factor).

It remains to be seen whether this numerical relationship continues to occur in other cases...

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I wish you a very nice day!