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Drawing Celtic Knots

Age 11 to 14 Challenge Level:

William from Barnton Community Primary School discovered that:

If there is a rectangular Celtic knot that is M by N then the number of ribbons is the highest common factor of M and N.

In this case M = 5 and N = 3 so the number of ribbons is 1.

celtic knot

Therefore, if a square Celtic knot has side length x, the number of different ribbons will be x.

In this case x = 4 so the number of ribbons is 4.

celtic knot

The number of crossovers for a square Celtic knot is $$2x^2 - 2x$$ or $$2x (x - 1)$$

Students from Garden International School also worked on this problem. Here is what Kenn, Jong Woong, Jayme and Marana sent us.