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Drawing Celtic Knots

Age 11 to 14
Challenge Level Yellow starYellow star
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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.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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