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Maths of Celtic and African art Chris Budd

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Knots have been around for a very long time They have many uses Climbing Fishing Sailing

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They also appear in nature Enzyme DNA Vortices

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Knots are central to Celtic and African art Celtic African

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Book of Kells

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How to draw simple Celtic Knots Start with a grid (5, 4) grid

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(5,6)

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(4,8)

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(2,2) 2 (3,2) 1 (5,3) 1 (4,4) 4 How many pieces of string are needed?

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Simple Celtic Knots are very similar to plaited mat sona drawings Sona … African sand patterns These are used to tell stories (3,4) (2,4)

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J

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More advanced Celtic Knots are also based on a grid and a set of simple rules or

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ABC Grid Corner Patterns Corner Edge

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A (A B) First example B Notation

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Get the Trefoil Knot.. Also called the overhand knot Two trefoils = one reef knot

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B AAB (B A A B) Notation Second example

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Get the Carrick Bend This is the simplest example of a Josephine Knot

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… or even … A A A A B B B B C (A B A) (B C B) (A B A) Symmetry makes the best knots Notation Four reflexions One rotation

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… producing the knot

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We can also produce more advanced African knots … Such as the Chased Chicken design

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