Maths of Celtic and African art

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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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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
(3,4)
(2,4)
These are used to tell stories
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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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Grid
Edge
Corner Patterns
Corner
A
B
C
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First example
A
B
(A B)
Notation
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Get the Trefoil Knot .. Also called the
overhand knot
Two trefoils one reef knot
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Second example
A
A
B
B
(B A A B)
Notation
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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
B
Symmetry makes the best knots
B
B
C
A
A
B
Four reflexions One rotation
Notation
(A B A) (B C B) (A B A)
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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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