Maths of Celtic and African art

Chris Budd

Knots have been around for a very long time

They have many uses

• Climbing

• Fishing

• Sailing

They also appear in nature

Enzyme DNA Vortices

Knots are central to Celtic and African art

Celtic

African

Book of Kells

How to draw simple Celtic Knots

Start with a grid

(5 , 4) grid

(5,6)

(4,8)

(2,2) 2

(3,2) 1

(5,3) 1

(4,4) 4

How many pieces of string are needed?

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)

J

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

or

A B C

Grid

Corner

PatternsCorner

Edge

A

(A B)

First example

B

Notation

Get the Trefoil Knot .. Also called the overhand knot

Two trefoils = one reef knot

B A A B

(B A A B) Notation

Second example

Get the Carrick Bend

This is the simplest example of a Josephine Knot

… 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

… producing the knot

We can also produce more advanced African knots …

Such as the Chased Chicken design