# Celtic Art Exploration

From EscherMath

**Objective:**
Symmetry in non-geometric shapes is quite interesting. Celtic art is quite symmetrical in nature.

## Rosette groups

Recall that for a finite shape, we may classify it by its symmetry group. We first check if the figure has reflectional symmetry or not.

- If there is reflectional symmetry, then the symmetry group is called a
*dihedral group*, abbreviated 'D'. - If there is no reflectional symmetry, then the symmetry group is called a
*cyclic group*, abbreviated 'C'. - Finally, we check what the highest order of rotational symmetry is for our figure. This number is appended to the ‘D’ or ‘C' to form the symmetry group name.

With Celtic art one should be careful! The under- and over-crossings have a tendency to destroy reflection symmetry. Hence most Celtic designs will be classified as a cyclic group *Cn* where *n* denotes the degree of rotational symmetry.

Above we see a knot that has 3-fold (order 3) rotational symmetry and hence would be classsified as a *C3*.

## Questions

Determine the Rosette Groups for these Celtic Knots:

**Handin:**
A sheet with answers to all questions.

## External links

- Celtic Knotwork: the Ultimate Tutorial A Look at the Construction and Mathematics of Celtic Knots
- Draw Your Own Celtic Knotwork Comprehensive list of links to both knotwork tutorials and a knotwork bibliography.
- Celtic Knots (Wikipedia) Original source for the image of the Lindisfarne Knot and the two links mentioned above.