# Difference between revisions of "Symmetry and Celtic Knots Exploration"

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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. | 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. | ||

<ol> | <ol> | ||

− | <li>If | + | <li>If there is reflectional symmetry, then it is denoted as a ‘D’ group. </li> |

− | <li>If | + | <li>If there is no reflectional symmetry, then it is denoted as a ‘C’ group. </li> |

<li>Finally, we check what the largest degree of rotational symmetry is for our figure. This number is the added to the ‘D’ or ‘C’ we assigned before.</li> | <li>Finally, we check what the largest degree of rotational symmetry is for our figure. This number is the added to the ‘D’ or ‘C’ we assigned before.</li> | ||

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− | [[Image: | + | [[Image:Lindisfarne.png|center]] |

− | + | Above we see a knot that has 3-fold rotational symmetry and hence would be classsified as a ''C3''. | |

+ | |||

+ | == Questions== | ||

+ | |||

+ | |||

+ | Determine the Rozette Groups for these Celtic Knots: | ||

+ | |||

+ | A: [[Image:Knot1.png]] B: [[Image:Knot2.png]] C: [[Image:Knot3.png]] | ||

+ | |||

+ | |||

+ | D: [[Image:Knot4.png]] E: [[Image:Knot5.png]] F: [[Image:Knot6.png]] |

## Revision as of 09:43, 15 March 2007

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

## Rozette 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 it is denoted as a ‘D’ group.
- If there is no reflectional symmetry, then it is denoted as a ‘C’ group.
- Finally, we check what the largest degree of rotational symmetry is for our figure. This number is the added to the ‘D’ or ‘C’ we assigned before.

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

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

## Questions

Determine the Rozette Groups for these Celtic Knots: