Caren DiefenderferHollins University

Roanoke, VA

History of Change Ringing

Bells on ropes in towers

17th century England

Specific Vocabulary

Today, many ringing groups

1 2 3 42 1 4 3

2 4 1 3

4 2 3 1

4 3 2 1

3 4 1 2

3 1 4 2

1 3 2 4

1 2 3 4

Eight good rows

Rules of Change RingingThe bells are first rung from highest to lowest

(rounds)

Every bell is rung once in each “row”

Each bell may move at most one position from one row to the next.

No permutation is repeated, until the last row repeats rounds.

Practice with chimes

Cross and Stretch on 4 bells

Cross and Stretch on 6 bells

Cross and Stretch on 8 bells

Connections to MathematicsRigid Motions of a Triangle

Permutation functions

Rigid Motions of a Square

Dihedral group, Permutation group, Normal subgroup, cosets

Sparks of Genius: The 13 Thinking Tools of the World’s Most Creative People

Robert S. & Michele M. Root-Bernstein, 2001