This document discusses the history and rules of change ringing, a method of ringing church bells in ordered sequences. It covers how change ringing originated in 17th century England using specific techniques and vocabulary. The rules dictate that each bell must move only one position between rows and no permutation can be repeated until the final row, which repeats the starting pattern. The document also notes how change ringing is connected to mathematical concepts like permutations and group theory. It concludes by listing some thinking tools that creative people use as discussed in the book "Sparks of Genius."

1. Caren Diefenderfer
Hollins University
Roanoke, VA

2. History of Change Ringing
Bells on ropes in towers
17th
century England
Specific Vocabulary
Today, many ringing groups

3. 1 2 3 4
2 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

4. Rules of Change Ringing
The 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.

5. Practice with chimes
Cross and Stretch on 4 bells
Cross and Stretch on 6 bells
Cross and Stretch on 8 bells

6. Connections to Mathematics
Rigid Motions of a Triangle
Permutation functions
Rigid Motions of a Square
Dihedral group, Permutation group, Normal subgroup,
cosets

8. Sparks of Genius:
The 13 Thinking Tools of the World’s Most Creative People
Robert S. & Michele M. Root-Bernstein, 2001