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Maths and ringing

This is an overview of a talk I gave to maths pupils at Park House School, Newbury , together with references for further study following the talk. I later gave a shortened version of the talk to pupils at Sir William Borlase's Grammar School, Marlow.

Read the article about the talk that was published in The Ringing World.

 If you would like a similar talk, please contact me .


Overview

The talk explains the mathematical underpinning of change ringing, and in the process introduces many mathematical concepts that have more widespread applicability, including: permutations, factorials, symbolic transformations, groups and group theory, Hamiltonian circuits, symmetry and the Fibonacci series.

See also: my general Talk on the Maths of Bellringing . See also: details of other Lectures for secondary school pupils  See also: Music and Ringing 

References

1 – Stedman, Fabian, “Campanologia”, 1677

2 – Griffiths, Deryn, “Twin Bob Plan Compositions of Stedman Triples: Partitioning of graphs into Hamiltonian subgraphs as used in bellringing”, Nov 1994 http://maths.usyd.edu.au/res/CompAlg/Gri/2bob-sted.ps  

3 – Johnson, Andrew, “Bobs-only Stedman Triples made easy”, The Ringing World, 11 August 1995, p841

4 – Price, Brian D, “More about Q-Set Laws”, The Ringing World, 3 April 1953

5 – “QED”, “A Note upon Some Aspects of Stedman Triples”, The Ringing World, 20 February 1953 also http://myweb.tiscali.co.uk/saddleton/stedman/qed.htm 

6 – Saddleton, Philip and Johnson, Andrew, “Peals of Stedman Triples with bobs only”, 1995, – http://myweb.tiscali.co.uk/saddleton/stedman/bdp.htm 

7 – “Software Firsts” http://www.ringing.info/shaggy.html 

8 – King, Frank H, “ Equations of Motion of a Free Bell and Clapper” http://www.cl.cam.ac.uk/~fhk1/equations.pdf 

9 – White, Arthur T, “Graphs, groups and surfaces”, 1973

10 – White, Arthur & Wilson, Robin, “The Hunting Group” , The Mathematical Gazette, Vol. 79, No. 484. (Mar., 1995), pp. 5-16. http://links.jstor.org/stable/3619985

11 – White, Arthur T, “Fabian Stedman: The First Group Theorist?”, The American Mathematical Monthly, Vol. 103, No. 9 (Nov., 1996), pp. 771-778 http://links.jstor.org/stable/2974446  

12 – Leigh Silver, A. L. “Some Musico-Mathematical Curiosities” The Mathematical Gazette, Vol. 48, No. 363 (Feb., 1964), pp. 1-17. http://www.jstor.org/stable/3614300 

13 – Roaf, Dermot & White, Arthur, “Ringing the changes: bells & mathematics” in “Music and Mathematics”, 2003 12 – Fortran Friends, (polyhedra to download, etc) http://fortran.orpheusweb.co.uk/Bells/polyhedra/ 

14 – Pumphrey, Hugh, “Bell-ringing methods as polyhedra”, http://xweb.geos.ed.ac.uk/~hcp/bells/  

15 – Burkard Polster and Marty Ross, “Ringing the Changes”, http://plus.maths.org/issue53/features/polsteross/ 

16 – Harrison, John “Ringing shapes” http://jaharrison.me.uk/Ringing/RingingShapes/  

17 – Harrison, John, Downloadable Minimus model ” http://jaharrison.me.uk/Ringing/RingingShapes/Download/Minimus.pdf  

18 – Harrison, John “ Bellringing and Music” http://jaharrison.me.uk/Ringing/Music/ 

19 – Harrison, John “Murder in the belfry” http://jaharrison.me.uk/New/Articles/RingOutDead.html  

20 – More links on ringing and maths – http://www.ringing.info/  Look under ‘Compositions’ -> Group Theory

21 – YouTube video, Change ringing on handbells with the 'cross & stretch' style – http://www.youtube.com/watch?v=yRy7YmUS3uQ 

22 – YouTube video, Change ringing on 24 handbells (including mega-tittums) at The Ringing World Centenary – http://www.youtube.com/watch?v=4-fCRBNTNp0 

23 – 'Mobel', mobile bellringing simulator for i-Phone – http://abelsim.co.uk/MobelNews.htm 

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