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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 I wrote for The Ringing World.

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


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 Lecture for secondary school pupils  See also: Music and Ringing 


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 

24 – Ringers and bells ringing at Docklands Ringing Centre – http://cccbr.org.uk/learn2ring/Bermondsey.mpg 

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