The Mathematics of Bell Ringing

The mathematics of bell ringing. One thing bell ringers might want to do is ring out all possible combinations of their bells. For example, Plain Bob Minimus is a method that rings all 24 possible combinations of four bells. On the other hand, there are also 24 possible orientations of a cube - in fact underneath the mathematics is the same, and the sequences act as a bridge between the mathematical world of rotations of a cube and the musical world of bell ringing.

Category:

Education

Tags:

• maths
• math
• mathematics
• problem
• puzzle
• bell
• ringing
• sequences
• combinations
• permutations
• rotations
• cube
• group
• theory
• isomorphic
• jam
• mathsjam

[superfluousness321]

@singingbanana Oh I see so you get the whole of S_4, but can you ring the changes of not just rotational symmetry but the full reflection group?

[singingbanana]

@superfluousness321 No, the group of permutations of n bells is S_n, which I can't represent with rotations and reflections of a physical object beyond n=4. But I may do this again someday with something else...

[boumbh]

There are only two permutations used, alternatively:

(1,2,3,4) -> (2,1,4,3)

which corresponds to a roll(180) of the cube

(1,2,3,4) -> (1,3,2,4)

which corresponds to a roll(180) x yaw(-90) of the cube

And you get all the combinations.

[singingbanana]

@boumbh That's it :) Have a closer look for a third permutation.

[Thatguy7109]

Is you name Jim or James

[singingbanana]

@Thatguy7109 I use both. It always surprises me that some people find that confusing.

[gozar221]

what was the thing on your chest

[norrisonthespot]

That actually sounded lovely as a piece of bell ringing music in itself.

[bonzifan]

oh my - I'd predict that took several takes!!! rather impressed by the man spinning the cube,  its quite interesting.

[peterrowlett]

@burny1 yes, I got a new job working on university maths teaching enhancement project for the Maths, Stats and OR Network. I really enjoyed the IMA job but this job is good too :) New IMA University Liaison Officer is starting later this month, afaik.

[scotland7yard]

next instalment: the mathematics of beetles who can't turn around when they fall on their backs

[burny1]

@peterrowlett I thought it was you. How come you no longer do the IMA? We all miss you here at york.

[TheCrazyYoyo]

i bet some people ask you this and you might have already awnsered, but what is your IQ?

[peterrowlett]

Finally got round to watching this. It came out pretty well, well done Jim!

I also listened to the Math/Maths Podcast recording we did at MathsJam, where Jim gets up and says "I have a plan. I'm going to make a video about bell ringing..." (pulse-project . org) :)

[sequencius]

@PEZenfuego

It does look like Lucas Garron, he is a math major at Stanford I believe

[koipod13]

There is a much simpler way of doing this

It should 4 possibelits *3 possibelits *2 possiblelits