Fish, Chips and Peas Squared, Calculus, Apache and Guitars

Every year I scan the Edinburgh International Book festival Programme for something different.  All the events are fantastic but I am looking for something that is extra special.  This year I spotted Music and Calculus.  David Acheson was promoting his book and during this session there were many examples of how calculus and maths is applied.  David’s examples focused on Music.  But there are many others.  Therefore, you may be surprised but…

Throughout the land – thousands listen to some applied maths. People play this game either at home or in their local  hall.   For them it is  an every day game, providing fun and entertainment – everyone waiting for a special moment.  This is what happens as the tension builds…

Sheila is close.    Only one to go – all she needs is a number 10.  The caller shouts out “Theresa’s Den”, number 10.   (Early in 2017 it would have been David’s Den – David Cameron Prime Minister did live at 10 Downing Street until Theresa took over the role). 

Without fear the words  “House!” are shouted out in excitement.  And a prize is on its way.  She is a bingo winner.

For bingo on your computer/phone some maths are involved, as there is no physical ball!  A mathematical calculation is performed in some cases to establish the number of the next ball.   That  calculation gives a magic number for the virtual bingo caller to shout out!

David in his talk did mention a magic number and I am now going to tell you all about it.   I have called it Fish, Chips and Peas Squared.  And for this meal there are three portions and of course the number 3 is a prime and odd number.  But that is not the number that David introduced me and the audience to.

But what would happen if I invited my friend for a bite to  eat.  Of course being completely compatible we eat the same meal. That would be 2 meals of fish chips and peas – dare I say it – it is squared!

That is two sets of 3 but what can I do with this?

  • Well I can add them together and that will give 6. But that is not the number David mentioned..
  • I can subtract 3 from 3 and again I get a number 0, and zero is a magic number.  Therefore, if I divide 0 into three I get… infinity?   David did talk about infinity but that wasn’t the number at the start of the event he focused on.
  • It also follows that I can square 3 and that is not quite right.. As the answer is 9 and not…

The answer is simpler if my friend and I become one in this example. One mathematically I mean. That is by joining together we have some magic and the number 33 appears.  This is nearly the number that David introduced  me and the rest of the audience to.  The clue here is in the title Fish, Chips and Peas Squared.

Now we should just do that calculation . That is 33 x 33 and write down the answer.  Yes, top marks if you have calculated 1089!

Please, make a note of this number and now try the following exercise.

Think of any three digit number above 500 that descends in value the distance between the first and second number must be at least 2.

Write this number down.

For example 754

Then reverse the order 

that gives  457

subtract from your original number






reverse the order and it gives


add both numbers together and it gives 1089

Is that not amazing!

And of course he has written another book about maths and it is  simply called 1089 and all that.

But that is not the book he is promoting at the book festival it is the calculus story.  This book became a Christmas Stocking filler after a surprise article in the New Scientist.

And on that theme he went on to show how calculus can be applied to ordinary things such as guitar strings.  A demonstration followed in which two children held a piece of string and applied movement to it to generate single and a variety of multiple waves.

Other examples followed and the event closed with a superb finale. Did he quickly give us two plates of Fish, Chips and Peas to digest?

Image Courtesy of Edinburgh International Book Festival
David John Acheson is a British applied mathematician at Jesus College, Oxford. He was educated at Highgate School, King’s College London and the University of East Anglia.

No, in food terms it was the sweet that he served up to his audience.  A superb performance on his electric guitar showing the applied use of  calculus.  A standing ovation almost ensued.  The music on exit,  Apache by the Shadows.   David by all accounts should have been in that recording,

Well that is the end of that story and if you are mathematically inclined you can purchase David’s book here….

But why is the headline Fish, Chips and Peas squared? What has that got to do with anything.

Well here comes the clues…

Theresa’s Den –  Bingo Ball (10)

Garden Gate – Bingo Ball (8)

Two little ducks – Bingo Ball (22)  

Two Fat ladies – Bingo Ball (88)

Fish, Chips and peas or All the threes is Bingo Ball  (33) 

Yes, they are all bingo calling rhymes and of course Fish, Chips and Peas is 33 in Bingo slang.  And as you all know 33 squared is… 33 x 33 = 1089

Another interesting fact is that in 1089 the Northumbria was split into many smaller counties….

As a result of many rebellions by the county of Northumbria it was decided to make  the County more manageable.  Subsequently it was divided into the counties of Northumberland, County Palatine of Durham, Yorkshire, Westmorland and Lancashire.

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