Walk (in circles) like an Egyptian

(Explanation for people under 40….Walk like an Egyptian was a hit record in 1986 by the Bangles)

(Warning for Tom, Alice and Sophie…if you are with your parents at a party where this is played, get ready to be mightily embarrassed by said parents walking like Egyptians).

(Final preliminary diversion…the Wikipedia entry for the song says it was on a list of records to be avoided drawn up by the BBC during the 1990-91 Gulf War, along with ' Bang, Bang (My Baby Shot me Down), ' Boom Bang-a-Bang' and 'Sailing').

Jane recently bought a 'making maths fun' book for her teaching. It is probably the one and only perk in being married to a teacher that she occasionally buys maths books. I dipped into this one, and the following caught my eye.

The book says that an Egyptian mathematician, Eratothenes, 276-195 BC, worked out PI as being approx 3.143 by this method, applying it to a 96 side polygon.

I had not heard of this method before, but decided to try it. The first problem I thought of was 'did Eratothenes know about sines, cosines and tangents? I haven't been able to confirm or disprove this, though since Pythagorus lived three centuries earlier (570-495 BC) at least he would have known of Pythagorus's theorem. (Another diversion: both these mathematicians lived to a good old age)

Today, with algebra and trig, the calculations are straightforward enough. Inserting a value of n=96, gives 3.142.

Later, I put the formula into Excel with these results:

By the time n=20, or thereabouts, PI is calculated to within 1% accuracy.

Unanswered question: how did Eratothenes do the calculations?

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