Walk like an Egyptian (2): further thoughts on pi

Earlier this year, I posted this blog https://allanbeardsworth.com/2013/04/15/walk-in-circles-like-an-egyptian/ on pi, and specifically about what I read about Eratosthenes calculating pi to a good degree of accuracy.

Or did he?

I have since, in random googling, found other comments that maybe he didn't, and maybe the Egyptians didn't know about pi to a good approximation.

This journey has shown me how little I really know. In Donald Rumsfeld's terms, I have numerous known unknowns:

How do you calculate any particular trig function, such as say sine 43 (43 chosen at random);

How were sine and other trig functions calculated?;

Alternatively, how did Eratosthenes calculate pi, if indeed he did?;

Are most trig functions irrational, and are there very few precisely accurate functions, such as sin30? –

Alas, I suspect I shall never know.

Perhaps I should have asked the person sitting at the next table to me earlier this week at Caffe Nero who had a screen saver of Euler's formula. One thing that I am sure of is that I have no practical change of understanding why e^i*pi+1=0; unless someone can help??

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