🚀 go-pugleaf

Martin Ward <martin@ward-hull.demon.co.uk> wrote:
MW> Pi day
MW>
MW> I saw a posting in one of the humour groups to the effect that 14 March
MW> is Pi Day because 3/14 was a good approximation to pi.  Someone had
MW> replied that 3/14 was closer to 0.2142857...

They probably meant 3.14, not 3/14.

MW> Any Briton and most other Europeans would consider 14 March as 14/3 any
MW> way, and 4.666666...  is still not very close to pi.
MW> At this point any mathematically literate reader will think as I did:
MW> *22 July* should be Pi Day.  22/7 = 3.142857...  is the good
MW> approximation to pi known since the days of the ancient Greeks.

It's the best approximation with a denomiator <= 12.

MW> That made me think, what about e Day?  This should be 19 July, since
MW> 19/7 = 2.714285 is close to e = 2.718281...  The problem is to find the
MW> best rational approximation to e with denominator no more than 12  (and
MW> some constraints on the numerator that create no difficulty).

Uhm, the best thing you can do is to do continued fractions.  I forgot
how to do continued fractions off my head, but it'll give you
sucessive *BEST* approximations with increasing denimators.  Look
in a number theory book.

MW> Then there is Phi Day (phi is the so called golden ratio defined by
MW> 1/phi = phi - 1), this turns out to be 13 August.
MW>
MW> Some are not unique.  I have presented all the possibilities but I think
MW> we should accept the canceled form as the day, so i^i Day is 1 May
MW> rather than 2 October.  The latter could be (i^i Day)'.

Isn't it ironic how the imaginary number raised to the imaginary
power equals a real number? (Involving the important constants pi,
and e)  :-)

MW> Martin Ward
MW> (5 Day)'' 1997
MW>

<snip>
(Impressive list, by the way)

MW> Martin Ward

Scott Phung