On 25/07/2012 07:07, Steven D'Aprano wrote:
On Wed, 25 Jul 2012 13:07:03 +1000, Ben Finney wrote:
Maarten <maarten.sn...@knmi.nl> writes:
You just missed it:
22/7
Which is appropriate, since 22/7 misses π by a wide margin. (355/113 is
my favourite approximation to π, and is far more accurate.)
Approximation? Pffft. I use the exact value:
π = 16*arctan(1/5) - 4*arctan(1/239)
For those lacking ambition, another approximation is:
π ≈ 9801 ÷ (2206*√2)
Other interesting approximations are:
π ≈ 9/5 + √(9/5)
π ≈ √√(2143/22)
See more here:
http://mathworld.wolfram.com/PiFormulas.html
http://mathworld.wolfram.com/PiApproximations.html
−1 on associating 22/7 as anything to do with π.
I believe that 22/7 is the closest approximation to π with a denominator
under 100. It is the second convergent of the continued fraction:
π = [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, ...]
which means that, like it or not, 22/7 *is* associated with π.
Any civil engineers reading this who would find 22/7 perfectly adequate
for their task?
--
Cheers.
Mark Lawrence.
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