# the meaning of rï¾•.......ï¾

Mark Lawrence breamoreboy at yahoo.co.uk
Wed Jul 25 08:37:33 CEST 2012

```On 25/07/2012 07:07, Steven D'Aprano wrote:
> On Wed, 25 Jul 2012 13:07:03 +1000, Ben Finney wrote:
>
>> Maarten <maarten.sneep at 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.
>
>
>