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Re: is e < pi ?
Posted:
Mar 9, 2013 8:18 AM
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El 11/01/2013 17:57, pepstein5@gmail.com escribió:
> On Friday, January 11, 2013 4:10:28 PM UTC, rodp...@gmail.com wrote:
>> An obvious answer. But can you prove it ?
>>
>
> 1 + 1 + 1/2! + 1/3! is bounded by 1 + 1 + 1/2 + 1/(2^2) + 1/(2^3) ... = 3
> So e < 3.
>
> Unlike e, pi is defined differently by different authors. Any definition should enable the conclusion that pi > 3.
>
> That's a bit vague. It can be shown that pi = 4 - 4/3 + 4/5 - 4/7 + 4/9 etc.
> Expand that series to about 10^6 terms using your favourite software. Use a finite expansion that gets chopped off before a positive term. That way you get a lower bound. This lower bound is > 3 . So pi > 3.
>
> Paul Epstein
>
Compare the perimeter of a circle, 2pi*r (the most primitive definition
of pi), with the perimeter of a regular hexagon inscribed, 6r.
--
Saludos,
Ignacio Larrosa Cañestro
A Coruña (España)
ilarrosa@mundo-r.com
http://www.xente.mundo-r.com/ilarrosa/GeoGebra/
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