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Re: is e < pi ?
Posted:
Mar 9, 2013 8:18 AM


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@mundor.com http://www.xente.mundor.com/ilarrosa/GeoGebra/



