Article View: uk.education.maths
Article #61Re: Pi day
From: R.W.Dirksen
Date: Fri, 28 Mar 1997 00:00
Date: Fri, 28 Mar 1997 00:00
49 lines
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3369 bytes
Dik T. Winter wrote: > > In article <5heh6s$ooa@raven.cc.ukans.edu> ipsifend@eagle.cc.ukans.edu (Greffindel) writes: > > So, it's pi x 1000 light-years, right? > > Speed of light: 3x10E8 m/s > > Seconds in a year: 60 x 60 x 24 x 365.25 = 31557600 > > sec/min min/hour hour/day day/year > > m in a light-year: 9467280000000000 =9.46728 x 10E15 (I'm doing this > > all w/pencil and paper, so hit me if I biff the arithmetic). > > m in 1000 light-years: 9.46728 X 10E18 > > Now, running a little c program on my home computer, > > 3.141592653589793239 is as much of pi as I can get without inventing > > my own quadruple=precision storage class, so let's see what that gives > > us: > ... > > 2.852008848434121673571912 x 10E19, which in real numbers is > > 28520088484341216735.1912 meters. > > 18 decimal digits of pi gives you the distance correct down to the > > millimeter. How much more pi do you need? > > Are you sure? I think the error in the speed of light and in the number > of days in a year is much too large to warrant this assertion. > > It is true, in real life 22/7 is mostly good enough, and if not you > go to 355/133 which probably is excellent (it would be good enough > in the calculation above). On the other hand, there are indeed > situations where you need an extremely good approximation of pi, or > your calculations can go wrong. There are highly unstable calculations > (like some of the higher zeros of the Riemann zeta function) that > require this. (In the latter case to verify that all non-trivial zeros > are on a particular line, you need to separate them. The problem is > that they can get arbitrarily close to each other. And the calculations > involve cosines.) > -- > dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 > home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ The speed of light is known very exact because it is a constant value. They actually made it a definition: 1 meter = the distance that light travels in 1/299792458 seconds Therefore, the light speed c is defined as 299,792.458 km/s. p.s. why celebrate pi-day anyway. I personally like the number 0.3157894736842105263157894736842105263157894736842105263157894736... or 6/19. That's why I celebrate that day instead! Gerben Dirksen
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f458d,30fff994c7ddd7d9 X-Google-Attributes: gidf458d,public X-Google-Thread: 1130d6,30fff994c7ddd7d9 X-Google-Attributes: gid1130d6,public X-Google-Thread: 10d67e,30fff994c7ddd7d9 X-Google-Attributes: gid10d67e,public X-Google-Thread: 1077c2,30fff994c7ddd7d9 X-Google-Attributes: gid1077c2,public X-Google-Thread: f7972,30fff994c7ddd7d9 X-Google-Attributes: gidf7972,public X-Google-Thread: 109d8a,30fff994c7ddd7d9 X-Google-Attributes: gid109d8a,public From: "R.W.Dirksen" <R.W.Dirksen@caiw.nl> Subject: Re: Pi day Date: 1997/03/28 Message-ID: <333C2695.5661@caiw.nl> X-Deja-AN: 229108875 References: <AF5DA45C96685884D@sofluc.demon.co.uk> <ant262248d076Quo@cartmell.demon.co.uk> <5heh6s$ooa@raven.cc.ukans.edu> <E7qArI.1KD@cwi.nl> Organization: CAI Westland/Kabelfoon Newsgroups: uk.education.maths,alt.uu.math.misc,aus.mathematics,can.schoolnet.math.sr,alt.math.recreational,sci.math