There are times today when one has to use very small microcontrollers -- that is computers which do not support floating point arithmetic -- and the programmer has to deal with so-called real numbers. These can best be dealt with using rational number arithmetic to acheive the fastest and best approximations to real numbers.
marion moon ------ Original Message ------ Received: Sat, 15 Oct 2005 08:16:36 PM PDT From: "Daniel" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]>, "U.S. Metric Association" <[email protected]> Subject: Re: [USMA:34887] Re: common fractions fail for some numbers I don't know why we need to care about a fractional representation of π. There was a time in the past when such was needed, and that was in the days of doing math with complex logarithms on a slide rule. This is the 21-st century, we use calculators. If I want to know the value of π, I press the π key on my calculator and get a number more accurate then any fractional representation can ever hope to give me. If you run Windows, you can run a program called calc.exe, I can with the click of a mouse have it display the value of π as: 3.1415926535897932384626433832795. Can any fraction display this much accuracy? Fractions are obsolete, we really need to forget about them. Dan ----- Original Message ----- From: "m.f.moon" <[EMAIL PROTECTED]> To: "U.S. Metric Association" <[email protected]> Sent: Saturday, 2005-10-15 14:56 Subject: [USMA:34887] Re: common fractions fail for some numbers > For another data point, the next regular convergent of the rational fraction > expansion of pi is 102573/32650 which has an error of 2.2x10^-8. There are > many other ratios between 355/113 and the above one which will yield small > ratios and better accuracy if you want the take the time to find them. > > marion moon > > ------ Original Message ------ > Received: Wed, 12 Oct 2005 06:24:25 AM PDT > From: Pierre Abbat <[EMAIL PROTECTED]> > To: "U.S. Metric Association" <[email protected]> > Subject: [USMA:34819] Re: common fractions fail for some numbers > > On Wednesday 12 October 2005 03:09, Brij Bhushan Vij wrote: >> Pierre Abbat & list: >> The Pi question has been discussed several times over. If Pi is the ratio >> between circumference to the diametre of a circle, the BEST and only >> fractional value for Pi in the form *a/b ratio* happen to be simple: >> 100000/31831, which also defines the angle radian at 57.2958 degree. Also, >> visit: http://www.the-light.com/cal/bbv_pi-radian.jpg > > 100000/31831 is off by 1.1e-6. 355/113 is off by only 0.3e-6. > > phma > > > > > > > -- > No virus found in this incoming message. > Checked by AVG Anti-Virus. > Version: 7.0.344 / Virus Database: 267.12.0/134 - Release Date: 2005-10-14 > >
