Subject: Re: EXTRAORDINARY PI
From: bstan@datasync.com (BLStansbury)
Date: Mon, 30 Dec 1996 02:58:01 GMT
On Sun, 29 Dec 1996 22:24:17 GMT, juanvp@impsat1.com.ar (JuanVP)
wrote:
>No, you can use different expressions of Pi, there are many
>analytical expression of the EXACT value of Pi. One of the first
>we always learn at calculus is 4 * Sum( n, 0, oo, (-1)^n/(2n+1) ).
Another number of the infinite persuasion. You can't draw a line with
this exact measure, but you sure could come close. Close enough for
any practical reason, but you will never quite get there.
>But as in reality, we cannot detect this differences, there is
>no problem in using the ideal formulas as the error is not
>very significant.
I agree, but you have to admit that a an error occurs in an
approximation--no matter how how insignificant.
>Well, that would be 200/3 (the exact value) which is not
>expressible in the standard decimal positional notation.
So how much money $200/3? I don't care what base or notation you use,
you will not be able to give me a definitive answer.
BLS
Subject: Re: Day Number calculation
From: Robin Becker
Date: Mon, 30 Dec 1996 00:57:00 +0000
In article , Craig Markwardt
writes
>
>nmm1@cus.cam.ac.uk (Nick Maclaren) writes:
>Then again, there's no need to re-invent the wheel. Astronomers (and
>I presume many date-keeping people) have been using Julian days for a
>long time, and are probably exactly what the original requester
>wanted. There is a one-to-one mapping between m/d/y format and there
>is a simple algorithm to calculate it which accounts for things like
>leap years. I suggest he look it up in "Astronomical Algorithms" by
>Jean Meeus or the equivalent to get acquainted with the concept.
>
>To start, here is simple C code which converts from m/d/y to Julian
>days. The return value is "double" but that's because we deal with
>fractional days here. Apologies, but I don't have the inverse
>calculation coded. One gotcha is that Julian days flip from one day
>to the next at *noon* instead of midnight.
>
>/* Function mdtotjd:
> Given a month m (1-12), day d (1-31), and year yr (example: 1996),
> Returns the (double precision) Julian day. */
>double mdtotjd(int m, double d, int yr)
>{
> int a, b;
> double jd;
> int a1, a2;
>
> if (m <= 2)
> {
> yr --;
> m += 12;
> }
> a = ((int)(yr/100));
> b = 2 - a + ((int)(0.25*a));
> a1 = ((int)(365.25*(4716.+yr)));
> a2 = ((int)(30.6001*(1.0+m)));
> jd = d + a1 + a2 + b - 1524.5;
> return (jd);
>}
>
>
>
>
thanks very much, I already had code with references to 1752 etc & it
seemed a bit excessive.
--
Robin Becker
Subject: Re: Day Number calculation
From: nmm1@cus.cam.ac.uk (Nick Maclaren)
Date: 30 Dec 1996 11:15:16 GMT
In article , Craig Markwardt writes:
|>
|> Then again, there's no need to re-invent the wheel. ...
No, but there is much greater chance of installing wheels correctly
if you know how they work!
I assume that you are aware that there are at least three aspects
of your code where it makes non-standard assumptions about the
arithmetic? One of them is quite commonly false, too.
Nick Maclaren,
University of Cambridge Computer Laboratory,
New Museums Site, Pembroke Street, Cambridge CB2 3QG, England.
Email: nmm1@cam.ac.uk
Tel.: +44 1223 334761 Fax: +44 1223 334679
Subject: Re: Day Number calculation
From: nmm1@cus.cam.ac.uk (Nick Maclaren)
Date: 30 Dec 1996 11:19:23 GMT
In article <5a82a3$1qp@news.rwth-aachen.de>, jarausch@numa1.igpm.rwth-aachen.de (Helmut Jarausch) writes:
|>
|> There is a quite short formula published by M. Keith und T. Craver
|> in J. Recreational Mathematics 1990
|>
|> (23*m/9 + d+4 + ( m < 3 ? (yt=y-1) : (yt=y)-2 )+ yt/4 - yt/100 + yt/400 )
It contains at least one gross breach of the C standard, and will
give wrong answers under some compilers.
Nick Maclaren,
University of Cambridge Computer Laboratory,
New Museums Site, Pembroke Street, Cambridge CB2 3QG, England.
Email: nmm1@cam.ac.uk
Tel.: +44 1223 334761 Fax: +44 1223 334679
Subject: Re: EXTRAORDINARY PI
From: bstan@datasync.com (BLStansbury)
Date: Tue, 31 Dec 1996 01:51:34 GMT
On 30 Dec 1996 10:16:13 -0600, Dave Dodson wrote:
>>So how much money $200/3? I don't care what base or notation you use,
>>you will not be able to give me a definitive answer.
>
>Sure I can! In base 3, the amount would be $2110.2, which seems pretty
>definitive to me.
>
Great, but we don't use base 3 in our monetary system. If you can find
a way to do this, then your answer would be definitive; otherwise, we
are just not quite getting there--which is my point.
BLS
Subject: Re: EXTRAORDINARY PI
From: juanvp@impsat1.com.ar (JuanVP)
Date: Tue, 31 Dec 1996 04:38:43 GMT
On Mon, 30 Dec 1996 02:58:01 GMT, bstan@datasync.com (BLStansbury)
wrote:
>On Sun, 29 Dec 1996 22:24:17 GMT, juanvp@impsat1.com.ar (JuanVP)
>wrote:
>
>Another number of the infinite persuasion. You can't draw a line with
>this exact measure, but you sure could come close. Close enough for
>any practical reason, but you will never quite get there.
No you can't, but I think that the most important problem is not
the measure but the tools you are using, those make it impossible,
perhaps with ideal tools of infinite precision working
in a continuos reality (I mean, not made by atoms) you could make
whatever line you please.
>>But as in reality, we cannot detect this differences, there is
>>no problem in using the ideal formulas as the error is not
>>very significant.
>I agree, but you have to admit that a an error occurs in an
>approximation--no matter how how insignificant.
Well, that is the reason for the existance of Numerical
Analysis, isn't it? Absolute error, relative error, and
the whole paraphernalia. This branch of maths deals with
the intrinsic limitations of the numerical representation
people is used to working with. As errors are cumulative
you should avoid working with approximations as much
as possible, only use it when there is no analytical
way of dealing with the problem.
>>Well, that would be 200/3 (the exact value) which is not
>>expressible in the standard decimal positional notation.
>So how much money $200/3? I don't care what base or notation you use,
>you will not be able to give me a definitive answer.
I don't know about you, but I've seen this argument time and time
again. I used to do it myself. People tend to see the numbers as the
only ligitimate way of representing quantities, the other expressions
such as series, integrals, fractions, etc are merely mathematical
fantasies. Well, representing a quantity as 200/3 is as legal
and legitimate as 66.66666.... or as Integral( 0, 1, 200*x^2 dx )
or as 6 * Sum( i, 0, oo, 10^(-n+1) ). The thing is that for some
problems some representation is better than other. I think the
problem (well, maybe is not a problem) is that people is taught from
day 1 to think in term of numbers, they equate maths=number crunching,
instead of maths=symbolical relations. In abstract algebra, even the
numbers lose their importance, they are just another set that
you can put into rings, groups, etc, not much different from a set of
sets, or a set of functions. The important things are the axiomatic
systems you can define. Numbers are just symbols that represent
quantities and there are some rules defined to combine them,
if you define other symbols for quantities and other rules of
combination to represent and operate with that symbols, and you
don't have contradictions, well, you can replace numbers and
conceptually you will be working on the same quantities.
Have you ever read how number sets are defined? How
the integers, the rationals and the reals can be defined
beginning from the positive integers? That is really
interesting, then this question about which is the most
natural representation of a number loses its meaning as
every representation is arbitrary and as legitimate as any other.
Juan
Subject: Linear Algebra C Source
From: "Lawrence K. Chilton"
Date: Mon, 30 Dec 1996 23:22:29 -0500
I am looking for a quality linear algebra library written in C which
provides source code for each routine. Hopefully it would
provide routines for solving Ax=b, eigensystems, etc. I am aware of
clapack, which I use in binary form on a Linux box, but it would be very
convenient to have modularized C source code to make the applications more
portable. I also use the Matlab engine library, which is very nice except
when the machine I want to use doesn't have Matlab. I would appreciate
hearing from anyone who has a package they can recommend. I prefer a
public domain package, but will also consider a reasonably priced (~$100
US) commercial library. Thanks in advance.
-Larry C.
lkchilt@math.umbc.edu
