Subject: Re: EXTRAORDINARY PI
From: Jay Cox
Date: Mon, 06 Jan 1997 22:09:49 -0600
BLStansbury wrote:
>
> On 31 Dec 1996 18:40:25 GMT, caj@sherlock.math.niu.edu (Xcott Craver)
> wrote:
>
> >Sure. How about 6*arcsin(1/2)?
> Approximation to pi.
>
> > If you respond to "I
> >bumped into Scott Craverpi the other day" with, "NO YOU DIDN'T!!
> >YOU JUST BUMPED INTO AN APPROXIMATION OF Scott Craverpi!!", then
> >you are probably not clear on the use-mention distinction,
> >between the name of something and its value. This is what you
> >seem to be displaying here.
> Cute.
>
> >We will never be able to do base-10 arithmetic with the
> >exact value of PI, because we would have to write PI in base-10,
> >which would require an infinite number of digits. But mathematics
> >IS NOT COMPUTATION. We use the exact value of PI in mathematics.
> >We just don't restrict ourselves to writing answers entirely in
> >decimal, get it? A circle of radius 2 has area 4pi, exactly.
> But a square can't have an area of exactly 4pi unless its a circle.
did you forget about the square roots? if the side is 2 * the square
root of pi, then that square has an area of exactly 4*pi. The reason we
do this is rather basically for bookkeeping reasons; it's much easier to
calculate Pi*Pi*Pi=Pi^3 than to find (22/7)^3 or (3.14)^3.
Subject: Re: EXTRAORDINARY PI
From: Jay Cox
Date: Mon, 06 Jan 1997 22:28:05 -0600
BLStansbury wrote:
>
> On Wed, 01 Jan 1997 01:11:46 GMT, juanvp@impsat1.com.ar (JuanVP)
> wrote:
>
> >>>Sure. How about 6*arcsin(1/2)?
> >>Approximation to pi.
> >No, it's the real McCoy. :)
> I am sorry, you are correct. I meant to say it is an infinite
> number--like pi.
>
> >>>We just don't restrict ourselves to writing answers entirely in
> >>>decimal, get it? A circle of radius 2 has area 4pi, exactly.
> >>But a square can't have an area of exactly 4pi unless its a circle.
> >Is this a flame bait or just a lapsus?
> Probably just flame bait.
>
> >>>Again, just because we can't write it in base-10 doesn't mean we
> >>>can't use its exact value.
> >>You can't write its exact value in any base.
> >How about in base Pi? It would be 10, wouldn't it?
> Two things: if you are going to use pi as the base for a number
> system, then you are going to either use the exact value of pi as it
> is determined by the relation of the radius and area of a circle OR
> you are not.
>
> In the first case, there is not an exact value for pi yet.
yet? Decimals are symbols which represents numbers. pi is a symbol
that represents a number. for the purposes of computation in formulas,
"pi" is the exact value of the circumference of a circle devided by its
diameter. Division, of course, implies the usage of a base etc, but
really, we use the symbol pi to simplify calculations. We can figure up
all the esentially easy calculations and then multiply by by our
approximation of pi.
Also, remember that 6*arcsin(1/2) is equivalant to pi. We could also
use any sort of notation to symbolize pi, like "Jay'sFormulaforpiwith
anynumberusedasaparameter(473)." your acting as if all exact values have
to be so that they can be written with a finite number of decimals.
>
> In the second case, you can use whatever value of pi you wish to use,
> but you could not "circle the square" to get the same area exactly.
if you use a decimal value, of course. I hate those oversimplifications
like "square the circle."
Subject: Re: Need to handle Big Matrix (800x800) to use optimization algorith
From: dlv@bwalk.dm.com (Dr.Dimitri Vulis KOTM)
Date: Mon, 06 Jan 97 22:32:38 EST
benigno writes:
> Hi,
> I need to handle Big matrix of around 800 x 800 to implement
> some optimization algorithms, I would use C++ libraries if
> possible to use on BorlandC++ 4.5, but if there is any shareware
> program that allows me to do it, it would be fine.. Matlab
> doesnt give me enough memory to allow me do it.
It's "only" 640,000 entries... :-)
If a lot of these entries are zeroes or repetitions, then there are
C++ classes out there for handling "sparse matrices". (I think
Rogue Wave sells something, even.)
However your bigger problem is not fitting this matrix in memory, but
doing the actual computations with it. It may take a very long time
on a personal computer.
---
Dr.Dimitri Vulis KOTM
Brighton Beach Boardwalk BBS, Forest Hills, N.Y.: +1-718-261-2013, 14.4Kbps
Subject: Re: Need to handle Big Matrix (800x800) to use optimization algorithms
From: zaykin@stat.ncsu.edu (Dmitri Zaykin)
Date: 3 Jan 1997 06:42:11 GMT
benigno wrote:
> I need to handle Big matrix of around 800 x 800 to implement
> some optimization algorithms, I would use C++ libraries if
> possible to use on BorlandC++ 4.5, but if there is any shareware
> program that allows me to do it, it would be fine.. Matlab
> doesnt give me enough memory to allow me do it.
You can use any (C/C++) matrix library for such matrix size if your
executable target is 32 bit. However, if you use 16 bit, you should pay
attention whether matrices are represented as 2D or one-dimensional
arrays internally. Some very good libraries (such as
ftp://tahi.isor.vuw.ac.nz/pub/newmat08/) have their matrices
represented as a single piece of memory (i.e. 1D), which makes them not
suitable for the calculations of that large size when your executable
is compiled 16 bit. You have an alternative though: get the latest
Borland C++ (5.*) -- it can do "console" 32 bits targets with all
C/C++ I/O functions/operators, or better yet, switch to Linux!
Dmitri
