Subject: Re: Ugly Mathematics?
From: Dan Kotlow
Date: Mon, 06 Jan 1997 20:16:54 -0800
Marnix Klooster wrote:
>
>
> I don't agree that Van Gasteren's proof is awful, but I admit
> that the alternative proofs are nicer. Still, calling someone a
> non-mathematician because he or she gives an awful proof isn't
> really appropriate.
I wouldn't do that -- mathematicians prefer elegance, but they do
what they have to do to get a result (expecially when they don't
have tenure yet).
I tried very hard not to criticize anyone's taste in my response,
or to call anybody anything. I just said the issue was "called into
question". This is relevant [only] because (I repeat) this thread started out
being about what [professional] mathematicians think is elegant
and beautiful, so one wants to know whether a proposed standard is
that of a mathematician.
Besides, since when is "non-mathematician" an epithet?
> There are a number of text books (written by
> professional mathematicians, I presume) out there that contain
> ugly proofs where more elegant ones exist.
>
Proofs in textbooks are hopefully chosen to be instructive, not
necessarily elegant.
> Calling someone who does things the inelegant way a
> non-mathematician doesn't seem to be productive. Rather, point
> him or her the right way. (As you all have done by giving me
> alternative proofs. Thanks!)
>
> Incidentally, in "On the Shape of Mathematical Arguments" Van
> Gasteren gives a lot of advice on how to design notation and
> present proofs. Most of it is good advice, too. (At least, it
> helped me in writing clearer proofs.) Looking back, perhaps Van
> Gasteren has ignored her own advice in the proof that I posted.
>
I have not, of course, read the book. What moved me to reply
was the notion that someone holding themselves up as an authority
on proof construction would hold that proof to be superior to the
simplest available. It now occurs to me that that's probably not
her point -- that she was just using a simple example to
illustrate a proof technique, or to compare two, without regard
to whether better proofs were available for that particular
simple example.
Subject: Re: ESP ! propabiliies...???
From: "Robert E Sawyer"
Date: 5 Jan 1997 20:54:58 GMT
In each of your questions there is insufficient consideration of
how the (random) outcome is being generated:
SCN User wrote in article ...
|
| could some nice person give me the formula(s) for how to
| determine the probabilities for how likely it would be
| to guess the correct card in a standard Zeno (???) deck of
| ESP cards...
| deck consists of 25 cards, 5 kinds of cards
| star, cirlcle, square, cross, wavy lines.
|
Defining what constitutes a deck of cards doesn't define what it
means "to guess the correct card". Is the ESP candidate told what
the 5 possibilities are? Does the person merely draw one card from
the deck and then guess what it is? I suspect you are interested in
more complicated things, like laying out n cards from the deck and
then having the person guess and look at them in sequence, in which
case the later guesses have a greater (conditional) probability of
being correct.
| and a second problem:
| i have a program on my 48sx that displays a jiggling dot on the
| screen, what is the probability, over a fixed amount of time, that
| it will deviate from the center of the screen...???
| ( the program allows the user to hit various keys which un(?)-
| predictably fudge the random number generator )
|
Similarly, without defining how the random dot positions are being
generated (and what "unpredictably fudge" means), this question is
inadequately posed. Of course someone could make assumptions
(probably incorrectly) for you.
| and the third problem:
| i have another program on my 42 and 48 ( HP calculators )
| that play a game very much like mastermind
| but with 'bug-brain' the user tries to guess a 6 digit
| number, such that no two digits are the same
| and after each guess the program tells the user how
| many digits, both position & value, are correct
| with zero blind luck allowed, how many guess', given the
| most perfect guessing strategy, should be nesessary to guess all
| 6 digits...???
| ( i can get all 6 in 6 to 8 guess' (usually))
|
It isn't clear how the program responds to your six-digit guess.
Does it report something like
"2 digits are correct in both position & value", or
"1 digit is correct in position and 1 digit is correct in value",or
"the following digits are correct in both position & value ...", or
etc?
In any case, discounting "blind luck" means that you are not
allowing for "chance". But any guess you make to start with is
"by chance" -- you start with no reason to favor any digits over
others and could, by chance, hit upon a favorable choice.
--
Robert E Sawyer
soen@pacbell.net
Subject: Re: Question on Math Software
From: darthu1@grfn.org (David Arthur)
Date: 6 Jan 1997 20:59:30 GMT
Hey Rod...
Amemba me? I posted the same question a few weeks back. Never
figured out that "Granny" thing, but instead decided to give a rather
inexpensive & low-tech technique a try. I went to the public library and
picked up a textbook & workbook (luckily, they had the matching pair) for
the first year college algebra with trig course. Since it's review, I
figure I can go through two or three chapters a week... after about a
month or so, I'll move on to reviewing the geometry material... and then
on to pre-calc & calculus (the latter of which I still own my textbook
from the calc I course I took 10 years ago, which is convenient).
I figure, not only does this save me money, electricity, and
eyestrain, but it also get's me back in the habit of reading and working
out of a textbook. Of course, I'm lucky to have a public library with a
really nice math & science collection. Still, if you're already enrolled
in college, or live near the campus, the campus library might have some of
the old texts from the courses they offer.
Trying to save up to return to college myself, I know how much
that extra $40 or so can come in handy... I mean, that's a good down
payment on the average textbook today. :)
Good luck to ya.
--
David
Subject: Re: Evidence for God's Existence - TRY reading then Math
From: messenger.34@system.net (won_who_kares)
Date: Tue, 07 Jan 97 02:35:20 GMT
In article ,
Puck wrote:
>In article <32C3F92B.85D@heaven.net>, awareness seeker
> writes
>>> Ultimately the proof of GOD's existence must be
Mathematical in
>>> nature in order to transcend the Universe's Diversity
based on Laws
>>> derived from geometrical rules.~
>
> Hay! does that mean that geometry aint math ??
> Wow Cool Bollix!
>>>
>>> >> The formal proof will be given in the form of a
simple y=f(x) equation
>>> >> and the list of eight points used to derive it
>>> >> whose (X,Y) coordinates or differences include
these numbers
>>>
>>> >> (1/4, P^3, 1/3, Pi/2, P^2,"e","Pi", 3,4,5,8 and -1;
P = golden ratio )
>
> Golden ratio huh? Wasn't that to do with folding
bits of paper?
> But havent you over looked the "Golden numbers",
you know :-
> 11,22,3,25,6,17,28,9,20,1,12,23,4,15,26,7,18,29,
or when you
> learned your numerology did your teacher forget
about "epacts"?
>
> You see, a simple rule of math is that if you hope
to find the
> right answer, you must first have all the data.
> Even if your idea right, you would be unable to
make the
> calculation, because you would not risk adding
data that
> appeared contradictory
>
>>>
>>> >> Wow! linking all these seems divine to me from a
mathematical view.
>>>
>>> If you can still discount the above as a co-incidence,
>
> Not even that good.
>
>>and ignore its
>>> significance in the on-going debate about GOD;
>
> I can.
>
>> then pls excuse yourself.
>
> I'll do better than that , I'll excuse you, I mean
, you
> have given us a laugh.
> I would point out though that numerology, which is
what
> you are expounding on, comes under the general
heading of
> witchcraft.
>
>>>
>
My guess is that your knowledge about witchcraft
and science/math is about the same;
Subject: Re: algebra problem
From: ftww@cs.su.oz.au (Fred the Wonder Worm)
Date: 7 Jan 1997 13:39:27 +1100
In article <5am5f3$b3b@sun15.lri.fr>, Charles Delorme wrote:
>The equation in integers p^3-q^2=1 can be rewritten as
>(p-1)(p^2+p+1)=q^2.
>
>Let us discard the trivial solution q=0, p=1.
>
>Since p^2+p+1=3 modulo p-1, the gcd of p-1 and p^2+p+1
>is 1 or 3.
>
>If it is 1, then p-1 and p^2+p+1 must be squares, but
>if p>=1 then p^2no solution is obtained that way.
>
>If it is 3, then p-1 and p^2+p+1 must be 3 times a square.
>Let p=3t+1, with t>=0, then p^2+p+1=3(t^2+3t+1).
===========
This is incorrect. See below.
>But (t+1)^2no solution is obtained that way.
If p = 3t + 1, then p^2 + p + 1 = 3(3t^2 + 3t + 1). Continuing the way
you try to no longer works - you need to take into account that t is a
square to have any hope of success (for example, if t = 7, then p = 22
and p^2 + p + 1 = 507 = 3*13^2).
Cheers,
Geoff.
-------------------------------------------------------------------------------
Geoff Bailey (Fred the Wonder Worm) | Programmer by trade --
ftww@cs.su.oz.au | Gameplayer by vocation.
-------------------------------------------------------------------------------
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: Complex Question !
From: dik@cwi.nl (Dik T. Winter)
Date: Tue, 7 Jan 1997 02:31:32 GMT
In article <19970106165000.LAA29625@ladder01.news.aol.com> tleko@aol.com writes:
> e^z=(sqrt(R^2+I^2))*(e^(i*atan(I/R)))=(e^x)*(e^(i*atan(tan(y)))
> =(e^x)*(e^(i*y))=(e^x)*(cos(y)+i*sin(y))
Where do you find that atan(tan(y)) = y? Make a plot with MATLAB for
y ranging from say -10 to 10.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
Subject: re: Urgent Simple Question
From: dk058@cleveland.Freenet.Edu (Walter Nissen)
Date: 7 Jan 1997 02:56:21 GMT
Ricky Taylor writes:
> I need a name for the line / the divide by line,
> especially when it is used, with one olt of stuff over an other.
> Does this line have a name, if not, why not &
> Could some one suggest a logical name for it.
The ASCII character "/" has at least the following four names in
relatively common use:
slash
forward slash
virgule and
stroke.
"------------------" has at least the following four names in
relatively common use:
horizonal bar
fraction bar
bar and
vinculum.
I have seen some usages mixing the names.
You might try running these, and possibly the additional search terms
"glossary" and/or "aggregation" into a search engine and see if you can
pop up a few more.
Cheers.
Walter Nissen dk058@cleveland.freenet.edu
---
It's ok to add a parent; it's not ok to subtract one.
Subject: Re: 1997 is a prime year
From: Richard Mentock
Date: Tue, 07 Jan 1997 00:32:34 -0500
James Tuttle wrote:
>
> Denis Constales (whose reply I've irretrievably lost) replied to my
> original post in a self-styled "pedantic" fashion, saying in effect that
> I've failed to be politically correct; by writing about the calendar
> year 1997 I may have offended the Muslims, the Jews, the Chinese, and
> the freemasons, all of whom have their own calendars.
>
> To continue his thought, I guess I've also offended the Aztec, the
> Babylonians, and the ancient Egyptians, among others.
>
> He points out that all my analysis (of the primes contained in the
> number 1997) depends on the year of Christ's birth. To this I must
> respectfully take exception. My encyclopedia says that the western
> calendar now used secularly throughout the world was first suggested by
> a Christian monk in the year 525. He determined that Christ was born
> 753 years after Romulus and Remus founded Rome. Modern scholars dispute
> that, and it's now generally accepted that Christ was born in 4 BC. To
> compound the problem, the monk made no allowance for a year zero, so 1
> BC is immediately followed by 1 AD.
>
> It's worth noting here that the BC/AD system makes no use of negative
> numbers; rather, it uses natural numbers only. Newsgroup readers who
> are historians of mathematics may be able to help us out here ... I
> speculate that the monk may not have had the concepts of zero and
> negativity available to him. That may well have been true in the 6th
> century if these concepts were later introduced in the west from India
> or from the Islamic world.
>
> So my analysis of the number 1997 does not depend on when Christ was
> born; rather, it depends on current common usage and on the fact that we
> use a base-10 number system. It was the Babylonians, I think, who used
> a base-60 system, and if that had survived, the year 1997 in base-60
> would not be a 4-digit number (although it would still be prime ... I
> don't think the characteristic of being prime depends on the base of the
> number system).
>
> To continue Denis Constales' train of thought, since the present
> calendar was first suggested in 525, first-century Christians could not
> have known they were living in the first century, Julius Caesar could
> not have known it was 44 BC when Brutus got to him (although he did know
> it was the Ides of March), and separately, the Arawak were certainly
> surprised when Columbus told them the year was 1492.
>
> Also separately, I've been notified by e-mail that I made a typo in my
> original post ... 37 is a prime contained in 1373, not 27 as posted.
> Two people have reminded me that 1 is not a prime, nor is it composite.
> (I thought of a prime as a number you could only get by multiplying
> itself by 1; according to that definition, 1 is prime but 0 is not.)
>
> Finally, I failed to mention that in 1373, Wycliffe and Petrarch were
> forerunners of the Protestant Reformation and the early Italian
> Renaissance respectively, while in Korea, the 500-year Koryo dynasty was
> about to be replaced by the Yi dynasty that would endure for the next
> 500 years -- until the Russo-Japanese War brought it to an end in
> 1905-10.
I'm glad you cleared that up. I was worried.
--
D.
mentock@mindspring.com
http://www.mindspring.com/~mentock/index.htm
Subject: Re: x^y+y^x>=1
From: Jay Cox
Date: Mon, 06 Jan 1997 21:43:01 -0600
E.M. wrote:
>
> sfly wrote:
> >
> > who can poof that x^y+y^x>=1 with x,y>=0?
> > it's seem to be easy,but not..
> Why, for at least one of x, y >1 the theorem is obviuos. When
> both x,y<1 we have A = x^y + y^x = (1/p)^(1/q) + (1/q)^(1/p),
> where p = 1/x, q=1/y. Then A^(pq) > 1/p + 1/q > 1., Q.E.D.
I don't think you really proved that x^y + y^x is greater than one.
you basically said in that last statement that x+y is greater than 1.
what if x=y=.0005?
Subject: Re: Wlod about Inside
From: everest@netcom.com (Wlodzimierz Holsztynski)
Date: Tue, 7 Jan 1997 02:50:26 GMT
Ryan,
you had no reason to mention my name in your post.
Certainly no reason to have it in the subject line,
which is precisely what you did.
Now, since you did this, I'll justify it for you,
not that I wanted.
Once again you are writing about your piece without
even reposting it. Well...
Your post is a total bullshit. Keep bullshitting and you will
never learn anything about poetry. And yes, I looked at that
other poem you wanted me to look at. If possible it is even
worse. In your case, and in the case of most of authors, it's
better to write for a better reason than to settle an
argument in five minutes. Anyway, don't waste your time on
that junk, try to find out, if you care, what poetry is about,
then start your poetic carrier anew, afresh, with no reference
to what you do now. Don't try to be smart. Go for the utmost
simplicity.
Till then no more bandwidth from me about your texts.
(Dragging my name again will not provoke me :-)
Good luck,
Wlod
In article <32CF7F67.5267@scf.usc.edu>,
Ryan Cormney wrote:
>I wrote a response to someone else's comment to "Inside" that may
>interest you, maybe not. Question from me: how did you pull up my poem
>into your text? did you retype it or is there an easier way?
>
>Here is my response and his comment:(I'll retype it)
>
>He wrote: The erotic tension derivable from telling your girlfriend she
>gives you a woody is almost inexpressable. Almost.
>
>I wrote: The poem is not about her giving me a woody, but rather the
>fact that she is the only one that doesn't simply give me a woody. It's
>not about sex, the poem is about love! My penis is irrelevant for the
>overall meaning of the poem. It is the one way I can be physically
>inside her, but I was writing more along the lines of being mentally
>inside her. The definition of confide: rely on, to tell something
>confidentially, to tell private matters in confidence, etc. She is
>basically my support group, probably a lot like your psychiatrist( just
>kidding of course).
>
>There's more, but it pertains to something else he said(read it if you
>care to).
>
>I think this is what is original about this poem. The idea that I can
>be inside her without having sex, but get the pleasure of an emotional
>release(someone I can tell everything). SEX, is just a way to highlight
>the pleasure this confidence gives me.
>
>P.S. I think this was a bad poem to post for my first time. It means a
>lot to me and I have reacted unfairly to it's critism. But, I have
>learned a great deal in the past week since it was posted. I still do
>not think it is generic and maybe you won't after you read this.
>-RBC
Subject: Re: trig equation (tangents) solution?
From: mikea@ensoniq.com (M. Arnao)
Date: Tue, 07 Jan 97 03:25:23 GMT
In article <5art0h$s95@totara.its.vuw.ac.nz>, harper@kauri.vuw.ac.nz (John Harper) wrote:
>In article <5arodk$3ph@client3.news.psi.net>,
>M. Arnao wrote:
>
>> tan (x / 2) tan (K x / 2) = (tan (w / 2)) ^ 2
>>
>> 0 < x < pi, 0 < w < pi, K > 0, (w and K are known)
>>
>>it's not clear whether a closed-form solution exists, although
>>it seems that a unique solution does exist.
>
>Not unique if K large enough! Plot graph of LHS for 0
>John Harper Mathematics Dept. Victoria University Wellington New Zealand
oops: I failed to specify
K x < pi
Subject: Re: Why No Math and Science TV Station?
From: sbennett@gate.net (Stephen Bennett)
Date: Tue, 07 Jan 97 03:03:23 GMT
In article <5abh5j$l3h@news.fsu.edu>, jac@margit.scri.fsu.edu (Jim Carr) wrote:
>davk@netcom.com (David Kaufman) writes:
>> Why not have our best teachers on TV, showing how to teach all
>>grade levels in math and science?
>
> Why not have them in the classroom, actually doing it and serving as
> mentors to the apprentice science teachers? We already have some
> pretty good ones on TV, but it has to carry over into the schools to
> be effective as a learning tool.
In the late 50's the Louisville, Ky. Board of Education instituted a few closed
circuit TV classes, to try and place the best teachers in front of more
students. My favorite Jr. High School science teacher was selected as one of the
best. I was saddened to see how his best trait, interpersonal interaction with
students, was stiffled by the remoteness imposed by the camera. It was difficult
to feel the excitement he could infect a class with when he was in that little
box. It was frustrating not to be able to raise my hand and ask him directly for
a clarification..., to spark that ad lib interplay which always led to fresh
modes of explanation, and made the student feel part of the learning process,
not just a spectator.
I do see a roll for TV education, but a mass voluntary audience is not likely to
tune in to a classroom like show. Nova, Cosmos, Nature, and their like, do a
good job of educating, but they hide the experience inside a sense of
entertainment. The degree to which learning is achieved is not easily measured,
so good teacher in a controled classroom environment, with high standards set,
is the best proven way to increase student performance.
At least that's what I think,
Steve Bennett
Subject: Why is a finite set not an open set?
From: u13839@pauline.sdsc.edu (Jose Unpingco)
Date: 7 Jan 1997 06:42:24 GMT
hi,
This should be simple.
A = {1,2,3} is an example of a finite set. Now, for every point in
this set I can wrap a neighborhood about it of radius < 1/2. This
means that the neighborhood of the point contains only itself and the
neighborhood is a subset of A. Thus, every point is an interior point
and the set A is open.
What's wrong with this argument? There is not restriction of the
definition of neighborhood which says that it must contain a point
other than the point at its center.
I'm confused. Help.
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: Cardinals Was: Re: WHAT IS AN INTEGER (STUPID QUESTION)
From: mlerma@pythagoras.ma.utexas.edu (Miguel Lerma)
Date: 7 Jan 1997 04:26:41 GMT
Herman Rubin (hrubin@b.stat.purdue.edu) wrote:
> In article <5ap8rk$2e1@geraldo.cc.utexas.edu>,
> Miguel Lerma wrote:
[...]
> >Cardinals are particular cases of ordinals, and finite cardinals are
> >the same thing as finite ordinals.
> This is only with certain representations. It is certainly not the
> case without the Axiom of Choice.
Right, I assumed the Axiom of Choice.
I had a teacher who always replied to any discussion about the
consequences of rejecting the Axiom of Choice: "Don't be silly!,
the Axiom of Choice is obviously true!" To him those discussions
could have some academic interest, but they were not really
discussions about the actual properties of sets.
I have not that kind of "platonic" approach to Mathematics, but
I do use to assume the AC by default. I think Mathematics gets
unnecessarily weak without it.
Miguel A. Lerma
Subject: Re: Used Calculus books
From: dlv@bwalk.dm.com (Dr.Dimitri Vulis KOTM)
Date: Mon, 06 Jan 97 22:19:05 EST
James Tuttle writes:
> Jonathan Sussman wrote:
> >
> > My mother, a professor at Adelphi U in NY, recently passed away and
> > left hundreds of Calculus text books. Does anybody know a good "home"
> > for these books. It's a shame just to throw them out.
>
> Don't throw them out. If all else fails, get them to a used book
> dealer. Certainly there are people who'd like to have some of those
> books. Also, you might post a list of titles, authors, and dates.
It certainly would be a pity to throw out your mother's books.
1. If you make the list of them available, some folks in this newsgroup
might want to buy them. (I don't quite get it: are these hundreds of
copies of the same few texts? Are these different calculus texts?
Are there math books other than calculus texts?)
2. Many college math departments would be delighted to get a bunch of
math books as a gift. They'll put them someplace on the shelf to
gather dust... Perhaps an occasional adjunct will look for good
problems to assign to his student who already have the solutions
to the problems in the new texts. :-) Definitely beats rotting
in a landfill.
If all else fails, you can give them to a charity like Goodwill
Industries and have a tax deduction.
---
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 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: EXTRAORDINARY PI
From: Jay Cox
Date: Mon, 06 Jan 1997 22:48:26 -0600
JuanVP wrote:
>
> On Tue, 31 Dec 1996 19:43:50 GMT, bstan@datasync.com (BLStansbury)
> wrote:
>
> >If I ask 100 of my students to give me the area of a pi x pi square,
> >and each one of them gives me a right but different answer, which
> >value(s) should I accept? All of them right? And none of their answers
> >would be exactly the same.
>
> Well-defined maths problems like this have only 1 answer. You cannot
> have "right but different answers", if that were the case no relation
> containing products would be a function(!!). The only right answer is
> a pi^2 area,
wrong. let's see.. how many representations can I have of pi? of pi
squared? I think I'm going to let a tilde represent pi^2. And of course
I'm not going to forget using 4*(arcsin(1))^2. I could write it as ((sin
5)^2+(cos 5)^2)*5^0*(17/17)*pi*2*arcsin(1)*1! (note that ! normally has
presidence over multiplication.) There are an infinite amount of
"different" answers which would be equivalant. Of course, you could
give them zeros for being such smartasses as I :).
> but if you consider that the answer to this problem is
> right if it has for instance 3 significant digits or more, then any
> number in the interval [9.869, 9.870] would be considered correct, but
> bear in mind that every number in the interval but 1 (Pi^2) is
> only an approximation of the answer with an error less than 10^-3.
>
> Juan
Subject: Re: What is binary?? (or: how do you explain it to an idiot?)
From: jonl@cs.pdx.edu (Jon P LeVitre)
Date: 6 Jan 1997 09:12:51 -0800
mark@olm.net (Mark) writes:
>For some reason, I just can't seem to get the meaning of binary!
>I first noticed binary when I first got into computers. I noticed how
>everything was based on "two's", like 2, 4, 8, 16, 32, 64
>(i.e. 16 bit, 32 bit software etc.)
>So I went and got a book at the library and it said, binary is not
>based on 10, but on two!
>What really freaked me out, was that instead of "1" and "2", it had a
>big string of numbers like:
>(pardon me)
>001010110000011101001101001010101010101111
>I guess this means one!
No, one is 00000001
>and
>010101010010111110101010101010011010101010
>I guess this means two!
No, two is 00000010
A good way to think of numbers in different bases is to
remember that a number like 111 is 100 + 10 + 1. In base
ten these are one hundred, ten and one. In binary (base 2)
these are four, two and one (aka 2^2, 2^1, and 2^0).
Here are a few more powers of 2
number base2
00001000 8
00010000 16
00100000 32
01000000 64
10000000 128
So 10011011 is 128+16+8+2+1 = 155. I'll leave it up to you to
calculate up to 2^48 (which is what you'll need to convert the
numbers above)
>so now, what I don't understand, is how a person is suppossed to add
>these together? for instance (I'll snip it down some)
>1 + 2 = 3
>but in binary, it would be:
>010110
>011101 +
>---------------
>021211
>and yet I thought it had to have all 0's and 1's?
It's important to remember that (in binary) 1 + 1 = 10 (because
there is no '2'). After that just carry the same way that you
do in base 10.
111 (carry digits)
010110
011101 +
---------------
110011
Hope this helps
jonl
Subject: Re: Do you know any tricks to help a lightning (mental) calculator?
From: Jay Cox
Date: Mon, 06 Jan 1997 23:31:23 -0600
Jason Harrison wrote:
>
> Please email me any tricks you know to assist lightning mental
> calculations. For example, to square any two-digit number, the following
> pattern is very helpful:
>
> e.g. 77^2
>
> to solve this (77 squared), round 77 to the nearest 10 (i.e., 80). Since
> that number is 3 away from 77, also SUBTRACT 3 from 77 (i.e., 74). Now
> multiply 74 * 80 (much easier to do that 77^2) (= 5600 + 320 = 5920).
> Finally, since these two factors were 3 away from the original 77, we
> square that difference (3^2=9) and add it to our 74 * 80 product. Thus
> the answer is 5929. This pattern of course always works and of course is
> especially simple when multiplying squares ending in 5s (eg 45^2 = 40*50
> + 5^2 = 2000 + 25 = 2025).
>
> There,
>
> if you know any more of these PLEASE email me. I already got the calendar
> trick, cubes, and several others but I want to know MORE.
Normally I use a cross multiplication method.
for the multiplication of 2 digit numbers you go like this
a b
| x |
c d
the answer would be d*b+ 10*(a*d +b*c) +100*a*c. You use a similar
method with 3+ digit numbers, and then you can use a cross-out nines to
check if your wrong (othat method is only accurate 8/9 of the time,
though).
I've heard of another nice algorithm for division, but somehow I never
did get to talking with my professor about it to really understand how
to use it.
I can't say I'm a expert on this. I just this year got somewhat
interested in mental computation. But hope that method helps. I know
that using the cross multiplication method I can actually do fairly
easily 3 digit multipication in my head (of course, I haven't practiced
like I need to, so therefore my answers may be wrong).
I'd sure like to know where you got that calendar.
Jay
>
> --
> jwh@unixg.ubc.ca
> It is now safe to shut off your computer.
Subject: Re: Infinitude of Primes in P-adics
From: Archimedes.Plutonium@dartmouth.edu (Archimedes Plutonium)
Date: 7 Jan 1997 02:51:01 GMT
In article <5asb6a$ma6$1@dartvax.dartmouth.edu>
Archimedes.Plutonium@dartmouth.edu (Archimedes Plutonium) writes:
> The function, for example , one branch of the tangent function is a
> algebraic Field. What are the other parts of the graph (the points
> underneath the tangent function as an algebraic structure. That is 2nd
> dimensional but in third dimension (only existing true dimension) the
> surface of a sphere would be the 2-adics and all of its composite
> 2-adic associates would form the inside of this 2-adic sphere surface.
Perhaps the n-adics the composite adics such as 6-adics , 10-adics,
14-adics ad infinitum are not the inside of a sphere. Perhaps they are
the outside of the sphere surface that is the 2-adics. Thereby, the
prime adic forms a Riemannian sphere surface and the associated
composite adics of that particular prime adic forms the outer regions
of that sphere surface caused by that prime-adic.
Then, the Doubly Infinites of the 2-adics forms the disc or inside of
the 2-adic sphere.
The 2-adics forms a Riemannian sphere surface, the 2-adic composite
associated adics of 6-adics etc forms the outer regions of that 2-adic
surface and is still Riemannian geometry.
The 2-adics Doubly Infinite where the leftward string is 2-adics
forms a disc inside the 2-adic Riemannian sphere and is Lobachevskian
geometry.
Subject: Re: Infinitude of Primes in P-adics
From: Archimedes.Plutonium@dartmouth.edu (Archimedes Plutonium)
Date: 7 Jan 1997 02:08:10 GMT
In article
dik@cwi.nl (Dik T. Winter) writes:
> > Let me recap here some facts :
> > p-adics form a field
>
> No. Obviously, if there *are* primes you do not have a field.
3-adics form a field, 5-adics form a field
any p-adic where p is prime forms a field
> > (1) the conglomeration of P-adics as this set
> > {2-adics, 3-adics, 5-adics, 7-adics, ....
>
> I am still extremely unsure what your definition of "conglomerate" is.
> Suppose a is a 2-adic and b a 3-adic; how do you define a+b?
Conglomeration = set. Set of all prime-adics {2-adics, 3-adics, ....}
Instead of conglomeration, I am going to define a branch of the
tangent function, taking a branch of the tangent function that curve is
the 2-adics, and the next branch will be the 3-adics, another the
5-adics and so on. All of the points of the 2-adic branch of the
tangent function will be 2-adic numbers. But this is not the big deal
in this program. Now in this graph of the tangent function, each branch
is a function , but now consider all the points in that specific branch
itself, then all of those points do not make a function. Correspond all
of those points with the prime-associated-n-adic. Here are some prime
associated n adics for the 2-adics 6-adics, 10-adics, 14-adics etc.
Why do this program? Answer is threefold. To connect adics with
geometry. And another reason is to find, or discover what the
composite-adics are. Third reason: in a way, algebraic structures
fields, rings, groups should be connected with simply a function and a
graph.
The function, for example , one branch of the tangent function is a
algebraic Field. What are the other parts of the graph (the points
underneath the tangent function as an algebraic structure. That is 2nd
dimensional but in third dimension (only existing true dimension) the
surface of a sphere would be the 2-adics and all of its composite
2-adic associates would form the inside of this 2-adic sphere surface.
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
