HDTenEightyP/NetNews huggingface dataset:
From: petry@pythagoras.math.washington.edu (David Petry)
Newsgroups: sci.math
Subject: Re: Some musings on expensive journals
Date: 23 Jul 92 18:46:06 GMT
Article-I.D.: u.1992Jul23.184606.27323
Organization: University of Washington, Mathematics, Seattle

In article <BrtKAq.MH3@news.cso.uiuc.edu> sbrown@symcom.math.uiuc.edu (Scott Brown) writes:

>             There is a joy in wandering through a crowded
>library stacks with half an hour to kill, selecting a journal
>at random from a field of interest, and skimming the contents;
>many's the time I have discovered a useful tidbit in this
>fashion, or stumbled across some previously unmown to me 
>article which set me on a hunt for more information. Try
>as I might, I cannot reproduce this effect on-line,  ...


Researchers in the field of "virtual reality" here at the University
of Washington are working on solving this very problem.  I volunteered
for one of their experiments which I thought was quite fascinating.

They put a pair of goggles on me and a special glove, and all I had to
do was point my finger and I'd going flying off through their virtual
world, or turn my head to see what was around me.  The whole system was 
designed to make exploration natural.

The virtual world they had me exploring was called "Virtual Seattle" in
which I could fly into the Space Needle, or fly into the Kingdome, or 
go play with whales in the Puget Sound (I kid you not!). But they claimed 
one of their goals was to design a virtual library where users could have 
fun exploring the stacks.


David Petry
Newsgroups: sci.math
From: tycchow@riesz.mit.edu (Timothy Y. Chow)
Subject: Re: An interesting limit problem.
Organization: None.  This saves me from writing a disclaimer.
Date: Mon, 27 Jul 92 18:19:49 GMT

In article <Bs1xzu.DFp@news.cso.uiuc.edu> das50852@uxa.cso.uiuc.edu (dan) writes:
<mattm@lure.latrobe.edu.au writes:
<
<>                sin(tan x)    -    tan(sin x)
<>	lim  ----------------------------------  = ???
<>	x->0 arcsin(arctan x) - arctan(arcsin x)

By the way, how does Arnold solve this problem?
-- 
Tim Chow     tycchow@math.mit.edu
Where a calculator on the ENIAC is equipped with 18,000 vacuum tubes and weighs
30 tons, computers in the future may have only 1,000 vacuum tubes and weigh
only 1 1/2 tons.                               ---Popular Mechanics, March 1949
Newsgroups: sci.math
From: gerry@macadam.mpce.mq.edu.au (Gerry Myerson)
Subject: Re: Partition number question
Organization: ceNTRe for Number Theory Research
Date: Thu, 23 Jul 92 23:58:03 GMT

In article <4574@balrog.ctron.com>, wilson@web.ctron.com writes:
> 
> 
>     For n >= 0, let p(n) be the unrestricted partition number of n.
> 
>     1.  For all k >= 0, is it true that
> 
> 	a.  5  | p(5k+4)
> 	b.  7  | p(7k+5)
> 	c.  11 | p(11k+6)

Yes. These are due to Ramanujan.

>     2.  Given (1) is true, are there other triples (a > 0, b > 0, c >= 0)
> 	such that a | p(bk+c) for all k >= 0?

There are some with higher powers of 5, 7, and 11, e.g., 25 divides p(25k+24). 
There may be others--I'm no expert here. Latest edition of Hardy and Wright, 
The Theory of Numbers, should be a good place to start. 

>     3.  Why does 11 divide so many small partition numbers?
> -- 
> David W. Wilson (wilson@ctron.com)
> 
> Disclaimer: "Truth is just truth...You can't have opinions about truth."
> - Peter Schikele, introduction to P.D.Q. Bach's oratorio "The Seasonings."

Gerry Myerson
From: mckay@alcor.concordia.ca ( John Mckay )
Newsgroups: sci.math
Subject: Math or Maths
Date: 23 Jul 92 18:44:17 GMT
Organization: Concordia University, Montreal, Quebec
Originator: mckay@alcor


 The Greek is MATHEMATIKOS - when did the abbreviations first occur?
From: logan@qucis.queensu.ca (Adam Logan)
Newsgroups: sci.math
Subject: Algebraic Number Theory Textbooks
Summary: Looking for one
Date: 27 Jul 92 14:23:00 GMT
Organization: Computing & Information Science, Queen's University at Kingston

Does anyone know of a good introductory book on algebraic number theory?
E-mail, please; I'll summarize to the net.

Adam
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Journal prices (was: Gordon & Breach suit against AMS
Date: 24 Jul 1992 14:43:09 -0400
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu



This survey of 1988 journals (Notices AMS, vol 36, no. 9, page 1193--1198)
has some interesting items.  Prices range from 1.2 cents per thousand
characters (for the J. of the Amer. Statistical Assoc.) up to
93.5 cents per thousand characters (for Applicable Analysis).  On the
other hand the J. of the Amer. Statistical Assoc. had the
highest page charges of any journal ($65), while Applicable Analysis
had no page charges.  And the J. of the Amer. Statistical Assoc.
had the second-highest circulation (18,500), while Applicable Analysis
presumably had a very small circulation ("not available" from the publisher,
perhaps comparable to Semigroup Forum with a circulation of 500).
-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
Newsgroups: sci.math
From: Dave Dodson <dodson@convex.COM>
Subject: Re: Problem: find smallest box around points in 3D
Originator: dodson@bach.convex.com
Reply-To: dodson@convex.COM (Dave Dodson)
Organization: Engineering, CONVEX Computer Corp., Richardson, Tx., USA
Date: Fri, 24 Jul 1992 22:04:43 GMT
X-Disclaimer: This message was written by a user at CONVEX Computer
              Corp. The opinions expressed are those of the user and
              not necessarily those of CONVEX.

In article <BrvsH1.Myp@iai.kfk.de> harry@issun1.kfk.de writes:
>I have some points in 3D space and I want to find the smallest rectangular box
>which encloses these points. The orientation of the box in 3D is arbitrary (otherwise
>the problem would be trivial).
>Any hints, references, algorithms, code???
>Thank you!

Isn't this just an optimization problem?

You need a specific definition of what "the smallest rectangular box" is.
E.g., smallest in volume, total edge length, surface area, or combined length
and girth.  Then minimize the box size with respect to the 3 rotation angles.

----------------------------------------------------------------------

Dave Dodson		                             dodson@convex.COM
Convex Computer Corporation      Richardson, Texas      (214) 497-4234
Newsgroups: sci.math
From: andyc@eliot.uucp (Andrew Collins)
Subject: 3d Transformations
Keywords: Graphics
Organization: Systems Center, Inc., Reston, VA, USA
Distribution: na
Date: Fri, 24 Jul 1992 19:51:47 GMT


I'm looking for the transformation matrices used in converting
3-space coordinates into 2-space coordinates for doing graphics.
I'm also looking for the generalized transformation matrices that
rotate a 3-space point, translation, etc.
Thanks to anyone who replies.
Xref: sparky sci.math:9516 comp.sys.handhelds:1729 comp.sys.hp48:4013
From: kraai4712@iscsvax.uni.edu (jim kraai)
Newsgroups: sci.math,comp.sys.handhelds,comp.sys.hp48
Subject: Arbitrary-base calculation algorithms?
Date: 24 Jul 92 14:45:15 -0500
Organization: University of Northern Iowa

I've been thinking about writing a library of routines to do integer (and
later real, explicit rational and complex) math on my HP48sx handheld computer 
in arbitrary integer (and later real and complex) bases instead of just 
bases 2, 4, 8, 10,and 16.

I've finally run into a few situations where twelve digit integers are simply
not enough.  Later after real functions are implemented, this will spell out
into an arbitrary number of significant figures (anyone interested yet? ...
arbitrary number of sig-figs on a handheld?)

So, if anyone out there has already written such routines for the HP48
computer, that would be GREAT, let me know and I will grant you my eternal
gratitude!

But I doubt anyone has.

Next if:  If anyone knows of good references for algorithms for arithmetic
routines (multiplication, division, direct conversion between number bases
and later some of the real functions), I would much rather benefit from
someone else's experience than to reinvent another wheel.

Since this has probably not been of great concern in the last few centuries,
I doubt that many would want us to waste the bandwidth with references and
discussion of this.  Please use E-Mail.

If I get MANY requests, I will summarize on the net.
                                                     
Thank you in advance.                       
***************************************************************************
*jim kraai                 * WARNING, .SIG construction zone,             *
*kraai4712@iscsvax.uni.edu * decrease typing speed to 35 cps.             *
***************************************************************************
From: rose@fsu1.cc.fsu.edu (Kermit Rose)
Newsgroups: sci.math
Subject: Re: An interesting limit problem.
Date: 31 Jul 92 15:39:15 GMT
Reply-To: rose@fsu1.cc.fsu.edu
Organization: Florida State University
News-Software: VAX/VMS VNEWS 1.3-4

In article <1992Jul25.201805.14172@husc3.harvard.edu>, elkies@ramanujan.harvard.edu (Noam Elkies) writes...
>In article <1992Jul25.212844.1@lure.latrobe.edu.au>
>mattm@lure.latrobe.edu.au writes:
> 
>>A challenge to all mathematicians. A 100 years ago, this would probably have 
>>been solved fairly simply in a natural way, but can you? I think that this
>>problem was first posed by the Russian mathematician Arnold. Hope you find this
>>problem as interesting as I did when I first solved it.
>>
>>                sin(tan x)    -    tan(sin x)
>>	lim  ----------------------------------  = ???
>>	x->0 arcsin(arctan x) - arctan(arcsin x)
> 
>I don't know how they sould have done this 100 years ago.  One direct
>approach is to expand both numerator and denominator in Taylor series
>about x=0 and compare leading terms.  Since we're doing this today instead
>of 100 years ago, we can obtain the Taylor expansions instantaneously using
>a symbolic manipulation package.  We find that both numerator and denominator
>are -x^7/30+O(x^9), so the limit equals 1.  This also suggests that you
>*don't* want to find this limit using the L'Hospital rule, especially if
>you have to do all the derivatives by hand!
> 
>--Noam D. Elkies (elkies@zariski.harvard.edu)
>  Dept. of Mathematics, Harvard University

Indeed.  The fact that the limit is 1 suggests that we could have simplied 
the problem by taken the sin of the denominator.  Since z/sin(z) goes to 1 
as z goes to zero, we could proceed as follows.  Let z1 be the numerator in 
the above.  Let z2 be the denominator.   Find the limit of z1/sin(z2) as x 
goes to zero. This should be 1.  In any case, the limit of z1/z2 will be 
limit (z1/sin(z2) ) limit(sin(z2)/z2).


rose@fsu1.cc.fsu.edu          To be sure I see your response, use e-mail.
-----------------------------------------------------------------------
Be of good cheer, for it is much more fun than being depressed.
Newsgroups: sci.math
From: niall@nmsu.edu (Niall Graham)
Subject: Re: Calling all Generatingfunctionologists
Organization: Computing Research Lab
Distribution: sci
Date: Tue, 21 Jul 1992 19:04:50 GMT

Corrected Version (with thanks to Dan Hoey):

The following innocuous looking recurrence generates
sequence 300 in Sloane (1 1 1 2 3 6 11 24 47 103 ...):

c(1) = 1

      [n/2]
c(n) = sum  c(i)c(n-i)           where [n/2] is the FLOOR of n/2.
       i=1                      (sum is over partitions of n into 2 parts)

As far as I know, no generating function has been found for this
sequence, (as the ref in Sloane doesn't offer one).
Setting 
          C(x) = sum c(n)x^n   and  S(x) = sum c(n)^2 x^2n  
                                                      ****
we now seek a solution to  S = C(2-C).
Any takers?

Niall Graham             This isn't homework but I'd be delighted
nmg@c3.lanl.gov          if some brave soul would assign it as such :-).
Organization: University of Illinois at Chicago
Date: Wednesday, 29 Jul 1992 03:45:15 CDT
From: <U53644@uicvm.uic.edu>
Newsgroups: sci.math
Subject: Re: library cutbacks
Distribution: sci
 <1992Jul17.212740.16594@ariel.ec.usf.edu> <92210.010238U53644@uicvm.uic.edu>
 <1992Jul28.184718.24280@alchemy.chem.utoronto.ca>

While there may be some validity to the previous poster's point that some
pointless articles do get printed (today, I observed a series of articles by
one particular solid state research team that were almost duplicates of each
other - no, I won't mention who), that is really a seperate issue. Smaller
colleges may not be able to afford the high-priced journals that do exist.
Even if the smaller publications fold, the better known research teams aren't
likely to reduce the torrent of redundant articles. The lesser known ones
(and everyone is that at some point in his or her career) will simply get
squeezed out.

The more 'fringy' journals also provide one essential function - they provide
a forum for those who are not well viewed by the community at present to be
published in. While this means that cranks do occasionally get published, it
also means that those wrongly viewed as such have the opportunity to do so.
At one point, not so long in the past, I am told that the subject of
Mathematical Statistics was not viewed very highly at all. Had the Mathematical
community in general had the sort of tight control over who could publish and
who couldn't (that having a shortage of journal space would give it) this
entire subject might never have been developed.

Need I even point out how low Albert Einstein began his career in the eyes of
his research community ? To give a more recent example, remember the
professor at Purdue who proved the Bieberbach conjecture ? A combination of
a few mistaken proofs in the past, and (I'm told) an abrasive personality
(my apologies to Prof. de Branges if this rumor is unjustified) lead a
number of publishers to reject his proof without a second glance. The only
problem was, he had actually proved the thing !

So, when Mathematicians become perfect, and their judgements about the
research of others flawless and unbiased, then maybe I'll be comfortable with
this sort of restriction on publishing. Until then, some borderline journals
will be needed as a safety valve in case the consensus on someone's research
is seriously off.

And, my original point remains - funds grow scarce, money can be saved by
doing this - so why not ? (Don't do it with one of the cheaper printers,
though, the 'ink' wears off).

                                        Joseph B. Dunphy

Newsgroups: sci.math
From: ehobbs@nmt.edu (Eric Hobbs)
Subject: Angle on a sphere?
Organization: New Mexico Tech
Date: Thu, 23 Jul 1992 17:06:31 GMT


Here's a geometry question that I have:

Say I have two points on the surface of the Earth which are
sufficiently close enough to regard the line connecting
them as being straight and not an arc.  I need to find the
angle between the line connecting the two positions and the 
arc connecting the southernmost point to the north pole.

         N.Pole
  pt 1     |
      *    | 
       \   | <-- An arc
        \--|
         \ | <-- The angle
          \|
           *pt 2

I need a formula for the angle given the points' latitude and
longitude.

email any responses to

Eric A. Hobbs
ehobbs@jupiter.nmt.edu

Thanks.
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.math
Subject: It's turtles all the way up and spiders all the way down
Date: 21 Jul 92 15:01:44 GMT
Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Organization: The Wistar Institute of Anatomy and Biology
In-reply-to: fc03@ns1.cc.lehigh.edu (Frederick W. Chapman)

In article <1992Jul21.132554.152734@ns1.cc.lehigh.edu>, fc03@ns1 (Frederick W. Chapman) writes:
>If I am not mistaken, there are no *KNOWN* models for ZFC, standard or
>otherwise!  The consistency of ZFC set theory is not known; if a model
>for ZFC were to exist, then ZFC would be consistent.

Sure it's known.  Start with an inaccessible cardinal ...

>I can't speak for anyone else, but I find the notion that the
>consistency of ZFC has not yet been established to be the most
>singularly disturbing mathematical news to ever reach my ears,

I think most mathematicians consider it one of the most boring questions in
the world.  If ZFC were proved inconsistent tomorrow, they'd just laugh at
the set theorists, and get back to doing "real" mathematics.  Let someone
else figure out what they are "really" doing.  Relativistic quantum physics
has existed in a foundational void for half a century.

>given that ZFC is intended to serve as a foundation for the rest of
>mathematics.

That's leftover propaganda from the beginning of the century.  Set theory
has its own vitality, and like any good branch of mathematics, has things
to say about other branches.  The fact that the other branches often don't
like what set theory says about them ("Hey wait, what are you doing to my
conjecture? Stop that!") is not the same as being foundational.

Martin Davis tells a wonderful parable to begin his BAMS review of Donald
Monk MATHEMATICAL LOGIC.  There was a castle far away in the forests, and
in the deep basements and subbasements, there were thousands of thousands
of spiders, with ancient webs that had been there for unknown eons.  One
day, a humungous flood swept through the castle.  When it had passed, the
surviving spiders furiously respun their webs as fast as they could.  For
you see, they thought their webs were holding the castle up.

Cf Conway's Mathematical Liberation Movement, in his ONAG.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
From: columbus@strident.think.com (Michael Weiss)
Newsgroups: sci.math
Subject: Re: You know, the integers (Or: how do we know anything?)
Date: 21 Jul 92 19:55:11 GMT
	<1992Jul21.163533.15492@galois.mit.edu>
Organization: Thinking Machines Corporation, Cambridge MA, USA
NNTP-Posting-Host: strident.think.com
In-reply-to: jbaez@zermelo.mit.edu's message of 21 Jul 92 16:35:33 GMT

In article <1992Jul21.163533.15492@galois.mit.edu> jbaez@zermelo.mit.edu
(John C. Baez) writes: 

   [discussion of impossibility of proving the consistency of ZF omitted]

   I used to crave certainty and this sort of thing bugged me.  Now I'm
   fairly used to it -- as well as the fact (which once seemed disturbing)
   that no r.e. set of axioms about the integers will have a unique model
   up to elementary equivalence, and NO set of axioms about the integers
   will have a unique model up to isomorphism.   It irritates Torkel when I
   say that this means we're not quite sure what the "real" integers ARE.
   I think the sense in which I mean this was most clearly indicated by my
   game show in which one tried to figure out which mathematician was using
   the real integers and which two were fakes.

Well... you presumably believe that there are nonstandard models of Peano
arithmetic (say) because you accept the sort of set-theoretic reasoning
used to establish the Compactness theorem of first order logic.

You may say you interpret this reasoning in a purely formal
sense, as another game played on the checkerboard of ZFC.  Or you may
prefer a more hedonistic interpretation, where the symbols simply
transcribe a symphony we hear directly with our mathematical ears.

Either way, I assume you would accept the following two theorems
of ZFC on the same philosophical level:

    (1) For any consistent extension T of Peano arithmetic, there are
    	non-isomorphic models of T-- i.e., nonstandard models exist.

    (2) There are models of Peano arithmetic that can be imbedded in any
    	model of Peano arithmetic, and any two such models are
    	isomorphic. 

If I wanted to dot all the i's, I would define a category of models of PA
and state the imbedding and isomorphism properties "canonically", but since
we're among friends, I won't bother.

While the proof of (2) is trivial, I consider it quite adequate
justification for talking about the Real Integers.  We can single out a
minimal model of Peano arithmetic, and this model is unique up to
isomorphism in a natural way.  What more could one ask for?

Of course, stepping "outside the system", one can see that the model isn't
*really* unique.  But if you can do enough set theory to construct
nonstandard models, you can tell which are the honest-to-Kronecker
integers, and which are the fakes.
From: ttyytt@mixcom.com (Adam Costello)
Newsgroups: sci.math
Subject: Re: You know, the integers (was: Re: Stupid question about FLT)
Date: 23 Jul 92 04:59:00 GMT
Article-I.D.: mixcom.1992Jul23.045900.11889
Organization: Milwaukee Internet Xchange BBS, Milwaukee, WI U.S.A.

In article <1992Jul23.042250.10738@mixcom.com> ttyytt@mixcom.com (Adam Costello) writes:
>
>I'm sorry if I begin to sound like a broken record, but please remember
>that this is only true if you restrict your axioms to first-order
>languages.  The REAL integers _can_ be defined (to within isomorphism)
>in a second-order language.  Of course, this still doesn't get you a
>complete number theory.  Also, using a second-order language requires
>that one already knows what sets are.  If these still have to be defined,
>then we're back to the same problem.  It's inescapable.  Set theory is
>built on logic, but logic is defined in terms of sets.  People obviously
>knew and understood both concepts well, before either was formalized.

Oops, I didn't realize when I posted this that it had already been
covered quite well (much better than I have done).  Unfortunately, rn
is confused and wouldn't let me cancel it.  Sorry.

AMC
From: tacchan@flab.fujitsu.co.jp (Tatsuo KONDO)
Newsgroups: sci.math
Subject: [SPOILER] Re: Another puzzle
Date: 31 Jul 92 10:36:30 GMT
Organization: Fujitsu Laboratories Ltd., Kawasaki, Japan.
In-reply-to: ycchin@tartarus.uwa.edu.au's message of 30 Jul 92 07:34:26 GMT

In article <1992Jul30.073426.14230@uniwa.uwa.edu.au>
ycchin@tartarus.uwa.edu.au (Chin Yih Chong) writes:

:>  Try to crack this

Now please make sure you would like to see the answer :-)

The n-th number is 16 (in decimal system) written in (17-n)-ary
system.
# How expensive the unary system is ! :-)

A piece of cake.
Thank you for your greatest hint :-)
-----
	Tatsuo Kondo
	tacchan@flab.fujitsu.co.jp
From: brnstnd@nyu.edu (Dan Bernstein)
Newsgroups: sci.math
Subject: Re: You know, the integers (was: Re: Stupid question about FLT)
Date: 23 Jul 92 00:06:36 GMT
Organization: IR

In article <1992Jul22.094640.1@amherst.edu> djvelleman@amherst.edu writes:
>   This is not *at all* what mathematicians have always done.  If you took the
> syntactic objects to be the sets, then since there are only countably many
> syntactic objects, there would only be countably many sets.

You're equating the mathematical term ``the sets'' with some particular
collection which you think of as modelling the sets. What I am saying is
that the word ``set,'' for all mathematical purposes, is a purely
syntactic object which we manipulate according to certain rules. Any
semantics beyond that syntax is irrelevant. This has nothing to do with
the countability of some particular mental model you may have conjured
up of what ``the sets'' really ``are.''

---Dan
From: dmnhieu@riemann.math.purdue.edu (Duy-Minh NHIEU)
Newsgroups: sci.math
Subject: NEED SOME HELP on Stein's book: Singular integral and diff...
Date: 31 Jul 92 20:42:14 GMT
Reply-To: dmnhieu@riemann.math.purdue.edu (Duy-Minh NHIEU)
Organization: Purdue University


Hi:

   I am a beginner to harmonic analysis and I am currently reading professor
Stein's famous book: Singular integral and differentiability of functions.

   Since I am a beginner, I wish to understand it and I am filling in lots of
details to make things rigorous.  There are things that I don't know how he
arrive at and I am unable to derive despite some hints are given.  Unfortunately the professor that we have here and who is familiar on this subject is now
on vacation.  So, if you have read this book or if you are currently reading it,and you are patient and kind enough to answer my questions or wish to discuss
these subjects with me, please get in touch with me through emails.

my email address:  dmnhieu@math.purdue.edu


Thanks.