HDTenEightyP/NetNews huggingface dataset:
From: vm0h+@andrew.cmu.edu (Vincent J. Matsko)
Newsgroups: sci.math
Subject: Re: Polyhedron problem
Date: 12 Oct 92 11:51:00 GMT
Article-I.D.: andrew.MeqRQYq00VpaE4SUUf
Organization: Doctoral student, Mathematics, Carnegie Mellon, Pittsburgh, PA

A few questions:

1.  Must the polyhedra be convex?

2.  How did the problem come up?

At first glance, I offer the following answer to (4).  Select P as the
cuboctahderon, and Q as that polyhedron formed by rotating one-half of
the cuboctahedron 60 degrees through a hexagonal cross-section.  Faces
number 14.

Vince Matsko
Xref: sparky sci.math:12996 sci.physics:16274
From: gilligan@bldrdoc.gov (Jonathan M. Gilligan)
Newsgroups: sci.math,sci.physics
Subject: Re: Math/Science Shareware-Suggestions?
Date: 10 Oct 92 00:14:04 GMT
Followup-To: sci.math
Organization: National Institute of Standards and Technology

Two useful pieces of free software I use a lot are:

gnuplot for 2D and 3D graphics. gnuplot is available for MS-DOS, UNIX,
        and other OS's. You can get it by anonymous ftp (check archie
        for a site near you).

bibdb for managing bibliographic references under MSDOS. bibdb works
        with BibTeX-compatible bibliography files, so you can use it
        in conjunction with bibTeX and either LaTeX or TeX (there's an
        excellent free TeX implementation called emTeX for MSDOS and
        OS/2). emTeX and bibdb are both available at many sites by
        anonymous ftp (again, check archie for a site near you).
         
---Jon
-- 

Disclaimer --- The government probably disagrees with my opinions.
From: neal@ctd.comsat.com (Neal Becker)
Newsgroups: sci.math
Subject: Need c-callable math/stat lib - Recommendations?
Date: 9 Oct 92 17:54:19 GMT
Organization: COMSAT Labs
NNTP-Posting-Host: neal.ctd.comsat.com
X-Md4-Signature: 5905e4ece88c4a9c5f3107b649e86ddc

We need c-callable routines to do things like:
 * Eigenvector extraction
 * Singular Value Decomposition
 * Root Finding
 * Numerical Optimization
 * etc...

We have Mathematica, but the c-language interface is cumbersome (and
not too time-efficient!).  Anyone have any recommendations?

Thanks.
From: P.Samet@cs.ucl.ac.uk (Paul Samet)
Newsgroups: sci.math
Subject: Re: Question on numerical integration
Date: 9 Oct 92 18:49:58 GMT

There are several ways of integrating numerically over an infinite integral;

1)  Truncate the range, because the end s cannot contribute very much (as
suggested by someone else);

2)  Make a change of variable, to reduce the interval to a finite one, eg if
you want to go from 0 to oo, put x = exp(-y), so 0 <= y < oo becomes 
0 <= x <= 1 ;

3)  Use some type of interpolation formula, you get an infinite sum (which may
not be very different fromfirst method);

4) Use some sort of gaussian formula, with an appropriate weighting function.
Look for "Laguerre Integration" for 0 to oo, and "Hermite Integration" for -oo
to oo in textbooks on numerical methods.

The book "Numerical Integration" by P. J. Davis and P. Rabinowitz, published by
Blaisdell, 1967, gives a good account.

Paul Samet
From: hougen@vision.csl.uiuc.edu (Darrell Roy Hougen)
Newsgroups: sci.math
Subject: Re: Mattel says "Math is tough."
Date: 15 Oct 92 15:52:43 GMT
Organization: Center for Reliable and High-Performance Computing, University of Illinois at Urbana-Champaign
NNTP-Posting-Host: vision.csl.uiuc.edu

mbk@jacobi.ucsd.edu (Matt Kennel) writes:

*>Note that this is in contrast to the usual pop-psych generalization that
*>men are competitive loners vs cooperative social women, but appears to be 
*>true.

I just have to respond to this since I have done virtually all of the
math problems I have ever been assigned from gradeschool through
gradschool by myself.  I guess I fit the "pop-psych" stereotype pretty
well.

Darrell
Newsgroups: sci.math
From: deghare@daisy.uwaterloo.ca (Dave Hare)
Subject: Re: Looking for a slick proof
Organization: University of Waterloo
Date: Wed, 7 Oct 1992 13:58:38 GMT

In article <hunt.718423655@shy.umd.edu> hunt@shy.umd.edu (Brian Hunt) writes:
>bubai@matt.ksu.ksu.edu (P.Chatterjee) writes:
>>How does one prove that 2^n divides n*(n+1)*(n+2)*......*(2n) without     
>>having to resort to the 'odd' and 'even' induction? Any ideas?
>
>In fact 2^n divides (n+1)(n+2)...(2n), and it's the largest power of 2
>to do so.  Let [x] be the greatest integer less than or equal to x.
>Then the largest power of 2 which divides n! is
>
>[n/2] + [n/4] + [n/8] + ...
>
>(above is {# of multiples of 2 <= n} + {# of multiples of 4 <= n} + ...)
>while the largest power of 2 which divides (2n)! is
>
>[n] + [n/2] + [n/4] + ...
>
>so the largest power of 2 which divides (2n)!/n! is [n] = n.
>
>Brian Hunt
>hunt@ipst.umd.edu

I think this is easier:  (2n)! = 1*3*5*...*(2n-1)*2*4*6*...*(2n)
                               = 1*3*5*...*(2n-1)*2^n*n!
                   so (2n)!/n! = (n+1)*(n+2)*...*(2n) 
                               = 2^n * 1*3*5*...*(2n-1)

Dave Hare
Newsgroups: sci.math,sci.physics
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: How do you draw a straight line?
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Mon, 12 Oct 92 22:09:26 GMT

In article <1992Oct12.083128.29023@nuscc.nus.sg> scip1061@nuscc.nus.sg (Marc Paul Jozef) writes:
>jbaez@riesz.mit.edu (John C. Baez) writes:
>: In article <1992Oct8.115013.2533@nuscc.nus.sg> scip1061@nuscc.nus.sg (Marc Paul Jozef) writes:
>: >
>: > The spacetime metric of GR defines geodesics
>: >in spacetime. A string or a rod or whatever
>: >define world*sheets* in spacetime; `straightness'
>: >of a line has nothing to do with geodesics of GR.
>: 
>: While it's true that over time a rod covers a 2-dimensional surface
>: in spacetime, the closest thing there is to a straight (spacelike) line
>: in GR is a spacelike geodesic.

>    So what? 
>    The correspondence may be `close', but it can
>    never be precise (except in static spacetimes
>    which have a unique timelike Killing-field,
>    so that there is a unique 3+1 splitting of
>    spacetime).

So what?  Close is the best you can do when it comes to trying to 
find a reasonable notion of straight lines on a curved spacetime.
Close is good enough when it comes to the everyday notion of a "straight
line", which assumes that line is not too long compared to
characteristic length scale of the curvature.
From: hoey@AIC.NRL.Navy.Mil (Dan Hoey)
Newsgroups: sci.math
Subject: Re: Irrational?
Date: 7 Oct 92 21:09:12 GMT
Organization: Naval Research Laboratory, Washington, DC

The dictionary (I peeked) says that the Latin word _ratio_ means
reason, computation, or reasoning, from which we get the words ratio
and reason.  I believe that long division was a canonical example of
computation, from which come the words having to do with division, and
the rest of the words deal with thought process

So irrational numbers are numbers you can't get by dividing integers,
while irrational people are the ones who can't do the division.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil
From: fc03@ns1.cc.lehigh.edu (Frederick W. Chapman)
Newsgroups: sci.math
Subject: Re: Mattel says "Math is tough."
Date: 8 Oct 92 01:56:58 GMT
Organization: Lehigh University

In article <1992Oct5.165510.3841@cylink.COM>, tedh@cylink.COM (Ted
Hadley) writes:

>In article <1992Oct5.084002.25808@nuscc.nus.sg> matmcinn@nuscc.nus.sg (Mcinnes B T (Dr)) writes:
>>iltiss@owlnet.rice.edu (Steven Patrick Iltis) writes:
>>: I don't normally read this news group, so I apologize if this is not
>>: the appropriate place to post this. But I believe this is relevant.
>>: 
>>:         Mattel has just released a new product. A Barbie doll that says
>>: "Math is tough".
>>
>>What would you have her say?: 
>
>How about "Math is Important" or "Learn math well and get a good job as a
>[computer scientist | engineer | physicist | ...]"


I like that!  How about "Learn Mathematical Finance well and make
$1,000,000/year"?  :-)  

How about some positive reinforcement like "I *CAN* solve this math
problem!"  There's no substitute for self-confidence.

-- 

o ------------------------------------------------------------------------- o
|  Frederick W. Chapman, User Services, Computing Center, Lehigh University |
|    Campus Phone:  8-3218     Preferred E-mail Address:  fc03@Lehigh.Edu   | 
|         "The day after yesterday is the second-to-last day before         |
|               the rest of your life the day after tomorrow."              |
o ------------------------------------------------------------------------- o
Newsgroups: sci.math
From: sippy+@CS.CMU.EDU (Jay Sipelstein)
Subject: Re: Zeno
Reply-To: Jay.Sipelstein@cs.cmu.edu
Organization: School of Computer Science
Date: Fri, 9 Oct 1992 19:57:40 GMT


Zeno was lots more clever than people now give him credit.  Zeno 
really had four separate paradoxes.  Each of these makes a different 
assumption about the "granularity" of space and time.  The walk across
the room paradox makes the assumption that time has a smallest
subdivision (the time to make a step) and that space has no smallest
division (you may make smaller and smaller steps).  The paradox is intended
to show that this makes no sense.  The three others paradoxes each treat the
other cases of "quantized" and "non-quantized" space and time.  Taken 
together, these paradoxes were intended to show that the Greeks
really didn't understand these basic issues of the universe.  More 
precisely, they were intended as a rebuke to the Pythagoreans who 
had ridiculed Zeno's teacher Parmenides' teachings.   Zeno wanted to 
show that although Parmenides' ideas may have been strange, the
common wisdom was just as problematic.

In article <1992Oct8.000340.1@opie.bgsu.edu>, bc205cs@opie.bgsu.edu writes:
>Ok.  I don't read this newsgroup, but I know that if anyone can help me, it
>will ne you guys.  If this problem has already been addressed in this
>newsgroup, go ahead and flame me, but please give me some kind of answer.
>
>Here's the problem:  My Calculus II professer was discussing the sum of the
>infinite series 1/2 + 1/4 + 1/8, and so on.  He compared this to a famous
>problem of Zeno's, in which zeno said that if you are trying to get from point
>A to point B, and you go half of the remaining distance with each step, you
>will never make it to point B.  This seems like common sense, because with
>every step, you are not allowed to go more than half of the remaining distance.
>
>Well, my professor showed us that the sum of this as the number of steps
>approaches infinity is 1 -- To which my answer was, Great: you have to walk
>_forever_ to make it to point B.  Then he explained, 'Let's say that you can
>move 1 unit per minute.  The first step will take 1/2 minute, the next will
>take 1/4 minute, and so on.  So, it will take 1 minute to get from point A to
>point B!'

Your teacher violated the hypothesis that time is not infinitely divisible.
You should point him at the appropriate paradox (which I unfortunately
can't recall at the moment).

-- Jay Sipelstein
sipelstein@cs.cmu.edu
Newsgroups: sci.math,geometry.research
From: west@symcom.math.uiuc.edu (Douglas West)
Subject: Re: Incident: definition?
Organization: University of Illinois at Urbana
Date: Thu, 15 Oct 1992 03:39:08 GMT

orourke@sophia.smith.edu (Joseph O'Rourke) writes:

>Is there a generally-accepted definition of the term "incident" 
>that works in several contexts?  An arc of a graph (x,y) is 
>incident to the nodes x and y.  An edge of an arrangement of 
>lines is incident to a vertex if that vertex is an endpoint of 
>the closure of the edge.  Note in this last case, incidence does 
>not imply nonempty intersection, because arrangement edges
>are usually considered open segments.  Are adjacent faces of 
>a polytope considered incident?  I think not.

Since intersecting edges of a graph are called incident, why not
intersecting faces of a polytope (perhaps with high-dimensional intersection)?
  The membership relation between a collection of sets and their elements
is also called an incidence relation.
From: mkrogers@unix.amherst.edu (MICHAEL K ROGERS)
Newsgroups: sci.math
Subject: Re: Philosophical Foundations of Probability?
Date: 14 Oct 92 12:19:49 GMT
Organization: Amherst College
X-Newsreader: TIN [version 1.1 PL6]

jimmy donal wales (jwales@silver.ucs.indiana.edu) wrote:
: I'm looking for pointers to books or review articles on modern
: views of the philosophical foundations of probability theory.
: 
: --Jimbo

The closest thing I know of are two books by Ian Hacking,
"The Emergence of Probability" and "The Taming of Chance."
They're published by Cambridge, I think
From: jxh@math.ksu.edu (James C. Hu)
Newsgroups: sci.math
Subject: Re: Mattel on women
Date: 13 Oct 1992 19:54:52 -0500
Organization: Dept. of Mathematics, Kansas State University
NNTP-Posting-Host: hilbert.math.ksu.edu
Keywords: Targetting females once again.

crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
>James Hu  (jxh@math.ksu.edu) wrote:
>>...  Having your doll tell you "Math is hard" is not a very
>>encouraging sentiment.  It certainly doesn't help foster a desire to
>>learn math. 
>     Leaving aside the question of whether this particular doll is
>     impeding a desire to learn math, should dolls 'foster a desire
>     to learn math'?   Is this a desirable attribute in a doll?

If were up to me, I don't think I would have a doll say anything at
all.  Leave more for the child's imagination.  But, if a doll says
anything at all, I certainly don't want it to say something that
creates the impression that a subject is too hard to learn.

>     In any case, I suspect that the sales of such a doll would not
>     be stellar, for the simple reason that that is not the function of
>     dolls.

What function does telling children that math is hard serve?
-- 
James C. Hu (jxh@math.ksu.edu), 1804 Denholm Dr., Manhattan, KS 66502
I speak for me, the whole me, and nothing but for me.  So help me me.
Xref: sparky sci.math:13243 sci.physics:16567
From: marlowe@paul.rutgers.edu (Thomas Marlowe)
Newsgroups: sci.math,sci.physics
Subject: Re: "The Universe of MOTION" (crackpot index)
Summary: suggestions for index
Date: 15 Oct 92 12:35:20 GMT
Followup-To: sci.math
Organization: Rutgers Univ., New Brunswick, N.J.

I think that jb's otherwise praiseworthy index leaves out a few
considerations:

(1)	misciting of physical principles should be worth quite a bit,
	especially:
		the laws of thermodynamics
		the observer effect and wave function collapse
		the big bang, etc.

(2)	quotes out of context, especially if reposted, are a real killer.

(3)	citing of myth as scientific fact superseding observation (see Ted
	Holden's postings on talk.origins; also compare Velikovsky and van
	Daniken) should also pile on the points.

i leave it to the esteemed author of the index to assign points for these
infractions.  

(4)	on the other hand,

	capital letters should be permitted for section headers, as well as
	for the keywords BIBLIOGRAPHY, REFERENCES, FOOTNOTES, and KEYWORDS.

(5)	in fact, significant credit should be given for providing a
	reasonable bibliography, complete citations, etc., or for responding
	lucidly to criticism and corrections, for modifying claims in
	response to discussion, etc.

tom marlowe
From: litow@csd4.csd.uwm.edu
Newsgroups: sci.math
Subject: real exponential sums
X-OLD-Message-ID: <1behulINNm4e@uwm.edu>
Date: 13 Oct 1992 13:11:49 GMT

Let a_k = exp(k/N) where 0 <= k < N and let S1 and S2 be two sums
over two disjoint subsets of the a_k. By Lindemann's Thm, 
S1 - S2 can never vanish but is there a decent lower bound on
|S1 - S2| ? In particular, 1/N^O(1) ?

Please send email to


Bruce Litow
Computing Services Division
P.O. Box 413
Univ. Wisconsin-Milwaukee, Milwaukee, WI, 53201
litow@proclus.csd.uwm.edu
Newsgroups: rec.arts.sf.written
From: "milan rezac" <milan.rezac@canrem.com>
Subject: tolkien ?
Reply-To: "milan rezac" <milan.rezac@canrem.com>
Organization: Canada Remote Systems
Distribution: rec
Date: 13 Oct 92 08:27:43 EST

KD>I believe the story went something like this:

KD>The Tolkien mailing list was started about a year before The Big
KD>Split. This drained the original rec.arts.sf.lovers of Tolkien-related
KD>postings, so when the split arrived, very few could see the need for a
KD>special tolkien group.

Aww, damn!  I can't subscribe to lists.  Guess I'll have to talk to my sysop
again...and again...and again....  Is it (either of them, actually)
interesting?

KD>Also in general people was opposed to special-groups like Heinlein or
KD>Tolkien.

Well, perhaps it could have been called Middle-earth.  After all, there's
enough stuff there to keep us occupied for decades to come!

Thanks for the info,

Milan
---
  DeLuxe 5.60 #7817  BBSi ye rima, nan sera indo-ninya smen, ullume
--
Canada Remote Systems  - Toronto, Ontario
World's Largest PCBOARD System - 416-629-7000/629-7044
Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Zeno
Organization: Computer Science Department,  Stanford University.
Date: Thu, 8 Oct 1992 17:25:50 GMT

In article <1992Oct8.000340.1@opie.bgsu.edu> bc205cs@opie.bgsu.edu writes:
>Now here is my question:  The rule of the game is that you can only step half
>of the remaining distance on each step.  Well, if you are standing at Point B,
>that implies that you stepped onto point B.  If you stepped _onto_ point B,
>then you broke the rule!  You were only supposed to step _halfway_ to point B. 
>Therefore, Zeno's paradox holds, and the greatest minds are wrong.

I like this paradox.  It would appear to among the oldest surviving
instances of common sense conflicting with the logic of infinities and
infinitesimals.  As they say, something's gotta give.

To put the paradox in its best light, consider yourself walking slowly
but steadily the mile from A to B at one mile per hour.  Clearly you
reach B one hour after leaving A.  Yet your motion can also be
described as "stepping" halfway from A to B in half an hour, thence
half the remaining distance in quarter of an hour, and so on "for
ever."  At which of those steps did you reach B?  Surely none, so you
can never reach B.

Here's one way out of the paradox.  Implicit in your argument is that
you stepped onto point B from a preceding point.  But who says every
step has to have a predecessor?  Certainly the 1st step steps from A,
and so on with the 2nd and 3rd steps.  But how does that prove that
*every* step steps from a particular point?  In fact we can turn the
argument in the paradox around to make it into a simple proof of the
claim that *not every step is from a preceding point*, in particular
the step that lands you on B.

So what is the number of the step that lands on B?  Not 666, or 10!!,
or any finite integer.  Rather it is the first infinite integer, better
known as the smallest limit ordinal, namely omega.  If we include for
completeness a fictitious "step 0" landing us at A, then we have two
steps neither having a predecessor, unlike all the steps in between.
Of the two predecessor-less steps, step 0 was not a limit step, not
being the limit of anything, but step omega certainly was the limit of
the process of stepping towards B.  Omega is the first limit ordinal.

Future research.  Now that we've reconciled Zeno's two pictures of
travel from A to B, at least for those willing to accept the idea of a
step with an infinite number, how does each picture extend to travel on
beyond B?  The steady-motion picture is fine, but what about the
ordinal picture?  Do we go to higher ordinals, or what?  Or have we
simply stepped out of the frying pan into the fire by replacing one
paradox with another?  Left to the reader.

-- 
=================================================== In short, I am floundering
Vaughan Pratt   pratt@cs.Stanford.EDU  415-494-2545 around and don't take what
=================================================== I say seriously.
From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Newsgroups: sci.math
Subject: Re: Mattel on women
Keywords: Targetting females once again.
Date: 13 Oct 92 20:50:52 GMT
Organization: University of Virginia

In article <1bfasbINNft9@hilbert.math.ksu.edu> jxh@math.ksu.edu (James C. Hu) writes:
>crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
>>    Inanimate objects are greatly overrated 'role models'.  Usually,
>>    what mommy or daddy say and do are much more important.
>
>I don't think anyone disagrees with this sentiment.  However,
>stereotypes get reinforced, and this is a bad thing.  I think a child
>should be encouraged to learn.  Having your doll tell you "Math is
>hard" is not a very encouraging sentiment.  It certainly doesn't help
>foster a desire to learn math.

     Leaving aside the question of whether this particular doll is
     impeding a desire to learn math, should dolls 'foster a desire
     to learn math'?   Is this a desirable attribute in a doll?

     In any case, I suspect that the sales of such a doll would not
     be stellar, for the simple reason that that is not the function of
     dolls.

                               dale bass

-- 
C. R. Bass                                           crb7q@virginia.edu
Department of Mechanical and Aerospace Engineering
University of Virginia
Charlottesville, Virginia                            (804) 924-7926
Xref: sparky sci.math:13344 rec.music.classical:14439
From: RHASKINS@UMAB.BITNET (Robert Haskins)
Newsgroups: sci.math,rec.music.classical
Subject: Re: P.Glass and math? [Re: famous non-mathematicians who majored in ma
Date: 15 Oct 92 19:58:34 GMT
Article-I.D.: UMAB.92289.145834RHASKINS
 <1992Oct13.202553.7542@aio.jsc.nasa.gov>
 <1992Oct13.223043.16366@husc3.harvard.edu>
Organization: University of Maryland at Baltimore

Noam Elkies queries rec.music.classical for a verification of
Glass's having majored in math as an undergraduate.  He double-
majored in math and philosophy at the University of Chicago,
graduating, I believe, at the age of eighteen.  But for a composer
who made use of his math skills, the award, I think, should go to
Babbitt, who applied mathematical principles to the analysis
and creation of twelve-tone music.

Bob Haskins
Newsgroups: sci.math
From: ara@zurich.ai.mit.edu (Allan Adler)
Subject: Re: references on algebraic geometry
Organization: M.I.T. Artificial Intelligence Lab.
Date: Wed, 14 Oct 1992 19:31:31 GMT

Salmon's books were all reprinted by Chelsea. Some individual volumes might
be out of print but they are in libraries all over the place.

Actually, Salmon was a reverend and also wrote theological books. One
was on the doctrine of the infallibility of the church and the
other was an historical introduction to the books of the new testament.
I think the former was reprinted in 1952 in abridged form while the
latter has been out of print almost since the beginning of the 20th century.

Allan Adler
ara@altdorf.ai.mit.edu
Xref: sparky sci.math:13349 sci.physics:16679 sci.astro:10886 sci.bio:3613 sci.chem:3956 soc.men:17832 soc.women:17826
From: lal@cs.arizona.edu (The Morning Sun)
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,soc.men,soc.women
Subject: Re: Is Math Hard?
Date: 16 Oct 92 21:40:09 GMT
Followup-To: sci.math
Organization: U of Arizona CS Dept, Tucson

Math is Easy. Life is Hard.
Math is Boring. Life is Interesting.
Math is without. Life is within.
Math is Formal. Life is Informal.
Math is Incomplete. Life is Complete.