HDTenEightyP/NetNews huggingface dataset:
From: mab@wdl39.wdl.loral.com (Mark A Biggar)
Newsgroups: sci.math
Subject: Re: p prime, p divides ab => pdivides a or b
Date: 2 Sep 92 20:40:39 GMT
Organization: Loral Western Development Labs

In article <Btyo8q.E63@ux1.cso.uiuc.edu> ceblair@ux1.cso.uiuc.edu (Charles Blair) writes:
>   My recollection is that a number theory course I took presented
>this as a difficult result, only proved after doing some stuff
>with the Euclidean algorithm.  Is there a proof which avoids that?

Let S be the set of prime factors of ab ignoring powers and Sa and Sb be
similar sets for a and b respectivly.  Now p is an element of S, therefor
is is an element of Sa union Sb = S, therefore is is a element of
Sa or Sb by the definition of set union, therefore p|a or p|b QED.
This all works because of the unique factorization theory.

--
Mark Biggar
mab@wdl1.wdl.loral.com
From: mueller@schaefer.math.wisc.edu (Carl Douglas Mueller)
Subject: Homework Problems
Reply-To: mueller@math.wisc.edu
Organization: Univ. of Wisconsin Dept. of Mathematics
Distribution: na
Date: Sun, 30 Aug 92 13:53:28 GMT

With a new school year at hand (and not having been a regular reader of this
group in the past), I wonder if there is a rule on this group that we do not
help people with things that look too much like homework problems.  Or, do
we simply trust that people will not ask about problems that are to be part
of their grade in a course.

        Just Wondering.
                           Carl Mueller (mueller@math.wisc.edu)

Newsgroups: sci.math
From: news@massey.ac.nz (USENET News System)
Subject: Re: Calendar (NEW)
Organization: Massey University
Date: Wed, 26 Aug 92 21:40:27 GMT

In article <1992Aug26.182823.3475@nas.nasa.gov>, asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:
> 
> In article <6xmpb6wb@csv.warwick.ac.uk> mareg@warwick.ac.uk (Dr D F Holt) writes:
> >In article <2906@ucl-cs.uucp> P.Samet@cs.ucl.ac.uk (Paul Samet) writes:
> >>Actually Easter is the first Sunday following the first full moon which occurs
>   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> >>on or after March 21 (Spring equinox), not March 20, as claimed.
> >>
> >
> >Surely 'on or after March 21' is the same as 'after March 20'. But am I
> >correct in thinking that if the full moon occurs on a Sunday then one has
> >to wait for the following Sunday? So the earliest possible date for Easter
> >is presumably March 22.
> >
> >Derek Holt.
> ----------------------------------------------------------------------------
> Although the date of Easter is usually described this way, the
> *actual* date of Easter is, I believe, based on traditional but
> now outdated calculations, which once in a great while disagree with
> modern, "correct" astronomical calculations.
> 
> Can anyone confirm or refute this?
> 
I would guess that you are right. The vernal equinox is not a day but the
instant in time when the sun crosses the plane of the equator (or for pedants,
when the plane of the equator contains the sun). ((Does this always happen on
21st March? I had an idea that it was sometimes on the 22nd)).
Similarly, the full moon is an instant in time. Then the full moon could
occur a few seconds before or after the vernal equinox, making Easter a
month later in the former case. I suspect that the calendar is based on only
working to the nearest day.

A book which discusses Easter quite well is "An Informal Introduction
to Algol 68". It makes the point that the date for Easter was specifically
chosen to avoid coinciding with the passover (but, nevertheless, this does
happen occasionally).
From: jtrsmith@garnet.berkeley.edu ()
Newsgroups: sci.math
Subject: A question on Laplace equation
Date: 3 Sep 1992 17:28:37 GMT
Organization: University of California, Berkeley
Distribution: world
NNTP-Posting-Host: garnet.berkeley.edu

Hi, Sirs,
I have a question about if a Laplace equation 

       div grad T = 0       in a smooth enough domain,

is well-posed under following boundary condition:

    - dT/dn = a ( T*T*T*T - c),  on the domain boundary, 

    (note: T*T*T*T means T to the fourth power.)
where n is in the direction of outward unit normal along the boundary,
a, c is constant, and  a>0.

This boundary is equivalent to a radiation along boundary; heat
conducted from the domain is radiated to out side environment.

Can anybody prove that the problem is well-posed? 

If possible, please reply to this account directly. Thanks.

JTR Smith
From: rcollins@cs.umass.edu (Bob Collins)
Newsgroups: sci.math
Subject: Re: HELP!! Inscribed Circle Problem
Date: 29 Aug 92 01:42:00 GMT
Reply-To: RCollins@cs.umass.edu
Organization: CS Dept, UMass at Amherst
News-Software: VAX/VMS VNEWS 1.41

> Madeleine Thomas:
>   ... "math whizzes" ...  [goes on to propose an interesting problem]"

> Bob Collins:
>   ...[what was hopefully a relevant solution]...
>   "As for the term 'math whiz'... kind of derogatory."

> Madeleine Thomas:
>   paraphrase: "Sorry."

> Dan Asimov:
>   ..."there is *nothing* to worry [be sorry] about"...


In an attempt to end this unfortunate spinoff right here, and
because my note reading system doesn't provide me enough information
to piece together Madeleine's email address for a personal reply:

Madeleine, if anyone has been offensive here it is I who have 
offended you.  I am truly sorry if that offhand remark at the
end of my posting has caused you any discomfort.  My Webster's
dictionary assures me that "whiz" is a derivative of "wizard",
and gives, as an example of correct usage, "a whiz at math"!!!!
I'm sorry... I'm an idiot... please don't hold it against me.

I did enjoy the problem you posted, since I have done some work
involving spatial data retrieval on the sphere.  If I can ever
be of any assistance in this area, please feel free to contact
me via email (and I promise not to be an idiot again).

In all sincerity,
  --Bob Collins
  --RCollins@cs.umass.edu
From: moon@mozart.llnl.gov (Steven Moon)
Newsgroups: sci.math
Subject: Re: Problematic smurfs! Spolier
Keywords: smurfs
Date: 31 Aug 92 16:41:56 GMT
Organization: Lawrence Livermore National Laboratory

In article <94952@bu.edu>, spacefox@acs.bu.edu (Godfrey Degamo) writes:
|> -------------------------------------------------------------------------------
|>      A group of 1000 smurfs wear either a red or blue hat on their head.
|> They can only wear one color. The color hat on their head is known to all, but
|> the wearer.  The wearer of the hat has no means whatsoever for obtaining the
|> color of his hat.  It is never the case that all 1000 smurfs will wear
|> the same color hat.
|>      One day the mayor, not apart of the 1000 smurfs, decides to call a
|> town meeting.  All 1000 smurfs are gathered into the town hall.  The mayor
|> is not wearing a hat.  During the meeting, the mayor asks that all the
|> smurfs wearing red hats to stand up.
|>      There is a bit of commotion in the crowd, but no one stands up.
|>      The mayor requests the same demand a bit more sternly.
|>      Again, commotion, but no one stands up.
|>      The mayor, irate, demands the red hatted smurfs to stand up.
|>      Then, a certain amount of smurfs rise.
|> 
|> find:
|>      The exact amount of smurfs that rise.  
|>          (Hint: This number will be greater than one.)
|>      The color of the hats of the smurfs that rise.
|> 
|> more importantly,
|>      Explain how you deduced your answer.
|> -------------------------------------------------------------------------------
|> 
|> I hope that's clear enough for you.  If not, post, but all the necessary
|> information has been supplied.  I'll only answer questions about my poor
|> grammar and writing style.  Put on your smurf hats and think!
|> 
|> 
|>                                         -G. Degamo,
|>                                          spacefox@acs.bu.edu

This problem is a variation of one I heard some time ago.
It is with three individuals each wearing one of five hats, three
brown two black.  They are standing in a line and can only see 
those in front of them.  The last in line can see the color of
the hats of the two in front of him.  The second in line can see
the only the one in front of him and the first in line can't see
anyones hat.  They can't talk or leave untill they are certain what
color hat they have on.  After a long time the person first in
line leaves.  What color hat does he have on.

.steve





Spolier




- What we know -
out of 1000 hats >= 2 are red.
each Smurf can see the other 999 hats.  
since the mayor was singling these red hat wearers out we
suspect they are in the minority.
since the mayor also knew of the 'rules of hat' yet demanded
the red hatted Smurfs stand.  the red hatted Smurfs must
be able to determine who they are.


- Thus I conclude two stand and each has on a red hat. -

since each of these Smurfs can see only one other
Smurf with a red hat.
From: gm115@cus.cam.ac.uk (Gabor Megyesi)
Newsgroups: sci.math
Subject: Re: p prime, p divides ab => pdivides a or b
Summary: Example of a non-Euclidean PID
Date: 3 Sep 92 08:40:46 GMT
Organization: U of Cambridge, England

In article <1992Sep2.183341.32017@mp.cs.niu.edu> rusin@mp.cs.niu.edu (David Rusin) writes:
>
>(Actually I think I remember some quadratic extensions of  Z  for
>which you can show no division algorithm exists but which are still
>PID's. Readers?)

Z[1/2+srqt(-19)/2] is an example, which is a principal ideal domain,
but not Euclidean.

Gabor Megyesi
gm115@phx.cam.ac.uk
From: cyeomans@ms.uky.edu (Charles Yeomans)
Newsgroups: sci.math
Subject: Re: Unix denies the axiom of choice
Date: 1 Sep 92 19:05:20 GMT
    <pmanne-010992093107@ma-mac29.uio.no.> 
    <1992Sep1.174532.19663@galileo.cc.rochester.edu>
Organization: University Of Kentucky, Dept. of Math Sciences

In article <1992Sep1.174532.19663@galileo.cc.rochester.edu> landsbur@troi.cc.rochester.edu (S. Landsburg) writes:
>In article <pmanne-010992093107@ma-mac29.uio.no.> pmanne@math.uio.no (Per Manne) writes:
>
>>The following proof is found in Seven Years of Manifold (1968-1980),
>>edited by Ian Stewart and John Jaworski.
>>
>>THEOREM (due to Anselm, Aquinas, and others.)
>>The Axiom of Choice is equivalent to the existence of a unique God.
>>
>>PROOF:
>
>    (Remainder of article deleted.)
>
>I tried to save this posting to a file called "god".  I got back the message
>that "god does not exist".
>
>
>Steve Landsburg
>landsbur@troi.cc.rochester.edu

But UNIX can create god in mailbox format.  

CHarles Yeomans
yeomans@austin.onu.edu
cyeomans@ms.uky.edu
Newsgroups: sci.math
From: mls@cbnewsm.cb.att.com (mike.siemon)
Subject: Re: Godel and the US constitution
Organization: AT&T
Date: Thu, 3 Sep 1992 00:59:23 GMT
Summary: does zilch

> Fortunately there is the second amendment of the Bill of Rights.

Utterly useless if the dictator comes to power with quasi-fascist
gun-toters as his storm troopers.  I suppose one could hold out the
"hope" that the urban mob might be opposed to a rural-right takeover,
but that is hardly what I regard as decent checks & balances.
-- 
Michael L. Siemon			"I know of nothing -- I suspect
					not even death -- that is so fixed
mls@usl.com				in the present tense as love."
standard disclaimer					-- Jess Anderson
From: radford@cs.toronto.edu (Radford Neal)
Newsgroups: sci.math
Subject: Re: Godel and the US constitution
Date: 2 Sep 92 00:58:20 GMT
Organization: Department of Computer Science, University of Toronto

In article <1992Sep1.175844.16825@nas.nasa.gov> asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:

>Out of curiosity, does anyone know how Godel envisioned a
>consitutional dictatorship possibly arising in the U.S. ???


Well... My recollection is fuzzy, but can't the US congress create new
states just by passing a bill? It should be no problem for them to
create several hundred of them, each containing only a single
resident, namely, one of themselves. They can then run in these new
states come next election, elect themselves, and out-vote any
uncooperative representatives from the old states...
   
    Radford Neal
From: maj@waikato.ac.nz
Newsgroups: sci.math
Subject: Re: Parallel axiom.
Date: 29 Aug 92 10:57:40 +1200
Organization: University of Waikato, Hamilton, New Zealand

In article <COLUMBUS.92Aug27105326@strident.think.com>, columbus@strident.think.com (Michael Weiss) writes:
> In article <1992Aug27.115903.10390@waikato.ac.nz> maj@waikato.ac.nz writes:
> 
>    I have always felt that Euclid's form is superior because it contains
>    no mention of the mysterious undefined concept 'parallel'. And how
>    are we supposed to have any intuition of what 'parallel' means in the
>    various possible geometries that may exist without the axiom. I don't
>    think Playfairs Axiom plays fair in the least. It has always struck
>    me as question begging.
> 
>    -- 
>    Murray A. Jorgensen [ maj@waikato.ac.nz ]    University of Waikato
>    Department of Mathematics and Statistics     Hamilton, New Zealand      
> 
> Definition: two lines are parallel if they have no points in common.
> What's mysterious about that?
> [rest deleted]

Squirm, yeah maybe that's not to bad, still. . . there is something
about Playfairs form that I dont like. I'll try to explain.

It seems to me that Playfair's form has an infinitary character that
Euclid's form lacks. It asks me to contemplate a finite diagram
whereas Playfair's demands that I think of an infinite one. Of
course the two are equivalent in classical logic but it seems to me
that Euclid's might be a better starting point if you were trying
to do things constructively. I'd better ask my boss sometime. 

-- 
Murray A. Jorgensen [ maj@waikato.ac.nz ]    University of Waikato
Department of Mathematics and Statistics     Hamilton, New Zealand      
__________________________________________________________________
'Tis the song of the Jubjub! the proof is complete,
if only I've stated it thrice.'
Newsgroups: sci.math
From: asimov@wk223.nas.nasa.gov (Daniel A. Asimov)
Subject:  Intersection of 4 Solid Cylinders Along Main Diagonal of Cube
Organization: NAS, NASA Ames Research Center, Moffett Field, CA
Date: Fri, 4 Sep 92 18:26:11 GMT

It is well known that if 3 congruent solid cylinders with mutually orthogonal
axes are intersected in 3-space, the result has 12 curved faces
arranged like a rhombic dodecahedron.

QUESTION:	What is the intersection of 4 congruent solid cylinders
in 3-space whose axes are the major diagonals of a cube?


--Dan Asimov
asimov@nas.nasa.gov

Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000
(415) 604-4799
From: petry@pythagoras.math.washington.edu (David Petry)
Newsgroups: sci.math
Subject: Re: Proof of God's Existence
Date: 2 Sep 92 20:24:39 GMT
Organization: University of Washington, Mathematics, Seattle

In article <17ui6kINNsft@matt.ksu.ksu.edu>, bubai@matt.ksu.ksu.edu
(P.Chatterjee) wrote:

>I was told by somebody that there is a mathematical proof of God's existence; 
>was wondering if somebody could shed some light on the same.

Being a really sharp guy, I almost immediately recognized the importance of 
the above question, and I commenced at once to consume enormous quantities of 
caffiene in hopes of producing an enormous theorem.  Here's what I came up
with:

THEOREM 1:  Any logical system which is strong enough to prove that G*d doesn't
exist is not strong enough to prove it's own consistency, or else it is in fact
inconsistent.

Proof.  (Left to the reader)


Corollary A:  G*d exists.

Proof.  Assume not.  Then you can't be sure of your own consistency.  If you're
not sure of your own consistency, you have no right to question whether G*d
exists.   QED


Corollary B:  You can fool some of the people some of time, blah blah blah.

Proof.  Obvious.



David Petry

If I have to take it, I may as well dish it out.
Newsgroups: sci.math
From: radford@cs.toronto.edu (Radford Neal)
Subject: Re: Polygon point enclosure
Organization: Department of Computer Science, University of Toronto
Date: 27 Aug 92 21:17:48 GMT

In article <1992Aug27.193751.26737@news.eng.convex.com> dodson@convex.COM (Dave Dodson) writes:

>Yes, but only a convex polygon can be represented by a set of linear
>inequalities, whereas counting the edge crossings of a ray from the
>point in question to infinity can be made to work whether the polygon
>is convex or not.
>
>Dave Dodson		                             dodson@convex.COM
>Convex Computer Corporation      Richardson, Texas      (214) 497-4234
 ******

It's good to see that business insiders are looking beyond their
traditional markets, hoping to enter new areas. It's a ray of hope
for the future... :-)
From: cjh@tinton.ccur.com (Christopher J. Henrich)
Newsgroups: sci.math
Subject: Re: Question about polyhedra
Date: 2 Sep 92 22:48:58 GMT
Organization: Concurrent Computer Corp., Tinton Falls, NJ

In article <17rbgqINNscd@agate.berkeley.edu> faustus@ygdrasil.CS.Berkeley.EDU (Wayne A. Christopher) writes:
>I need some information that must be in a book somewhere, but I can't
>seem to find it.  The question is this: for the various platonic
>solids, in particular the dodecahedron and the icosahedron, if the
>length of an edge is 1 and the polyhedron is centered about the origin,
>what are the coordinates of the vertices?  (For some convenient orientation.)
>Any references or numbers would be very much appreciated.  Thanks,
>
The classic reference for such questions is Coxeter, _Regular
Polytopes_.  It is IN PRINT as a high-quality, inexpensive  paperback 
from Dover. 

Somebody, posting on misc.books.technical, commented that Dover
Publications seemed almost too good to be true.  And so they are.
We can express our gratitude most effectively by buying books from
them.

Regards,
Chris Henrich
Newsgroups: sci.math,misc.misc
From: ekman@netcom.com (Crossly the Glad-Eyed Bear)
Subject: Re: value of pie
Date: Fri, 04 Sep 92 15:24:15 GMT
Organization: Home for the Terminally Infirm

In article <1992Sep2.160954.20723@fig.citib.com> ghica@fig.citib.com (Renato [Titanium Cranium] Ghica) writes:
>
>I can probably find this in a math book somewhere, but
>I don't have one handy.
>
>I seem to remember that PI was calcucalte with an infinite summation
>such as ....X + 1/3 - 1/5 + 1/7 ... 

Try this one:

  pi/4 = 1 - 1/3 + 1/5 - 1/7 + ...
-- 
Crossly the Glad-Eyed Bear              ekman@netcom.com
Home for the Terminally Infirm, Redwood City, California
Newsgroups: sci.math
From: columbus@strident.think.com (Michael Weiss)
Newsgroups: sci.math
Subject: Re: Parallel axiom.
Date: 31 Aug 92 10:38:47
Organization: Thinking Machines Corporation, Cambridge MA, USA
	<COLUMBUS.92Aug27105326@strident.think.com>
	<1992Aug29.105741.10445@waikato.ac.nz>
NNTP-Posting-Host: strident.think.com
In-reply-to: maj@waikato.ac.nz's message of 29 Aug 92 10:57:40 +1200

In article <1992Aug29.105741.10445@waikato.ac.nz> maj@waikato.ac.nz writes:

   [. . .] there is something
   about Playfairs form that I dont like. I'll try to explain.

   It seems to me that Playfair's form has an infinitary character that
   Euclid's form lacks. It asks me to contemplate a finite diagram
   whereas Playfair's demands that I think of an infinite one. Of
   course the two are equivalent in classical logic but it seems to me
   that Euclid's might be a better starting point if you were trying
   to do things constructively [. . .]

I suspect that you are right from a historical standpoint.  Euclid never
uses the modern concept of a line that is infinite in both directions.  On
the contrary, one of his postulates states that it is possible to prolong a
line indefinitely-- clear indication that by "line" he means "line
segment".  (One caveat: I don't read Greek, so maybe I'm completely off
base.  Though I doubt it.  Any classical scholars out there?)

This just shows that simplicity is in the eye of the beholder.  To modern
mathematical sensibilities (and by "modern", I mean "post-Renaissance"),
infinite lines are quite as acceptable philosophically as line segments.
With this outlook, Playfair's postulate is short and sweet, and Euclid's
parallel postulate is too long by half.

I should say a few words about intuitionism and constructive analysis here,
but I'm out of time.
Newsgroups: sci.math
From: palais@binah.cc.brandeis.edu
Subject: Re: Proof of God's Existence
Reply-To: palais@binah.cc.brandeis.edu
Organization: Brandeis University
Date: Wed, 2 Sep 1992 01:02:15 GMT

   I'm surprised that nobody has brought up the anecdote
of Euler's "proof" of the existence of God. As I heard it,
while at the court of Catherine the Great, Euler was asked 
to take part in a debate, and refute a famous skeptic who 
would argue against the existence of God. 

   After the skeptic had his say, Euler, who knew that his 
opponent knew nothing of Mathematics, got to his feet and 
said "e^{i\pi)} + 1 =0. Donc il existe!", and sat down.
His rival was completely taken aback and gave up the debate.
Newsgroups: sci.math
From: regeorge@magnus.acs.ohio-state.edu (Robert E George)
Subject: Re: Why don't we split the group?
Organization: The Ohio State University
Date: Fri, 4 Sep 1992 13:13:13 GMT

In article <4066@svin09.info.win.tue.nl> pwk@win.tue.nl writes:
>For those who don't read this group about twice a day,
>there are too much articles, of which some aren't interesting
>enough.
>My suggestion whould be to split the group even more
>Currently we have:
>sci.math
>sci.math.num-analysis
>sci.math.stat
>sci.math.symbolic
>sci.math.research
>I would like to see:
>sci.math.coding        (with error correcting/cryptology/information theory)
>sci.math.group         (group theory)
>sci.math.misc          (whatever...)
>sci.math.puzzles       (well, puzzles appear sometimes)
>and many more.
>
>Pieter Kuppens     (pwk@win.tue.nl)
>-----
>Pi is about 3.2 if you want to calculate the earth's surface.


I think we also need a sci.math.foundations (or maybe there's a better
name) for issues related to logical thought, abstract arguments (e.g.,
can we prove God exist). Such arguments are likely to be of intense interest
to some and of no interest to others.
Robert George
(speaking only for myself)

"The very essence of individual freedom is equal justice under a rule of
law, a law to which every man shall be subject and which no executive
can modify."
    Senator Robert Taft , March 11, 1944
Newsgroups: sci.math
From: devlin@csli.stanford.edu (Keith Devlin)
Subject: Position open THIS fall (September 1992)
Organization: CSLI, Stanford University
Distribution: na
Date: Thu, 27 Aug 1992 13:44:19 GMT

A faculty illness has created an opening for a one-year,
visiting position at Colby College (Maine) for the coming
year, starting September 1992. (First day of classes 9
September.) The position carries a teaching load of five
courses, each meeting for four fifty minute periods a
week. All the courses are at first year level for this
position: three in the fall, one in the special January
Program, and one in the spring. The fall and January courses
are all first-year calculus two of them duplicate sections,
the third closely related in content.

Colby is a highly selective, private, liberal arts college
located in mid-Maine. All classes are small, none more than
28. The college has 1700 students and 170 faculty. The
Department of Mathematics and Computer Science has 11 faculty,
all but one having a Ph.D. 

Local housing is plentiful and cheap (rental and purchases).
Please email a vita if you are interested in this position.
You must be able to make a decision and get here about a
week from now! (A vita in TeX or LaTeX would be most
convenient, but plain text is also okay.)

The position carries full benefits for a full-time, fixed-term
appointment of one year. Colby is an A.A. E.O. institution, and
encourages applications from women and minority candidates.

Keith Devlin
Chair
Department of Mathematics and Computer Science
Colby College
Waterville
Maine 04901

email: kjdevlin@colby.edu
Tel: 207/872 3257