HDTenEightyP/NetNews huggingface dataset:
From: bennett@math.ksu.edu (Andy Bennett)
Newsgroups: sci.math
Subject: Re: Jokes in papers (was Re: Einstein's Erdos number)
Date: 9 Sep 1992 10:36:28 -0500
Organization: Dept. of Mathematics, Kansas State University
NNTP-Posting-Host: hilbert.math.ksu.edu

neuhaus@vier.informatik.uni-kl.de (Stephan Neuhaus (HiWi Mattern)) writes:

>I vaguely recall from a math course that there was a paper published
>by three soviet mathematicians, the third of which having signed the
>paper only to make the three mathematicians' names sound like ``alpha,
>beta, gamma''.  The third mathematician's name was Gamow.  Does
>anybody know the names of the other two?

As I heard the story, it was Ahlfors, Bethe, and Gamow and Bethe was the
one who signed just to make it come out right. Did this really happen? Does
anyone have a reference to the article (which should be easy to find if
you have access to the cd rom version of math reviews)?


-- 
Andrew G. Bennett         bennett@math.ksu.edu         If you count too
Dept. of Mathematics      Voice: (913) 532-6750        much you turn
Kansas State University   Fax:   (913) 532-7004        purple.  -  SARAH
Manhattan, KS 66502       STRICTLY MY OWN OPINIONS
Newsgroups: sci.math
Subject: Re: Elevator mayhem
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 15 Sep 92 22:04:50 GMT

In <mcirvin.716585471@husc8> mcirvin@husc8.harvard.edu (Mcirvin) writes:

>hsieh@math.toronto.edu (Paul Hsieh) writes:

>>Well, I've though about this once (not too seriously) and figure that if your
>>timing is good enough that you could jump up at the last second before impact
>>to actually reduce the speed.  Then you could end up with method 2) with 
>>lesser impact.  :)  I don't know if there is any merit to what I've just said
>>but I'm wondering if there is anything fundamentally flawed with it (besides
>>the amazing timing that would be required).

>There is a fundamental flaw... Think about what happens when you come
>back down at the end of your jump.  Remember, you've jumped off of a
>floor that is traveling downward at high speed, and you land on a floor
>that has stopped moving!  All you've done is delay the injury a fraction
>of a second. 

No, actually, it seems that does have merit.  If you jump while the
elevator is falling, and land after it stops, you have (assuming no rebound
of the elevator) reduced your impact velocity.
--
Arthur L. Rubin: a_rubin@dsg4.dse.beckman.com (work) Beckman Instruments/Brea
216-5888@mcimail.com 70707.453@compuserve.com arthur@pnet01.cts.com (personal)
My opinions are my own, and do not represent those of my employer.
My interaction with our news system is unstable; please mail anything important.
From: jmount+@CS.CMU.EDU (John Mount)
Newsgroups: sci.math
Subject: Re: Partitioning of uncountable sets
Date: 8 Sep 92 14:41:18 GMT
Article-I.D.: cs.Bu9Ksv.G04.2
Organization: Carnegie Mellon University

In article <1992Sep8.182706.90039@vaxc.cc.monash.edu.au>, kevin@vaxc.cc.monash.edu.au writes:
|> A proof that every uncountable set can be partioned into two uncountable
|> sets.
|> Let X be an uncountable set. Consider the set of ordered pairs, (x,0),(x,1)
|> where x is in X. Call this set Y. Then Y is also uncountable, moreover,
|> {(x,0) with x in X}=Y(0) and {(x,1) with x in X}=Y(1) are both uncountable.
|> But the cardinaltiy of X is the cardinality of Y. Thus, there is a bijection
|> f from Y to X. f(Y(0)) and f(Y(1)) form the desired partition of X.
|> The proof is of course easier if one assumes A.C, which I have avoided.
|> 
|> Love,
|> Kevin Davey.

This seems correct, and like a good way to prove the theorem, but
are you sure this avoids the axiom of choice?  How do you show
card(X)=card(Y) without using AC?  (In general cardinal comparability
is equivalent to AC.  And the proof I know for the absorption law of
cardinal arithmetic uses AC pretty strongly.)

-- 
--- It is kind of strange being in CS theory, given computers really do exist.
John Mount: jmount+@cs.cmu.edu               (412)268-6247
School of Computer Science, Carnegie Mellon University, 
5000 Forbes Ave., Pittsburgh PA 15213-3891
From: mauax@warwick.ac.uk (Brazil)
Newsgroups: sci.math
Subject: Re: Proof of God's Existence
Date: 6 Sep 92 21:35:45 GMT
Organization: Computing Services, Warwick University, UK


I've been reading this thread and thought about it for a while. I hereby
conclude that the attempts to prove the existence of god (I have
deliberately left god in lower-case in the hope that some bible basher will
flame me - so don't bother) rely on knowing what god is. So far I find that
substituting the word 'universe' for 'god' doesn't make the slightest bit of
difference. 
If we are trying to evaluate the existence of god then I (notice that I use
a capital for the first person yo'ld bible bashers!) think that we should be
trying to prove the existence of a little bit more than the universe, which
incidentaly we cannot apply set theory to because of Russel's Paradox (note
the capitals again bb's!)

oh well - I'm probably wasting someone elses wavelength here. I'd be
interested in some serious,non-flaming comments though.


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Xref: sparky sci.math:11399 comp.graphics:9690
From: czako@yoko.rutgers.edu (Gabor M. Czako)
Newsgroups: sci.math,comp.graphics
Subject: Hyperbola intersection
Date: 14 Sep 92 13:29:13 GMT
Followup-To: sci.math
Organization: Rutgers Univ., New Brunswick, N.J.

In a computer program I am writing, I need to intersect two
arbitrarily oriented hyperbolas.  These hyperbolas are defined by the
following two equations:

	a_1*x^2 + b_1*x*y + c_1*y^2 + d_1*x + e_1*y + f_1 = 0
	a_2*x^2 + b_2*x*y + c_2*y^2 + d_2*x + e_2*y + f_2 = 0

where the two discriminants, b_1^2 - 4*a_1*c_1 and b_2^2 - 4*a_2*c_2,
are positive.  I have been unable to analytically solve for the
intersection points.

Any help would be greatly appreciated.

Gabe
Newsgroups: sci.math
Subject: Thanks and message to David Wilson.
From: wft@math.canterbury.ac.nz (Bill Taylor)
Date: 7 Sep 92 18:19:47 +1200
Distribution: world
Organization: Department of Mathematics, University of Canterbury

David Wilson posted an excellent list of 26 equivalents of Euclid's
parallel axiom. Thanks, David, for all the trouble you took. This was
exactly the kind of response I was hoping for.

I tried to send you an e-mail reply, to

wilson@web.ctron.com

but it bounced. Don't know what the problem was, so I'm posting here.
Hope you see it.     Cheers,

Bill Taylor.         wft@math.canterbury.ac.nz
From: mauax@warwick.ac.uk (Brazil)
Subject: Re: Proof of God's Existence
Organization: Computing Services, Warwick University, UK
Date: Sun, 6 Sep 1992 21:41:32 GMT

>
>Proof of God's inexistence:
>
>God can do anything.
>
>So he can make a stone which he cannot lift.
>
>So he cannot lift that stone.
>
>So "God can do anything" is wrong.
>
Nah - this is a part of a proof that God is not omnipotent, ie that he can't
do anything. If you now assume that he is not omnipotent and reach a
contradiction then you will have proved his inexistence.


>---------------------------------------------------------------------------
>J.CHEN                               |E-MAIL: jchen@tomahawk.me.gu.edu.au
>School of Microelectronic Engineering| Phone: +61-7-8755050
>Faculty of Science and Technology    |   Fax: +61-7-8755198
>Griffith University                  |   Fax: +61-7-8755050
>Nathan, QLD 4111, Australia          | 
>---------------------------------------------------------------------------



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From: G.Joly@cs.ucl.ac.uk (Gordon Joly)
Newsgroups: sci.math
Subject: Transformations onto Euclidean Space
Date: 10 Sep 92 14:43:18 GMT

David Griffith writes:
 > I apologize in advance for the hopelessly vague nature of this question but...
 > 
 > Can anyone suggest a few mathematical methods to transform or map _something_
 > onto Euclidean or Minkowskian space. In other words, you have some
 > representation or some geometry that describes various points, you apply
 > the mapping and you get points in Euclidean space.
 > 
 > As a for instance, let me make one up - each x, y and z coordinate is
 > actually the modulus of a complex number, so points in this six dimensional
 > complex space map onto the three dimensional real space.
 > 
 > Thanks,
 > 
 > Dave Griffiths
 > 
 > PS: I'd appreciate a _finite_ list! :-)


Here is a map:  (it,x,y,z) <-> (t,x,y,z)

Here is another map:  (it,x,y,z) <-> (-t,x,y,z)

I guess that is is wrong. Try looking a projective geometry
literature, perhaps.

Gordon.
Newsgroups: sci.math
From: ramsay@unixg.ubc.ca (Keith Ramsay)
Subject: Poincare on Set Theory (was Re: Philosophies...)
Summary: Didn't say it was a disease
Organization: University of British Columbia, Vancouver, B.C., Canada
Date: Tue, 15 Sep 1992 00:24:13 GMT

In article <TORKEL.92Sep11100055@isis.sics.se> torkel@sics.se 
(Torkel Franzen) writes:
>  This is not historically accurate. Set theory caught on chiefly
>because of its role in the creation and development of such subjects
>as point set topology (which Poincare considered a "disease") and
>measure theory.

I remember reading a debunking of the quote of Poincare. I think the
article was in the Mathematical Intelligencer, but I haven't been able
to find it. The author(s) went looking for the original quote from
Poincare. If I remember correctly, the closest thing they found was a
remark in which he said that the set-theoretic paradoxes were an
interesting challenge, and that the delight of this challenge was like
the delight of a physician, upon treating a particularly interesting
case. It appears that this remark was misquoted by someone and then
repeated. Wasn't Poincare responsible for much of the development of
point-set topology anyway? This is from memory, so if anyone has the
exact reference, please let me/us know.

Keith Ramsay
ramsay@unixg.ubc.ca
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: ZFC etc. (was Re: Report on Philosophies of Physicists)
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Tue, 15 Sep 92 16:56:35 GMT

In artic
>Some people suggest that that there are "statistical" reasons for taking
>ZFC to be consistent. That is, no inconsistency has been found in spite
>of the theory having been used a lot, so it is reasonable to think that

In my opinion this argument is fine and is the only way we know anything
at all.  (Ugh, now I'll have a pack of epistemologists, led by Torkel,
on my tail!)  Just as the laws of physics seem to be true (but might not
be) since so far they seem always to have held, so too the consistency
of mathematics is an empirical fact.  I claim that this holds, not only
for systems such as ZFC, but even systems such as the propositional
calculus for which there is a formal "proof" of consistency.  The
propositional calculus might be inconsistent and we have somehow failed
to notice this so far; whatever subtle flaw it had would also afflict
the reasoning of the consistency proof, and when someone finally noticed
a certain gigantic proposition that could be proved both true and false,
we would see how one could construct a formal proof of the inconsistency
of the propositional calculus.
>CH is undecidable in ZFC" is provable by an elementary combinatorial proof.


Newsgroups: sci.math
From: orourke@sophia.smith.edu (Joseph O'Rourke)
Subject: Re: Literature on Voronoi Cells?
Organization: Smith College, Northampton, MA, US
Date: Wed, 16 Sep 1992 00:40:04 GMT

In article <IQ26PAR@minnie.zdv.uni-mainz.de> 
	polani@Informatik.Mathematik.Uni-Mainz.DE (Daniel Polani) writes:
>as the subject line promises, I'm interested on literature on Voronoi
>cells.

Here is one reference that you might get directly from the author
in Berlin.  It is recent and has an extensive bibliography.

@techreport{Aurenhammer,
	author = "F. Aurenhammer",
	title = "Voronoi Diagrams: {A} survey of a fundamental data structure",
	number = "B 90-09",
	year = 1990,
	month = "November",
	institution = "Freie Universitat Berlin"
}
From: nabritta@teaching.cs.adelaide.edu.au (Nigel)
Newsgroups: sci.math
Subject: O(n)
Date: 11 Sep 92 16:40:24 GMT

Ok, this may seem a bit of a lame question to post in this group, but
can someone out there please give me a bit of an explaination about the
big 'o' function. I cant seem to understand what its for or the
principle behind it. Replies by email would be appreciated.

Nigel Brittain

-- 
________________________________________________________________________
Nigel Brittain              | This .sig is shareware. To register your
nabritta@cs.adelaide.edu.au | copy, please send A$25...
____________________________|___________________________________________
Newsgroups: sci.math
Subject: What's going on here ???
From: wft@math.canterbury.ac.nz (Bill Taylor)
Date: 11 Sep 92 21:46:59 +1200
Distribution: world
Organization: Department of Mathematics, University of Canterbury

The following rather silly problem cropped up in our department just now.

Evaluate    S = 0! - 1! + 2! - 3! + 4! - ....

(yes, I know it's divergent, but blame Euler, not me.)

------------------------
Crazy solution (1)

    oo           oo     oo            oo     oo          oo
   \~~   n      \~~   n /  n -x       /  -x \~~  n       /   -x 1
S = > (-1) n!  = > (-1) | x e  dx  =  | e    >(-x) dx  = |  e  --- dx
   /__          /__    /             /      /__         /      1+x
   n=0          n=0    0             0      n=0         0

  = .5963..

-----------------------
Crazy solution (2)

                                      2      3      4
S = f(1)   where  f(x) = 0! - x 1! + x 2! - x 3! + x 4! - ...

                              2      3
So   (x f(x))' = 1! - x 2! + x 3! - x 4! + ...

               = (1 - f(x))/x
        2                                                     1        1
Thus   x f' + (1+x)f = 1         this has integrating factor  - exp(- ---)
                                                              x        x

Thus  [ x exp(-1/x) f(x) ]' = exp(-1/x)/x

                               x
                              /
thus      x exp(-x) f(x)    = | exp(-1/t)/t dt      now put x=1
                              /
                             0
                               1
                              /
thus              f(1)/e  =   | exp(-1/t)/t dt      and put u=1/t
                              /
                             0
                               oo
                              /
                          = e | exp(-u)/u du    =  .5963..
                              /
                             1

being essentially the same integral as in crazy solution (1).
-----------------------

So what's going on here ????

Two crazy solutions to a crazy problem giving the same answer.   Why ?

--------------------------------------------------------------------------
            Bill Taylor              wft@math.canterbury.ac.nz
--------------------------------------------------------------------------
 MATH: necessary consequences of arbitrary axioms about meaningless things.
--------------------------------------------------------------------------

Newsgroups: sci.math
From: pierce@lanai.cs.ucla.edu (Brad Pierce)
Subject: Re: Jokes in papers (was Re: Einstein's Erdos number)
Organization: UCLA, Computer Science Department
Date: Wed, 9 Sep 92 15:49:40 GMT

In article <neuhaus.716039445@vier> neuhaus@vier.informatik.uni-kl.de (Stephan Neuhaus (HiWi Mattern)) writes:
>I vaguely recall from a math course that there was a paper published
>by three soviet mathematicians, the third of which having signed the
>paper only to make the three mathematicians' names sound like ``alpha,
>beta, gamma''.  The third mathematician's name was Gamow.  Does
>anybody know the names of the other two?

While the third author was Gamow, the physicist who allowed his name
to be added for humorous effect was the *second* author Hans Bethe.

The paper you refer to reports on Ralph Alpher's Ph.D. dissertation.
Alpher's Ph.D. supervisor was George Gamow. The article by Alpher,
Bethe and Gamow was published in Physical Review in 1948. (On April
Fool's Day no less.)

-- Brad Pierce --

Newsgroups: sci.math
From: hporopudas@tnclus.tele.nokia.fi
Subject: Re: Proof of God's Existence
Organization: Nokia Telecommunications.
Date: Mon, 7 Sep 1992 09:54:30 GMT


In article <1992Sep4.192528.21285@guinness.idbsu.edu>,
holmes@opal.idbsu.edu (Randall Holmes) writes:
> In article <1992Sep1.090011.1@tnclus.tele.nokia.fi>
hporopudas@tnclus.tele.nokia.fi writes:
>>
>>In article <17ui6kINNsft@matt.ksu.ksu.edu>, bubai@matt.ksu.ksu.edu
>>(P.Chatterjee) writes:
>>> 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.
>>>
>>> Thanks. Looking forward to the response.
>>
>>   I think that God's existence is an axiom. He says in the Holy Bible (Second
>> book of Moses 3:14-15 in Old Testament and also in Johannes 8:28-29 in New
>> Testament) that He is "Existence Himself".
>>   If someone is arguing that "Existence Himself" does not exist, I think that
>> at the same time he/she is arguing that he/she himself/herself does not exist.
>>
>>              Hannu.
>
> This reminds me of the student who responded to my (true) assertion
> that we can prove in ZF that the universe does not exist (i.e., there
> is no set containing everything) by asking why we were bothering with
> the course (or anything) if there were a mathematical proof that
> nothing exists.  It is not a prerequisite for the existence of
> individual objects that the abstract object "existence" exist.
> --
> The opinions expressed		|     --Sincerely,
> above are not the "official"	|     M. Randall Holmes
> opinions of any person		|     Math. Dept., Boise State Univ.
> or institution.			|     holmes@opal.idbsu.edu

  I would like to comment following sentence from above:

> nothing exists.  It is not a prerequisite for the existence of
> individual objects that the abstract object "existence" exist.

  I think that these your "individual objects" are part of "existence".

           Hannu.
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: The Last Number Theory Problem
Date: 14 Sep 92 21:10:31 GMT
Organization: U of Cambridge, England

In article <1992Sep14.134624.26925@cs.rose-hulman.edu> goddard@NeXTwork.Rose-Hulman.Edu (Bart Goddard) writes:

>5.2.11.a (Solved) Show that if n is a pseudoprime to the base a but not
>a pseudoprime to the base b, where (a,n)=(b,n)=1, then n is not a 
>pseudoprime to the base ab.
>
>5.2.11.b Show that if there is an integer b with (b,n)=1 such that n is
>not a pseudoprime to the base b, then n is a pseudoprime to <= \phi(n)
>different bases a, with 1<=a<n.  (Hint: Show that the sets a_1, a_2,  
>..., a_r, and ba_1, ba_2,...,ba_r have no common elements, where a_1,  
>a_2, ..., a_r, are the bases less than n to which n is a pseudoprime.)

OK. The HINT is true: if n is pp to base a and not to base b then it is
not pp to base ba.
So, if "\phi(n)" be replaced by "{n\over2}" the result is true.
(And clearly that's what was intended.)

The result stated does actually appear to be true, even in those cases
-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
Newsgroups: sci.math
From: chalcraft@uk.tele.nokia.fi (Adam Chalcraft)
Subject: Re: Partitioning of uncountable sets
Organization: cpd
Date: Tue, 8 Sep 1992 11:17:48 GMT

In article <1992Sep8.182706.90039@vaxc.cc.monash.edu.au> kevin@vaxc.cc.monash.edu.au writes:

>   Let X be an uncountable set. Consider the set of ordered pairs, (x,0),(x,1)
>   where x is in X. Call this set Y. Then Y is also uncountable, moreover,
>   {(x,0) with x in X}=Y(0) and {(x,1) with x in X}=Y(1) are both uncountable.
>   But the cardinality of X is the cardinality of Y.

>   The proof is of course easier if one assumes A.C, which I have avoided.

I'm probably being particularly dense here, but why (without AC) do X and Y
have the same cardinality? (Two sets have the same cardinality iff there is
a bijection between them, of course).
--
  ____________________________________________________________________________
 /  _Name: Adam|Names are linguistic constructs expressed in some language._  \
|\_|/|Chalcraft|They correspond to objects in some universe of discourse. |\|_/|
|`   |         |The corresponence between names (in the language) and     |`   |
|`   |Opinions:|objects (in the universe of discourse) is the  relation of|`   |
|`   |     Mine|identifying. A name identifies the object to which it is  |`   |
|`   |_________|bound.__________________________ISO_7498-3_:_1989_(E)_5.1_|`   |
 \__/                                                                      \__/
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: What's going on here ???
Date: 11 Sep 1992 08:35:40 -0400
Organization: The Ohio State University, Dept. of Math.
Distribution: world
NNTP-Posting-Host: function.mps.ohio-state.edu

Euler's function

                                      2      3      4
>                 f(x) = 0! - x 1! + x 2! - x 3! + x 4! - ...


of course diverges.  But in some sense (which I would like to
understand better) the "best" value for it is the one you found,

     f(x) = - exp(1/x) * Ei(1/x) * (1/x)
-- 
  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