HDTenEightyP/NetNews huggingface dataset:
From: bhoughto@sedona.intel.com (Blair P. Houghton)
Subject: Re: Is Math Hard?
Organization: Intel Corp., Chandler, Arizona
Date: Wed, 14 Oct 1992 03:54:31 GMT

In article <1992Oct13.202828.13373@pellns.alleg.edu> frisinv@alleg.edu writes:
>is the hardest thing on the face of this earth. I know others who laugh  
>insanely and say math is child's play. I want to take a little poll:

Now is the time for all good men to go edit a few
files full of uuencoded bytes; it will be as informative...

				--Blair
				  "All good women are taken."
From: rjchapma@cen.ex.ac.uk (R.J.Chapman)
Newsgroups: sci.math
Subject: Re: Reciprocals of Fibonaccis
Date: 9 Oct 92 08:38:46 GMT
Organization: Computer Unit. - University of Exeter. UK

In article <1992Oct08.195919.81736@Cookie.secapl.com> frank@Cookie.secapl.com (Frank Adams) writes:

>   This is a problem I've worked on off and on for several years, without
>   getting much of anywhere:
>
>   What is the sum of the reciprocals of the positive Fibonacci numbers?  (That
>   is, Sum(n>0, 1/F_n).)
>
>   Numerically, it is about 3.359885666243177.  The continued fraction starts:
>
>   3,2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,3,1
>
>   I'm not sure about the last two numbers here; the final 3 could be 4.  The
>   small numbers suggest the result may be algebraic.
>
>   Closely related is the sum of the reciprocals of the Lucas numbers
>   L_n = F_n-1 + F_n+1.  Sum(n>=0, 1/L_n) is about 2.462858173209645; the
>   continued fraction starts approximately,
>
>   2,2,6,4,3,31,2,1,1,1,1,2,3,2,1,3,10
>
>   Does anybody know anything about these numbers?


Landau gave formulae for Sum(n>0, 1/F_2n) and Sum(n>0, 1/F_{2n-1})
in terms of Lambert series, and Jacobi theta functions respectively.
Proofs can be found in

P. Ribenboim, "Representation of real numbers by means of Fibonacci numbers",
L'Enseignment Math., v.31 pp. 249-259.

These formulae are set as exercises, together with the formula for
Sum(n>0, 1/L_2n) in

Borwein & Borwein: Pi and the AGM, Wiley, 1987,

an amazing book!
--
Robin J. Chapman                 *
Department of Mathematics        *
University of Exeter, UK         *
R.J.Chapman@cen.exeter.ac.uk     *
-- 
Robin J. Chapman                 *
Department of Mathematics        *
University of Exeter, UK         *
R.J.Chapman@cen.exeter.ac.uk     *
From: columbus@strident.think.com (Michael Weiss)
Newsgroups: sci.math
Subject: Re: Well-known people who majored in math (other than mathematicians)
Date: 14 Oct 92 09:28:35
Organization: Thinking Machines Corporation, Cambridge MA, USA
Distribution: na
NNTP-Posting-Host: strident.think.com
In-reply-to: wjh@cbnewsl.cb.att.com's message of Tue, 13 Oct 1992 22:24:57 GMT

In article <1992Oct13.222457.11167@cbnewsl.cb.att.com>
wjh@cbnewsl.cb.att.com (william.j.hery) writes: 

   Art Garfunkel, folk-rock inger. BS math CUNY?

Ph.D., Columbia, was what I heard.  (Of course he might also have a BS from
City University of New York).
From: lhjensen@fish.Princeton.EDU (Leif Jensen)
Newsgroups: sci.math
Subject: Re: Another chocolate fish problem.
Date: 16 Oct 92 05:30:09 GMT
Article-I.D.: Princeto.1992Oct16.053009.24883
Organization: Princeton University
Originator: news@nimaster

OK, since my last proof was so popular, here is another.  First a rehash
of the problem.

u(n) is the number of distinct ordered partitions of a set of n elements
into sets of one or two elements. v(n) is the number of distinct ordered
partitions of a set of n elements into sets of two elements or more.
Prove that u(n) = v(n+2) for integers n >= 1.

We denote ordered partitions by a sequence of integers abcd... in which
the first digit represents the order of the first set of the partition,
the second the order of the second set of the partition, etc.

We define an algorithm to convert ordered partitions of n into ordered
partitions of n+2 and an algorithm to convert the other way.  Each
builds up a partition by saying "output x".  These xi's are to be collected
and when set in order x1x2x3... represent the resulting partition.

Algorithm 1: operates on ordered partitions into sets of 1 or 2.

1) Remove the leftmost group of n 1's followed by a 2 from the input
partition and output n+2.
2) Goto 1.
3) At this point only n 1's remain in the input.  Output n+2.

It is easy to see that this algorithm maps every ordered partition of n
into sets of 1 or 2 to a unique ordered partition of n+2 into sets of
2 or more.  Thus we have u(n) <= v(n+2).

Algorithm 2: operates on ordered partitions into sets of 2 or more.

1) If the input partition has only one element n, repeatedly output 1
(n-2) times and stop execution of the algorithm.
2) Remove the leftmost element n from the input partition, then
repeatedly output 1 (n-2) times, and then output 2
3) Goto 1

It is easy to see that this algorithm maps every ordered partition of n
into sets of 2 or more to a unique ordered partition of n-2 into sets of
1 or 2.  Thus we have v(n) <= u(n-2)

We can now conclude that u(n) = v(n+2) for all n >= 1.

OK, so which proof do you prefer?  Are they both correct? This second
one gives absolutely no insight into the problem.  Is that good or
bad?  Do you like defining algorithms as here in proof 2 to solve
math problems or does it remind you too much of Computer Science?

All comments are welcome.

--
Leif Jensen
lhjensen@phoenix.princeton.edu
Xref: sparky sci.math:12852 sci.math.num-analysis:2946
From: herberj@prism.CS.ORST.EDU (John Wesley Herberg)
Newsgroups: sci.math,sci.math.num-analysis
Subject: Next Highest Prime?
Date: 7 Oct 92 16:26:45 GMT
Article-I.D.: CS.1992Oct07.162645.23773
Organization: Oregon State University, Computer Science Dept.

Hope this isn't a FAQ, but does anyone know of a good algorithm to get the
next largest prime no. based on a given integer - within reason( < 200).  The
only algorithm I know of is the seive of Eratosthenes, but I'd like to find
something more effecient.

Please send e-mail as I'm not a regular reader of this group.

Thanks,
-- 
-----------------------------------------------------------------------
John W. Herberg	     		      Internet: herberj@prism.cs.orst.edu
From: luden@lehigh.edu (Dean E. Nelson)
Newsgroups: sci.math
Subject: Re: Philosophical Foundations of Probability?
Date: 16 Oct 92 21:06:18 GMT
Organization: Lehigh University Computing Center

In article <Bw2z06.Hq5@usenet.ucs.indiana.edu> jwales@silver.ucs.indiana.edu (jimmy donal wales) writes:
>From: jwales@silver.ucs.indiana.edu (jimmy donal wales)
>Subject: Philosophical Foundations of Probability?
>Date: 13 Oct 92 22:12:05 GMT

>I'm looking for pointers to books or review articles on modern
>views of the philosophical foundations of probability theory.

>--Jimbo

There was a conference in spring of '87 I believe at VPI in honor of I.J. 
Good on philosophy and statistics or probability.  Perhaps a proceedings is 
available.  As a poor student living in Colorado, I was unable to attend.

Dean Nelson  den0@lehigh.edu
Newsgroups: sci.math
From: mkrogers@unix.amherst.edu (MICHAEL K ROGERS)
Newsgroups: sci.math
Subject: Re: Why is slope denoted by m?
Date: 11 Oct 92 23:15:17 GMT
Organization: Amherst College
X-Newsreader: TIN [version 1.1 PL6]

D. J. Bernstein (brnstnd@nyu.edu) wrote:
: In article <1992Oct7.181405.18957@unlinfo.unl.edu> kwright@hoss.unl.edu (Kevin Wright) writes:
: > We use Z for the integers because of the German 'Zahlen' and we have
: > F for a closed set because of the French 'Ferme' and we have R for rings 
: > because of the English word 'ring.'  
: 
: No. According to Harvey Cohn (Advanced Number Theory, page 49), ``ring''
: is a contraction of ``Zahlring,'' a German word introduced by Hilbert.
: One might argue about the closeness of German ``ring'' and English
: ``ring,'' but the history of ``ring'' is not what you say.

'Ring' in German means 'ring' in English (hence, I suppose,
'anneau' in French)--so I'm not sure what there is to argue
about.  Also, I know that I use R for rings because I speak
English.  Unfortunately, I don't have Cohn's book.  Does he
say that the mathematical English word 'ring' is a contraction
of 'Zahlring'?  If so, it seems that Kevin Wright's comments
are consistent with yours.

BTW, any idea why English has the word 'field' whereas French
and German have the word for body, 'corps' and 'Korpen' resp.

	-mike
From: israel@unixg.ubc.ca (Robert B. Israel)
Newsgroups: sci.math
Subject: Re: The problem of Irish men
Date: 15 Oct 92 16:36:12 GMT
Organization: The University of British Columbia
NNTP-Posting-Host: unixg.ubc.ca

In <1992Oct15.111727.11840@cs.tcd.ie> dherity@cs.tcd.ie (Herity D.) writes:

>In article <1992Oct15.063757.4956@noose.ecn.purdue.edu> kavuri@lips.ecn.purdue.edu (Surya N Kavuri ) writes:
>>
>>  Prove that there are at least two Irish men who shook 
>>  hands the same number of times with other Irish men.
>>
>I can construct a case where that assertion is false. I'm an Irish man, so I'm
>fortunate to have the opportunity for experimental verification :-).

>Let there be four Irish men, none of whom have shaken hands.
>The first man ignores the second and shakes hands with the third. He then
>shakes hands with the fourth twice. Then :
>The first man has shaken hands three times.
>The second has shaken hands zero times.
>The third has shaken hands one time.
>The fourth has shaken hands two times.

Perhaps what Surya meant was:
  there are at least two Irish men who shook hands with the same
  number of other Irish men.
(i.e. multiple shakes with the same man don't count).  Actually you have
to add another clarification:  "there are two Irish men" seems to imply
that they are currently alive, while "shook" (in the past tense) would
appear to include the possibility of shaking hands with someone who
subsequently died.  To make it work, we have to either include both
the living and the dead in both places, or restrict to the living in
both places.

Once you do this, it's an easy application of the Pigeonhole Principle.

-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4
From: mueller@schaefer.math.wisc.edu (Carl Douglas Mueller)
Newsgroups: sci.math
Subject: Re: Aurora Borealis and the Last Digit of Pi
Date: 13 Oct 92 17:57:14 GMT
Reply-To: mueller@schaefer.UUCP (Carl Douglas Mueller)
Distribution: na
Organization: Univ. of Wisconsin Dept. of Mathematics

In article <Bw2FyJ.KD2@unix.amherst.edu> mkrogers@unix.amherst.edu (MICHAEL K ROGERS) writes:
>Did anyone see the episode of "Northern Exposure" last night?
>There was a mathematician in it loosely modelled on the Chudnovsky
>article in the New Yorker earlier this year.  

 I got exactly the same impression -- I hope that people (readers of 
 the New Yorker) don't get the idea that all mathematicians do is 
 compute PI to ever more places.

>She said that
>when she was in graduate school she had thought about studying
>other trancendental numbers, but pi was special.  She had also
>considered studying other fields such as imaginary numbers.

 I thought this was funny.  Studying imaginary numbers in grad school.
 The other fields mentionned as possible were reasonable (apart from 
 the imaginary numbers and her chosen field of PI).

>I think the Chudnovsky's were mentioned (my reception is not
>too good).  "The --novsky's have only gotten out to 2 billion
>digits", she says.  

 I wasn't sure what she said there either.


       Carl Mueller (mueller@math.wisc.edu)
Newsgroups: sci.math
From: myrberger@elmer.e.kth.se (Johan Myrberger)
Subject: 3x3x3-puzzles
Reply-To: myrberger@elmer.e.kth.se (Johan Myrberger)
Organization: School of EE, Royal Institute of Technolgy
Date: Fri, 16 Oct 1992 17:12:01 GMT

I have a file with descriptions of puzzles that in their final state are
a 3x3x3 cube. The file is in some sort of ASCII-graphics.

If you would like to have a copy of it and perhaps add a puzzle please
MAIL me.

I have just added a couple of puzzles and at the moment there are 16 of them.
Surely there must be more... Perhaps you know another?

Johan Myrberger

MAIL: myrberger@elmer.e.kth.se
Newsgroups: sci.math,sci.physics
From: tim@gold.iss.nus.sg (tim poston)
Subject: Re: How do you draw a straight line?
Reply-To: tim@iss.nus.sg (tim poston)
Organization: Institute of Systems Science, NUS, Singapore
Date: Thu, 8 Oct 1992 06:10:13 GMT

In article <PCL.92Oct7090415@black.oxford.ac.uk> pcl@oxford.ac.uk (Paul Leyland) writes:
>I've known people who *define* "straight line" to be equivalent to
>"geodesic", on the grounds that "a straight line is the shortest
>distance between two points".
In a curved space or spacetime
(such as we inhabit) there is no better
replacement of the idea `straight line'
than `geodesic', which reduces to `straight line'
in flat space.
But a geodesic is _not_ always the shortest distance between its ends.
First, the `long way round' route between two points on the equator
is longer than the nearby non-great-circle routes you can follow.
`Shortest' is true only for smaller pieces of the geodesic.
Second, a timelike geodesic (such as is followed by a freely
falling particle in General Relativity) is _longer_ than
any neighbouring curve (length being translated as `elapsed time'
here, we get the General Relativity version of the twins business;
the unaccelerated [=geodesic-following] particle gets older
than particles on nearby paths from meeting to meeting),
again as long as the pieces are small.
For larger bits you can get special nearby longer paths,
analogous to the shorter-circle routes around the sphere.
You also get multiple extrema,
like the different ways you can pull a string tight
between two points on a potato.
Satellites around the earth can follow different spacetime geodesics,
and re-encounter with different elapsed times,
though neither was accelerated.

In counter to the original question:
     How, for that matter,
     can you tell that the line you draw is gay?

References:
on relativity, do net advertising rules apply to mentioning
  Tensor Geometry, Dodson and Poston, Springer 1991?
on the sex life of straight lines
  The Dot and the Line: A Romance in Lower Mathematics, Norton Juster 1963,
  various editions: my UK copy published by Nelson 1964,
  a far better book, and much less expensive.

Tim Poston



_________________________________________________________________________________
    Time is just Nature's way of concealing that everything happens at once.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Newsgroups: sci.math
From: wjcastre@magnus.acs.ohio-state.edu (W.Jose Castrellon G.)
Subject: Re: Algebra problem
Organization: The Ohio State University,Math.Dept.(studnt)
Date: Mon, 12 Oct 1992 23:03:45 GMT


While we are at algebra, let me offer you the following problem:

Let G be a finite group and  H a normal subgroup of G with  (|H|,[G:H]) = 1.
Prove: If f is an automorphism of G, then  f(H) = H

[it's just for your fun; it appeared in a qualifying exam I took last month]
Newsgroups: sci.math
From: john@math.nwu.edu (John Franks)
Subject: Eudora and the Combined Membership List
Organization: Dept of Math, Northwestern Univ
Date: Sun, 11 Oct 1992 21:16:10 GMT


I recently learned a very useful capability of the "Eudora" electronic
mail client for the Macintosh.  It has the capability of directly
connecting with the online version of the Combined Membership List of
the AMS, MAA and SIAM.

Since a number of people use Eudora, I thought this might be of
interest to this group.  Here's how to do it.  You must first select
the "Special" menu and select "Configuration".  When the dialog box
opens file in the field labeled "Ph Server" with

	e-math.ams.org

This need be done only once.  Now to use it, click on the "Special"
menu and select "Ph".  Then fill in the ph command dialog entry with

	lname=Gauss

if you want to look up the entry for everyone name Gauss.  Note this is
the letter L (lower case) then name (stands for last name) followed by
=, then the name with no spaces.


John Franks 	Dept of Math. Northwestern University
		john@math.nwu.edu



John Franks 	Dept of Math. Northwestern University
		john@math.nwu.edu

Newsgroups: sci.math
From: Mitchell.Porter@bbs.oit.unc.edu (Mitchell Porter)
Subject: Electronic math notation
Organization: Extended Bulletin Board Service
Date: Fri, 9 Oct 1992 05:00:56 GMT


Given the limitations of ASCII mathematicians have had to develop
special notations in order to convey Greek characters, superscripts,
integral signs etc on the net, I suppose. Is there a (halfway)
definitive guide to such notations anywhere (after the fashion of
the `smiley' lists one may find in some places)?


--
   The opinions expressed are not necessarily those of the University of
     North Carolina at Chapel Hill, the Campus Office for Information
        Technology, or the Experimental Bulletin Board Service.
           internet:  bbs.oit.unc.edu or 152.2.22.80
Xref: sparky sci.math:13289 sci.physics:16620
From: dak@tabaqui.informatik.rwth-aachen.de (David Kastrup)
Subject: Re: Irrational?
Organization: Rechnerbetrieb Informatik  /  RWTH Aachen
Date:  9 Oct 92 18:44:41 GMT

chrisman@wheatena.berkeley.edu (chrisman) writes:

>In article <COLUMBUS.92Oct2172559@strident.think.com> columbus@strident.think.com (Michael Weiss) writes:
>>
>>I believe the term "irrational" actually derives from "not a ratio", i.e.,
>>of two integers.
>>

>Does anybody know if the common-use word "irrational" (meaning
>nonsensical) is actually derived from the mathematical term?

irrational in the common-use derives from the philosophist term ratio,
and does not mean nonsensical. irrational is everything not explainable
by ratio, namely reason. Although lots of proofs of God's existence
have been published in history, it is now rather believed to be
irrational, not expoundable by mere reason (the existence, that is).

Anything not accessible to reason can be called irrational. The latin
term ratio in this context does not pertain to a relation between
things, but to reason.
Newsgroups: sci.math
From: bs@fatima.mitre.org (Robert D. Silverman)
Subject: Re: puzzling squares
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Thu, 8 Oct 1992 01:15:07 GMT

In article <UDQ750@gwdu03.gwdg.de> moeller@gwdgv1.gwdg.de writes:
 
stuff deleted....

:To prove that this is indeed the smallest such number,
:one had to show that  (10^(2*k) + 1)  is square-free, for (2*k) < 136.
:Does the current state of the "art of factorization" allow for this check?
 
All number of the form 10^n + 1 have been factored for n = 1 to 148.
[10^149+1 is the first such that has not been completely factored].
10^{2k} + 1 is indeed squarefree for 2k < 136. For 2k=136, it is
divisible by 17^2.

--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
From: chrisman@wheatena.berkeley.edu (chrisman)
Newsgroups: sci.math
Subject: Elevator algorithms
Date: 13 Oct 1992 20:35:21 GMT
Organization: U.C. Berkeley Math. Department.
Distribution: usa
NNTP-Posting-Host: wheatena.berkeley.edu
Originator: chrisman@wheatena.berkeley.edu

Does anyone know of a reference for the problem of efficient 
elevator algorithms?  I mean, how are elevators programmed
to minimize (in some sense or another) the amount of time
people have to spend waiting for a car?


Newsgroups: sci.math
From: guckes@math.fu-berlin.de (Sven Guckes)
Subject: Re: 'Perfect' numbers
Originator: guckes@medusa
Organization: Free University of Berlin, Germany
Date: Mon, 12 Oct 1992 03:13:54 GMT

dagjo@ifi.uio.no (Dag Espolin Johnson) writes:

>Does someone have a list of the first numbers (as many as possible) that are
>'perfect'?
>
>With 'Perfect number' I mean those numbers such that if you add together all
>the numbers that is divideable with the numer, you get the number.
>
>The first one is 6     (1+2+3 = 6)
>The next one is 28     (1+2+4+7+14 = 28)

>If this is a FAQ, please tell me where I can find the answer.

"It's in the FAQ!" - Damn, it isn't. (I just checked in news.answers.)

If I remember correctly then the following are perfect numbers, too:

496
2128

Unfortunately I don't have a reference at hand.
Newsgroups: sci.math
From: wjcastre@magnus.acs.ohio-state.edu (W.Jose Castrellon G.)
Subject: Re: Order -> Algebraic Structure
Keywords: Rationals,Dense Ordering,Algebraic Structure
Organization: The Ohio State University,Math.Dept.(studnt)
Date: Sat, 10 Oct 1992 16:10:42 GMT

In article <BvvuD8.I26@world.std.com> rjk@world.std.com (robert j kolker)
writes:

>Let H be a denumerable completely ordered set, where the ordering is
>dense, and there are no maximum or minumum elements. It is well known that
>any two sets having these properties are order isomorphic. 
>
>The set of rationals Q is a fortiori this set (up to an isomorphism).
>Clearly the seemingly innocent densely ordered set inherits its algebraic
>properties via this isomorphism or does it? 
>
>Is there someway of showing independent of this coincidental isomorphism ,
>that denumerable,densely ordered -> the algebraic structure of Q, i.e. Q
>is a denumerable field or characteristic 0.
>
>Your input would be appreciated.
>

I think it is not possible to prove a statement along those lines, as one
can cook up examples of denumerable densely ordered fields of characteris-
tic zero that dont have the same global properties of Q ; for example Q is
an Archimedean field (i.e given any positive element  x, and an arbitrary 
positive  y, one of  x, x+x, x+x+x, ... will be greater than y) : one field 
that doesn't have that property is the set of quotients of polynomials 
in one variable, with rational coefficients, where you say that p(x)/q(x)
is positive if the limit as x goes to infinity is positive. It is not hard
to see that this is a densely denumerable non-Archimedean field of char 0.
It looks like an interesting question, IMO to ask what additional hypotheses
could characterize the structure of Q, or of other fields.
Newsgroups: sci.math
From: charlie@umnstat.stat.umn.edu (Charles Geyer)
Subject: Re: Philosophical Foundations of Probability?
Organization: School of Statistics, University of Minnesota
Date: Thu, 15 Oct 1992 23:51:12 GMT

In article <1bk8jfINNk1m@usenet.INS.CWRU.Edu> cxm7@po.CWRU.Edu (Colin Mclarty)
writes:

>	I really liked Gigerenzer et al. (six coauthors) _The Empire
> of Chance_.  This is a collaborative philosophical history whose 
> coauthors spent years working together--yet it is quite readable.  

I'll second the recommendation.  It's a very good book, understandable
but touching on many deep issues.

The authors spent *a* year all visiting at the same university (of course
all six share the same research area -- history of probability and
statistics).  To defend the authors against the charge of readability :-)
they also did a six-volume work that is more "academic".  Also three or four
have written books of their own on the subject.

-- 
Charles Geyer
School of Statistics
University of Minnesota
charlie@umnstat.stat.umn.edu
Xref: sparky sci.math:13187 rec.music.classical:14265