HDTenEightyP/NetNews huggingface dataset:
From: peters@yang.earlham.edu
Newsgroups: sci.math
Subject: Re: Solitaire games
Date: 5 Sep 92 03:38:18 GMT
Organization: Earlham College, Richmond, Indiana

Here is a solitaire game I invented to avoid learning High School algebra. 
It requires pencil and paper.  Make an even number of vertical bars, thus:

    ||||||||||  

Connect pairs of them by arcs across the top of the array until each bar 
has exactly one arc touching its top end.  The challenge is to connect the 
bars by arcs at their bottom ends so that the entire picture forms one 
continuous (but self-intersecting) line.

After a little practice, you'll find an algorithm.  But if the number of 
bars is large, finding a solution is still pleasingly difficult, at least 
if your standards are low because you're stuck at an airport layover.  You
can increase the interest by making a few random arcs on the bottom side
of the array and trying to discover whether a solution is still possible.

  Peter
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: measures of the `size' of infinite sets
Date: 10 Sep 92 01:46:52 GMT
Organization: U of Cambridge, England

Just to add a little confusion to the current discussion of measure, density
and such: In fact there are various different notions of the density of a set
of integers. Fortunately they all give the same answer for nice sets such as
{multiples of 29}...

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
From: loader@vax.oxford.ac.uk
Newsgroups: sci.math
Subject: Re: Chess Problem
Date: 12 Sep 92 14:46:32 GMT
Organization: Oxford University VAX 6620

In article <BuGA8t.DL8@cmptrc.lonestar.org>, carter@cmptrc.lonestar.org (Carter Bennett) writes:
> rairan@ecf.toronto.edu (RAI Ranjan) writes:
>>Chess Problem:
>> Eight rooks are placed at random on a chessboard.  
>> What is the probability that no two rooks can attack one another?
> 
> Ahoy!
> 
>    Oooh!  I like these problems.  Glad you sent it along!
> First, let's check the number of distributions of 8 rooks on the board.
> This is the combination calculation of 64 squares taken 8 at a time:
> 
>    / 64 \  -  (64!) / ( (64 - 8)! 8! )  = 4426165368
>    \  8 /  -
> 
>    So there are 4426165368 possible ways to place the 8 rooks on the 
> board.  My understanding is that no two rooks can attack each other 
> only when they are arranged such that they line up on one of the two 
> diagonals of the board.  Meaning there are 2 ways out of 4426165368 
> possible setups that meet the criteria.  Putting that in normalized odds:

There's a few more than this, aren't there? All we need is exactly one rook on
each row and one on each column, which gives us 8! possible ways...
> 
>     2 / 4426165368 -> 1 chance in 2213082684
> 
so isn't it 1 chance in (64!) / ((64-8)! 8! 8!)

> Two REALLY NEAT THINGS about this problem - 
> 
>   I've seen chess boards many times.  We've seen all kinds of arrangements
> of chess pieces.  Just knowing how many possible arrangements of eight
> pieces is still fascinatingly mind-boggling to me.
> 
>   BUT THE REALLY NEAT THING ABOUT THIS PROBLEM is that I was able to give
> you integer answers to this problem because I had a calculator (HP48SX)
> on hand that could handle them.  dc(1) on Unix would do it, too.  But
> just a few short years ago, we would have had to settle for approximations
> in exponential notation unless we actually multiplied 64x63x62...x56 out
> by hand, and then dividing the result by 40320, again by hand!!!  Too
> many significant digits to keep track of on yesterday's calculators!

THE REALLY NEAT THING about not having a calculator is that I get the answer as
an expression that means something to me, not a just a sequence of digits...

> 
>   FOLLOW-UP QUESTION FOR EXTRA CREDIT:
> 
>   Determine the odds for doing the same with eight bishops!  ;-)
> 
> Carter R. Bennett, Jr. - Scientist      No matter where you go...
> carter@scilab.lonestar.org - home                 .../dev/tty!
> carter@cmptrc.lonestar.org - work
> KI5SR
Newsgroups: sci.math
From: carter@cmptrc.lonestar.org (Carter Bennett)
Subject:  Apology for Chess inaccuracy!
Summary: Boy, is my face red!!!
Date: Sat, 12 Sep 1992 23:49:23 GMT
Organization: CompuTrac Inc., Richardson TX

Boy, is my face red!!!

  Thanks to Richard Pinch and Toby Kelsey for pointing out the error
in my ways!  I found my mailbox this morning with their polite notes
pointing out my mistake.  I'm glad they did that.  I hope I'm a     
better mathematician for it.

  There are certainly more than two distributions of 8 rooks where no
two can attack one another.  Richard sent a couple of messages, the first
containing only the figure below.
@ - - - - - - -
- @ - - - - - -    My (inaccurate) assumption was that the rooks would
- - @ - - - - -  have to be lined up on one of the two diagonals.  As
- - - @ - - - -  shown here, this is not true.  Had I though this through
- - - - @ - - -  correctly, I should have realized that I could consider
- - - - - @ - -  one diagonal and allow all permutations of rows (or all
- - - - - - - @  permutations of columns, if you prefer, but not both).
- - - - - - @ - 
  The upshot of this is that there are 8! distributions of 8 rooks that
meet the criteria that no two can attack each other; not 2, as I said
earlier.  >-X

  So, the chances of coming across this randomly are:
40320 in 4426165368 -> 560 in 61474519 or approximately 1 in 109776.

Carter R. Bennett, Jr. - Scientist      No matter where you go...
carter@scilab.lonestar.org - home                 .../dev/tty!
carter@cmptrc.lonestar.org - work
KI5SR
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Lebesgue integral (was: Couple of questions
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Thu, 10 Sep 92 17:36:19 GMT

In article <18neu6INN32k@function.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:

>I have been told that the Lebesgue integral is not needed in physics--
>presumably Riemann integral is enough.  Do you agree?

Last I heard, the Hilbert space of a free particle was L^2(R^3), the
space of all functions whose absolute value squared is LEBSEGUE integrable.
From: brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock)
Newsgroups: sci.math
Subject: Re: measures of the `size' of infinite sets
Date: 9 Sep 92 17:00:45 GMT
Organization: Rose-Hulman Institute of Technology


In article <1992Sep9.042345.7472@galois.mit.edu> jbaez@riesz.mit.edu (John C.  
Baez) writes:

[a discussion of a natural way to calculate the density of a subset of  
integers]

> The set of integers that are multiples of 29 has density 1/29.
> The set of integers that aren't has density 28/29.
> 
> Exercise to see if you get it: figure out, or guess, the density of the
> prime numbers.

Similarly, one can define the density of a subset of integer pairs in the set  
ZxZ.
A more interesting (though slightly more difficult) exercise is: determine the  
density of the set {(a,b) such that a and b are relatively prime}.

--
Bradley W. Brock, Department of Mathematics
Rose-Hulman Institute of Technology  | "Honor one another above yourselves."
brock@nextwork.rose-hulman.edu       | -Paul of Tarsus to the Romans
Newsgroups: sci.math
From: valoisj@polaris.cs.rpi.edu (John Valois)
Subject: References to a problem
Organization: Rensselaer Polytechnic Institute, Troy, NY
Distribution: usa
Date: Tue, 8 Sep 1992 00:34:38 GMT


Hello,

I'm looking for references to the following problem:

We are given p processors. Each processor, starting at some time s(i), 
attempts to perform a task. One "attempt" takes time w(i).
An attempt succeeds if no other processor has succeeded in its own attempt
since the current attempt was begun. Otherwise, the current attempt fails,
and the processor begins another attempt.

I'm interested in what the average number of "attempts" required to perform
the task is, given p, w(i), and some sort of distribution of s(i).

Please email any pointers.

-- 
--------------------------------------------------
 John D. Valois                    (518) 276-4857
 Computer Science Department   valoisj@cs.rpi.edu
 Rensselaer Polytechnic Institute, Troy, NY 12180
From: sl4q+@andrew.cmu.edu (Scott T. Lillis)
Newsgroups: sci.math
Subject: Cellular Automata
Date: 15 Sep 92 18:00:33 GMT
Organization: Freshman, MCS general, Carnegie Mellon, Pittsburgh, PA

I have been researching Cellular Automata similar to the popular "Life
Hack" program.  I have been looking in to more in depth algorithms than
the one found in life hack, using relatively more complex boolean
algebra to devise of a control structure.  If anyone has any ideas on
this subject in general, I'd like to here it.

Scott Lillis
sl4q+@andrew.cmu.edu
From: dlb@fanny.wash.inmet.com (David Barton)
Newsgroups: sci.math
Subject: Re: Chess Problem
Date: 12 Sep 92 19:26:42 GMT
	<DLB.92Sep12135413@fanny.wash.inmet.com>
Organization: Intermetrics Inc., Washington Division, USA

In article <DLB.92Sep12135413@fanny.wash.inmet.com>
dlb@fanny.wash.inmet.com (David Barton) writes:

   Let's see.  The first rook can go anywhere; it eliminates fifteen
   squares from possible next placement, leaving 49.  The second rook has
   49 out of 64 squares to choose from and eliminates thirteen squares
   from the next possible placement set, leaving 36.  Continuing:

     p = 49/64 * 36/64 * 25/64 * 16/64 * 9/64 * 4/64 * 1/64 

Oops.  I forgot to eliminate the square sat upon by each rook as they
occupy spaces.  Thilly moi.

I used to fail math tests like this.

  p = 49/63 * 36/62 * 25/61 * 16/60 * 9/59 * 4/58 * 1/57

Resulting in

  p = 9.10946533801e-6

or

  p = .00000910946533801

What's a factor of two between friends.

					Dave Barton
					dlb@hudson.wash.inmet.com
From: kevin@vaxc.cc.monash.edu.au
Newsgroups: sci.math
Subject: Partitioning of uncountable sets
Date: 8 Sep 92 18:27:06 +1000
Organization: Computer Centre, Monash University, Australia

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.

Newsgroups: sci.math
From: cfk6u@fermi.clas.Virginia.EDU (Charles F. Kramer)
Subject: Digits/Prog to compute pi?
Organization: University of Virginia
Date: Mon, 7 Sep 1992 16:00:21 GMT

Hello! I am looking for some machine-readable digits of pi and/or 
a program which computes pi to many digits.  Is there an FTP site,
or could someone email me this stuff?  Thanks!
Charlie

Newsgroups: sci.math
From: robt@is.morgan.com (Rob Torop)
Subject: Re: Jokes in papers (was Re: Einstein's Erdos number)
Organization: Morgan Stanley - IS
Date: Wed, 9 Sep 1992 16:04:33 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?
|> 
|> 
|> -- 
|> Stephan <neuhaus@informatik.uni-kl.de>
|> sig closed for inventory.  Please leave your pickaxe outside.

I believe the story is in Gamow's book "One Two Three Infinity'.  One of the others
was Hans Bethe.


-- 
-- Rob Torop

+---------------------------------------------------------------------+
| The views expressed here are neither mine nor those of my employer. |
+---------------------------------------------------------------------+
From: sven@cs.widener.edu (Sven Heinicke)
Newsgroups: sci.math
Subject: standard notation
Date: 12 Sep 1992 16:05:44 GMT
Organization: Widener CS Dept
Distribution: sci
NNTP-Posting-Host: betty.cs.widener.edu


Is there a file some place, on ftp or wasi or something, that has a
list of standard notation for subjects like algebra, graph theory and
others?


--
sven@cs.widener.edu                               Widener X-CS system manager
Sven Heinicke                                             and Student
``If at first you do succeed---try to hide your astonishment.''
 --Harry F. Banks
Newsgroups: sci.math
Subject: Re: A Question
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 15 Sep 92 21:13:19 GMT

In <191avdINNjs4@matt.ksu.ksu.edu> bubai@matt.ksu.ksu.edu (P.Chatterjee) writes:

>I've been stumped by this problem and can't seem to figure out a way to tackle  it.

>It goes like this:

>Characterize the functions f: X --> Y for which P(X) --> P(Y), F(A)=f(A), is
>  
>a)injective,
f is injective

>b)surjective, or
f is surjective

>c)bijective.
f is bijective

It seems obvious to me.
--
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: kodiak@matt.ksu.ksu.edu (Bryan D. Nehl)
Newsgroups: sci.math,rec.puzzles,comp.theory
Subject: Re: more on 9.999... = 10.0
Date: 7 Sep 1992 13:13:24 -0500
Organization: Kansas State University
Distribution: inet
NNTP-Posting-Host: matt.ksu.ksu.edu

From an email, I thought might be of interest to others.

> I am familiar with why .999... = 1, and that other such infinite
> series are equivalent to finite decimals, but how can one tell, when
> one has a infinitely repeating rational number, whether or not it can
> be reduced?

You pretty much use the same method as I posted. For example:

	x = 1.523523...
    1000x = 1523.523...   ( need to "move out" one group of the
			    repeating digits. )
  1000x-x = 1522
     999x = 1522
	x = 1522/999

I found all of the methods I posted with (except the series of course)
in a textbook Called "College Algebra: A Problem Solving Approach," by
Fleming and Varberg.  It is published by Prentice Hall.  It's ISBN
number is 0-13-141656-1.  The congressional call number is:
QA154.2.F53 1988,512.9-dc19.

Hope that helps.

Bryan.

/* === Bryan Nehl ========== kodiak@Kodiakpc.Manhattan.KS.US =========+
[            USDA-ARS-NPA-WERU          ][ bdn@chepil.weru.ksu.edu    ]
[     913.532.6233 or 913.532.6495      ][ kodiak@matt.ksu.ksu.edu    ]
+_______________ ...!rutgers!matt.ksu.ksu.edu!kodiak _______________ */

Xref: sparky sci.math:11353 comp.lang.misc:3056 comp.lang.fortran:3541 comp.std.c:2619 comp.lang.c:13611
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math,comp.lang.misc,comp.lang.fortran,comp.std.c,comp.lang.c
Subject: Re: Scientists as Programmers (was Re: Small Language Wanted)
Date: 13 Sep 92 18:23:16 GMT
Organization: Purdue University Statistics Department

In article <MEISSNER.92Sep11164441@curley.osf.org> meissner@osf.org (Michael Meissner) writes:
>In article <a_rubin.716152347@dn66> a_rubin@dsg4.dse.beckman.com
>(Arthur Rubin) writes:

>| Using, instead, 

>|     c = (long)a * b;

>| it becomes a "quality of implementation" issue; and using the 4/2->2,2
>| divide instruction would incorrect on 80x86 machines, as the divide
>| instruction would overflow in cases where the C operations would be legal.

>With most optimizing compilers, this is pretty simple to put in, since
>most optimizations are essentially pattern matching (you match the two
>converts, and long multiply).  Some time ago, I put long long multiply
>code into the MIPS port of GCC for instance in about 2 minutes of
>time.  The code:

>	long long mul (long a, long b) { return (long long)a * b; }

>produces the following code:

>	mul:
>		mult    $4,$5
>		mfhi    $3
>		mflo    $2
>		j       $31

>You are in a twisty little passage of standards, all conflicting.

This may or may not depend on the compiler, however.  And it still is
not quite adequate.  One should be able to have the option of overloading
the * operator so that if c is long long, and a and b are long, this can
be written as c = a * b.  

The point is that C is not the great answer, as many posters claim it is.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)
Newsgroups: sci.math,comp.lang.misc,comp.lang.fortran,comp.std.c,comp.lang.c
From: diamond@jit345.bad.jit.dec.com (Norman Diamond)
Subject: Re: Scientists as Programmers (was Re: Small Language Wanted)
Reply-To: diamond@jit.dec.com (Norman Diamond)
Organization: Digital Equipment Corporation Japan , Tokyo
Date: Fri, 11 Sep 1992 01:25:59 GMT

In article <a_rubin.716152347@dn66> a_rubin@dsg4.dse.beckman.com (Arthur Rubin) writes:
>In <id.I12T.GP4@ferranti.com> peter@ferranti.com (peter da silva) writes:
>>In article <Bu2r42.5xr@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>>>[nxn -> 2n multiplication]
>>	int a, b;   long c;
>>	c = a * b;
>(peter commented further that this works on a PDP-11).
>Aside from there being no guarantee that "long" is longer than "int",

True, and even if it is, there is no reason that it has to work.  If anyone
wants to pay me for it, I could write a C implementation for PDP-11(TM)
non-computers in which the above doesn't work.

>I don't think it is LEGAL for ANSI C to do this, although, I, also have seen
>it work in some C implementations.

ANSI C leaves the result of overflow undefined.  But I think the standard
could pretty well define whatever it wanted without breaking higher laws.

ANSI conforming IMPLEMENTATIONS are allowed to do it because, when the
standard doesn't define the result, the implementations can do whatever
they want.
--
Norman Diamond       diamond@jit081.enet.dec.com
If this were the company's opinion, I wouldn't be allowed to post it.
"Yeah -- bad wiring.  That was probably it.  Very bad."
Newsgroups: sci.math
From: mtymp15@epx.cis.umn.edu (David Hutton)
Subject: RE: TI-81 Sci Calculator Programming
Organization: University of Minnesota
Distribution: international
Date: Sun, 13 Sep 1992 16:19:15 GMT

I am the proud owner of one TI-81 calculator and need to get some simple
programming tips.  One program I need NOW is the quadratic equation.  IF
anyone out there has it handy, could they mail it to mtymp15@epx.cis.umn.edu
?


Thank you!   No.... really.   

mtymp15

-- 
It is better to light a candle then to curse the darkness....
mtymp15@epx.cis.umn.edu  OR  muffman@tfsquad.mn.org

meow
Newsgroups: sci.math
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Subject: Re: Proof of God's Existence
Organization: U of Cambridge, England
Date: Mon, 7 Sep 1992 22:55:58 GMT

In article <1992Sep7.074147.20800@dde.dk> ct@dde.dk (Claus Tondering) writes:
>It seems to me that all attempts to prove God's existence have to
>be postponed until we can define exactly what we mean by existence.
>
>Questions: Does New York exist? Does George Bush exist? Does an apple
>exist? etc. etc.
>
>Sure, I can see New York, I can hear George Bush, I can taste the apple.
>But in these cases I am only relying on my senses. And my senses can
>be deceived. How do I know that George Bush is not a hallucination, a
>mere product of my own mind? How do I know that everything I see actually
>exists and is not simply a hallucination?
>
>There is only one thing I can know for sure: My mind exists! Even if
>everything else is hallucinations, *something* must be seeing those halluci-
>nations, and that something is what I call "my mind". This is not necessarily
>my body. Hey, my arms, feet, even my head may be a hallucination! The only
>thing I know for certain is the existence of the slightly metaphysical
>concept of "my mind".
>
>Now for my real question: Bearing the above in mind, why is it considered
>unscientific to base a belief in the existence of God on personal
>experiences of Him, when a belief in the existence of, say, George Bush is
>based also on personal experiences of him?

1. I'm not at all happy about applying the predicate (if indeed it is one)
of existence to *objects*. Once you have an object... of course it exists!
Even when it's not explicitly so stated, existence only really applies to
*descriptions*. "George Bush exists" means "There exists something with
the following attributes: <insert description of what you mean by "George
Bush" here>". Part of the difficulty with discussions of whether God exists
is caused by the fact that there is much disagreement over what is meant
by "God".

2. Why don't people like proofs based on personal experiences of God? Because
they're less repeatable, somehow. Most people, at least in the USA, have seen
Bush on television, and heard his speeches, and seen reports about him in the
newspapers, and so on. And they've all seen much the same things. This makes
it very hard to believe that your experiences of Bush are the products of your
own mind. On the other hand, many people have had nothing that seems to them
to have been an encounter with God, and those who say they have are by no means
unanimous as to what God is like, or what it is like to encounter him. This
-- 
Newsgroups: sci.math
From: astrod@kentaurus.dftsrv.gsfc.nasa.gov (AstroD Developer)
Subject: what are quadturnians?
Keywords: coordinate transformations
Organization: Goddard Space Flight Center
Date: Tue, 8 Sep 1992 20:44:28 GMT

Would someone please give me a reference and a basic description of  
quadturnians. I understand them to be a compact representation for 3  
dimensional coordinate transformations(?). Please respond to my e-mail  
address unless you think the general reader would be interested.

-Kent Blackburn
kent@kentaurus.gsfc.nasa.gov
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Lebesgue integral (was: Couple of questions
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Fri, 11 Sep 92 01:19:32 GMT

In article <12tnxa#.kmc@netcom.com> kmc@netcom.com (Kevin McCarty) writes:

>But is this a question of convenience or necessity?
>In other words, how badly would you miss them if you threw out the
>non-Riemann-square-integrable functions from L^2(R^3)?
>Could still you do physics with but a slight limp, or would you be
>flat on your back?

Since I do mathematical physics I would be flat on my back.  Perhaps
people who only deal with explicit solutions or numerical analysis could
get away with the Riemann integral.  In any event, I have no desire for
even a slight limp, so it's the Lebesgue integral for me.  If someone 
invents a noticeably better one that's fine with me, too (cf Adler's post).


Newsgroups: sci.math,comp.graphics
From: chrisp@bilby.cs.uwa.edu.au (chris pudney)
Subject: Plane and rect. prism intersection
Organization: Dept. Computer Science, University of Western Australia.
Date: Thu, 10 Sep 1992 03:53:02 GMT

G'day,

To save me from re-inventing the wheel, could anyone point me in the
direction of code to intersect a plane with a rectangular prism in 3D.
The plane passes through the prism and I would like to compute the 
polygon that describes their intersection.

AtDhVaAnNkCsE.
--------------------------------------------------------------------------------
Chris Pudney 

Department  of  Computer  Science,    PHONE: (local: 09) (int'l: +61 9) 380 3455
University  of Western  Australia,   
Nedlands, Western AUSTRALIA, 6009.    FAX:   (local: 09) (int'l: +61 9) 382 1089 
E-MAIL:  chrisp@cs.uwa.edu.au