HDTenEightyP/NetNews huggingface dataset:
From: simpson@matt.ksu.ksu.edu (Phillip C Simpson)
Newsgroups: sci.math
Subject: Points on a sphere question
Date: 18 Dec 1992 16:26:49 -0600
Organization: Kansas State University
NNTP-Posting-Host: matt.ksu.ksu.edu
Summary: How many minima for n equally charged points on unit sphere
Keywords: sphere

I was wondering if the following problem is solved or solvable:

	Imagine n equally electrically charged points at unit distance from 
the origin. For any configuration of points we can associate an energy,

 n 
---  ---
\    \         1
 >    >    ---------        where xi is a point on the sphere 
/    /    ||xi - xj|| 
---  ---
i=1  j>i

	My question is, given n, for how many configurations does the gradient
of this energy term vanish? Or rather for how many unique configurations? Any
rotation of the entire sphere can be considered non-unique.

	The most natural way to set up this question is in sphereical
coordinates, where xi is a pair of angles and the gradient is differentiation
with respect to all four angles. However, this computation quickly gets very
messy. Is there a better (i.e. generalized) system of coordinates that will 
suite the problem? Or is there a purely geometric way to go about it?

	I am also wondering how this problem is related to problems of, for
instance, maximizing the total distance between all the points, or the squares
of the distances. These tasks all seem to be trying to do the same thing. Also,
how is the problem made different if distance is measured on the sphere rather
that through space? Or if a different force law (other than 1/r^2) is chosen?

	Most of the works I have found that approach this type of problem
consider the dynamics of such a system, while I am just wondering how many
energy minima there are. Any references or comments would be appreciated. 

David Skinner
skinner@next1.cs.ukans.edu

PS: In case there is any question, this is not a homework problem.
Newsgroups: sci.math
Subject: Re: Need help with a constraint problem
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Date: 14 Dec 92 23:02:50 GMT
Organization: Beckman Instruments, Inc.
Keywords: constraint, minimize area

In <1992Dec10.181800.27941@purelogic.cs.uwlax.edu> pisul_cj@glutamic.uwlax.edu (Charles Pisula S92) writes:

>here's the problem that I'm sure will prove to be trivial although 
>It's given me a hard time:

>Minimize the area inside an elipse of form  x^2        y^2
>                                            ---   +    ---   =  1
>                                            a^2        b^2
>such that it contains the circle x^2 + y^2 = 2y.


>HINTS:  Area of Ellipse = (Pi)ab

>PLEASE SEND ANY SOLUTIONS TO :
>****************************
>pisul_cj@cowley.uwlax.edu
>****************************

Looks like homework 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.
Xref: sparky sci.math:16790 sci.philosophy.tech:4554
From: haddadi@sipi.usc.edu (Navid Haddadi)
Newsgroups: sci.math
Subject: Re: Master Mind:A question.
Date: 15 Dec 1992 04:03:29 -0800
Organization: University of Southern California, Los Angeles, CA
NNTP-Posting-Host: sipi.usc.edu
Keywords: Master Mind Game

In article <gay.724358375@sfu.ca> gay@selkirk.sfu.ca (Ian D. Gay) writes:
>jimgar@scorch.apana.org.au (Jim Garner) writes:
>
>>evant@coos.dartmouth.edu (Evan E. Thomas) writes:
>
>>|My question regards the game "MasterMind" where 4 pegs are chosen (from an
>>[deletions]
>>|You would be told that 1 color is exactly right and that two others are in
>>|the solution.  You have exactly 10 guesses to find the solution.  Is there
>>|an algorithm that will insure victory?
>
>>There is an optimal strategy that has been published. It is very long
>>and divided into cases, so I wouldn't call it an algorithm. But it
>>certainly can be done in less than 10 guesses every time. All I
>>remember is that your first guess should contain 2 colours only, 2
>>pegs of each.
>
> ...
>that the 5-peg version can usually be solved in 6 guesses; presumably 
>...

Say we are dealing with 5 pegs and 10 colors. So that all possible
guesses can be represented by {00000,00001,00002,....} There are
obviously 100,000 possibilities. Say, that we have a way of generating
all the numbers between 00000 and 99999 in a random sequence (for example,
by a shift register). It is not too difficult to search the entire
space. For example, let the first guess be G1. Then let G2 be the
second sample of the entire space of possibilities. Now score G1 w.r.t.
G2 and compare the score to the actual score of G1. If they are not the same
discard G2 and take the next *random* sample. If they are the same then
propose G2 as a solution. If G2 is not the solution, start the process
again with G3. This time both G1 and G2 are scored w.r.t. G3 and the
resulting scores are compared to the acutal scores. We can discard G_N
as soon as a contradictory score is obtained for smallest n<N. In this
way searching the entire space only once, a solution is obtained.
The resulting program is very simple and also very fast. The key is that
the sequence must be generated in a random way. Although, I have not
done the analysis, I doubt that the "optimal" solution is any faster (in terms
of the number of guesses) than this simple method.

Navid. 
haddadi@sipi.usc.edu
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Re: Define "Mathematics"
Date: 12 Dec 1992 08:34:10 -0500
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu


More information about an earlier answer.  It was Lynn A. Steen who
defined:

Mathematics is the science of patterns.

-- 
  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,sci.physics,sci.bio,sci.chem,misc.education
From: pereiras@wl.aecl.ca
Subject: RE: what is the number ..
Organization: AECL RESEARCH
Date: Thu, 17 Dec 1992 21:38:52 GMT

1, *2*, 145, 40585
Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
From: polowin@chem.queensu.ca (Joel Polowin)
Subject: Re: TIME HAS INERTIA - BASS JEALOUS AND INSECURE-ABIAN VALIDATED
Organization: Dept. of Chemistry, Queen's University
Date: Sun, 13 Dec 1992 20:05:56 GMT

In article <abian.724200923@pv343f.vincent.iastate.edu> abian@iastate.edu (Alexander Abian) writes:

>   DO NOT ASK what is the Definition of "SECURITY" - nothing can define it 
>-it is the basic, the fundamentally elemental term 
>
>     IT IS THE LIFE ITSELF, IT IS THE SCIENCE, THE PHYSICS ITSELF
 
Great.  Sounds like the Force.  Straight from the mouth of Abian Kenobi.

Abian, you have made a specific prediction, based on your theory: that
particles are unstable, inversely proportional to how "big" they are.
I don't know how you define "big", but I can't think of any definition
which doesn't place mesons, with very short lifetimes, between electrons
and protons, which don't.  Your specific prediction contradicts tremendous
numbers of replicated, reliable experiments.  The usual conclusion that is
drawn from such results is that your theory is incorrect.

Joel Polowin
polowin@silicon.chem.queensu.ca, polowin@chem.queensu.ca,
polowinj@qucdn.queensu.ca

Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
From: maierj@edmund.cs.andrews.edu (Joey Maier)
Subject: Re: Can we have sci.chem back? (was Re: TIME HAS INERTIA abian stuff)
Organization: Andrews University
Date: Mon, 14 Dec 1992 20:41:47 GMT

>In article <1gh38uINN93b@chnews.intel.com> bhoughto@sedona.intel.com (Blair P. Houghton) writes:
>>In article <1992Dec13.195740.10476@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>>>Do they mention that I invented the crackpot index?  Probably not.  Yet
>>>another brilliant idea of mine leading to no tangible fame.  :-)
>>>Maybe I should write a letter to the editor.
>>
>
>
>Can we please not consume so many net.resources to bashing ABIAN?
>Will you all kindly look at how many groups you are crossposting to?
>How about making an alt.abian group or taking this to email?
>
>
>
>-- 
>David Knapp                                      University of Colorado, Boulder
>Perpetual Student                                   knapp@spot.colorado.edu

I second that.  sci.bio would be alot better if it had biology instead
of abian as a subject.

Joey                      maierj@andrews.edu

Newsgroups: sci.math
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: Alleged shortage of mathematicians (was Re: M
Date: 10 Dec 92 23:40:02 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <Byzw0x.MCv@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>In article <1401@kepler1.rentec.com> andrew@rentec.com (Andrew Mullhaupt) writes:
>> The question
>>as I see it is "should a  Ph. D. limit himself to employment as a pure
>>mathematics research professor?"

>Did you mean "ought not" instead? 

I have no problem with that wording. But I don't see a big difference.

>But I agree that few should limit
>themselves to pure mathematics research; they should get involve, on
>a part-time basis, with applications.  Conversely, those doing applications
>should get involved with teaching and supervising PhD research.  Even if
>this is not done, the applied people should keep their hands in the 
>"pure stuff."  Both the theory and applications suffer from the separation.

Absolutely. One of the important ways to stay sharp as an applied mathematician
is to continue to study pure math.

In fact I think one of the most important developments in mathematics is
the growing realization on the part of the mathematical community that
'pure' mathematics is not separated from applied mathemtics by some 
fortified border, but is really an adjective for things we don't know
how to use yet.

Later,
Andrew Mullhaupt
From: dreier@durban.berkeley.edu (Roland Dreier)
Newsgroups: sci.math
Subject: Re: Philosophy of Pi
Date: 18 Dec 92 09:41:57
Organization: U.C. Berkeley Math. Department.
	<1992Dec18.114450.22206@lth.se> <BzGovA.JzJ@news.cso.uiuc.edu>
NNTP-Posting-Host: durban.berkeley.edu
In-reply-to: brumleve@iboga's message of Fri, 18 Dec 1992 15:40:19 GMT

In article <BzGovA.JzJ@news.cso.uiuc.edu> brumleve@iboga (Dan Brumleve) writes:

   dat92oma@ludat.lth.se (Ola Martensson) writes:

   >A friend and I discussed if you can find any integer anywhere
   >in the expansion of PI?

   >1415 , 92 etc is obvious BUT can you really find ALL integer
   >even unlimited ones???

   Hmm...  I'd think that you would be able to find any integer in an
   irrational number.  Not sure though.

It is certainly false than one can find any integer in ANY irrational
number.  Consider the irrational number .101001000100001000001... (I
leave it as an exercise to prove that this is irrational ;-) Now,
certainly 2 does not appear in the decimal expansion of the number
above.

However, it is a very open question as to whether every integer
appears in the decimal expansion of Pi.  This is called the Goldbach
conjecture, and I'm not aware of any real progress toward a solution.
--
Roland Dreier                                        dreier@math.berkeley.edu
Newsgroups: sci.math
From: sbardhan@uncc.edu (Soumendu Bardhan)
Subject: Re: Interesting Discrete Math Question
Reply-To: sbardhan@uncc.edu
Organization: University of NC at Charlotte
Date: Fri, 18 Dec 1992 01:54:28 GMT

Ken writes:
  
This is all well and fine, except, how do you know you've found the best partition
of those integers?  That is, how do you know there isn't some other partition Q = 
{q_1, q_2, ... q_n} of the numbers 1-100 such that

(i) for all i, j, and for all a in q_i, b in q_j, |a - b| != 3; and
(ii) n > 51?

I bring this up since someone else answered 51, having found a way to choose 50
elements before guaranteeing that two would be 3 apart.  At first blush that
seemed plausible, until others got a little more clever.  Is

1 2 3, 7 8 9, ....., 97 98 99

as clever as we need to be?

For the record, I believe so (QED :-)).
 
I think this is what makes mathematics different from other subjects,
Great mathematicians have  discovered famous theories and numbers
without even leaving a clue to us regarding how they got it;
May be they themselves could not realize it.

Newsgroups: sci.math,rec.puzzles
From: rogerj@aix.rpi.edu (Diversion (Jeff Rogers))
Subject: Re: Marilyn Vos Savant's error?
Date: Tue, 15 Dec 1992 21:54:35 GMT

[various other people as well as ]
karr@cs.cornell.edu (David Karr) wrote about the subject...

>How about the following rephrasing of the problem.  You meet a man
>on the street and have the following conversation:
>"How many children have you?"
>"Two."
>"Is one of them a boy?"
>"Yes."
>What is the probability that the other child is also a boy?

What I didn't see in this thread ('tho I may have missed it earlier, I just
picked up the thread) is the simple biological argument. The probability of
any given child being a boy[girl] is 50%. Regardless of the sexes of any
siblings. 

Disregarding psychological implications:
"I have 100 children, (at least) 99 of which are boys"

The chance that the 100th child is a boy is _still_ 50%.

Diversion


-- 
"I can see 'em                          | "Want me to create a diversion?"
    I can see 'em                       | Diversion
        Someone wake me when it's over" | rogerj@rpi.edu
From: cazelaig@ERE.UMontreal.CA (Cazelais Gilles)
Newsgroups: sci.math
Subject: proof requested
Date: 15 Dec 92 14:53:55 GMT
Organization: Universite de Montreal

I would really appreciate if someone could give me a proof of the following
result. A reference which contains the proof would do the same.
 
The problem is: ......
 
 
       let F:B -> R be a continously differentiable function. Where B is
                         n
the closed unit ball in R .
 
Show that:  max{F(x): x in B} - min{F(x): x in B} >= 2min{||F'(z)||: z in B}
Newsgroups: sci.math,rec.puzzles
From: c60a-it@danube.Berkeley.EDU (The Trashcan Sinatra (Amit Sahai))
Subject: Re: Marilyn Vos Savant's error?
Organization: University of California, at Berkeley
Date: Wed, 16 Dec 1992 20:32:38 GMT

In article <1992Dec16.072922.21082@bnr.ca> bcash@crchh410.BNR.CA (Brian Cash) writes:
>In article <1992Dec15.091823.10100@nmt.edu>, jduncan@nmt.edu (John
>Duncan) writes:
>|>In article <1992Dec15.063213.11742@bnr.ca> bcash@crchh410.BNR.CA
>(Brian Cash) writes:
>|>>In article <1992Dec15.052211.24395@CSD-NewsHost.Stanford.EDU>,
>|>>snewman@Xenon.Stanford.EDU (Steven Newman) writes:
>|>>|>
>|>>|>   1) You meet a man on the street and ask him how many children he has.
>|>>|>      He replies "two, and one is a boy."  What is the probability that
>|>>|>      his other child is also a boy?
>|>>|>
>|>>|>   2) You meet a man on the street and ask him how many children he has.
>|>>|>      He replies "two, and the older one is a boy."  What is the
>|>>|>      probability that his other child is also a boy?
>|>>|>

>What am I doing wrong?
>
>I think you might be dividing the children in another way:
>
>a) child A = boy   child B = boy
>b) child A = boy   child B = girl
>c) child A = girl  child B = boy
>d) child A = girl  child B = girl
>
>Given this and "one is a boy" only d is invalid, but it also
>makes b and c the *same* (one boy, one girl...order is irrelevant).
>So now you have two events: a and b/c.  Odds = 1/2

>Does anyone follow what I am saying?
>
>Brian /-|-\ 

I think I follow, but you are wrong. Yes you do only have two events
a and b/c but the probability of a is 1/3 and b/c is 2/3.
Example: If you flip two coins and count the number of heads, there
are only 3 "events" possible: 0 heads, 1 head, 2 heads. But their
probabilities are not 1/3 each, obviously.

I think the original solution is right, except, of course,
we have neglected the possibility of identical twins (with one
twin possiblly deciding to have a sex change), in which
case the ages are exactly the same ;-) not very important, though.

Amit.
-----------------------------------------------------------------------------
Amit Sahai: amits@cory.berkeley.edu
   "We demand rigidly defined areas of doubt and uncertainty!" :)
From: rcbaaw@rw6.urc.tue.nl (Angelo Wentzler)
Newsgroups: sci.math
Subject: Re: Tiling problem
Date: 18 Dec 92 14:05:10 GMT
Reply-To: rcbaaw@urc.tue.nl

choy@skorpio.usask.ca (I am a terminator.) writes:

>In article <1gggutINN29q@access.usask.ca>, choy@skorpio.usask.ca (I am a terminator.) writes:
>|> In article <israel.723837962@unixg.ubc.ca>, israel@unixg.ubc.ca (Robert B. Israel) writes:
>|> |> In <rcbaaw.723228012@rwb.urc.tue.nl>, rwb.urc.tue.nl (Angelo
>|> |> Wentzler) writes:
>|> |> 
>|> |> >Given a grid of squares, tile it with black and white tiles and make
>|> |> >the largest possible square so that no square contained in it has four
>|> |> >equally colored corners.

>Never mind my previous post, but can such an n x n square be constructed
>as a permutation of an n x n checkerboard?

>Henry Choy
>choy@cs.usask.ca

Not all of them. There is only one 2x2 square that can be constructed from 
a 2x2 checkerboard. Manually (my search program is at home) I found some
squares with the same property for the smaller sizes. I have also added
some counterexamples.

solution       checkerboard         Counterexample

10             10                   11
01             01                   01

101            101                  111
011            010                  010
100            101                  011

1010           1010                 1111
0110           0101                 0101
1001           1010                 0110
0110           0101                 1100


For such solutions the following holds:
odd dimension: #black=#white+1
even dimension: #black=#white
So "balanced squares" would be a good name.
Note that a balanced square doesn't necessarily have two white and two black
corners.

In the small example each solution is derived from the previous one, but
I don't think that's necessary. You could make a balanced square from an
unbalanced smaller one. Just mirror the 3x3 to get an example.
Still, could the following be true?

Any balanced NxN square must contain at least one balanced ixi subsquare for
each 1<i<N

If this were true, then the same approach for normal squares would be
possible: just take a 2x2 balanced square (*the* 2x2 balanced square) and
just keep expanding it to obtain one for any dimension (up to a certain
limit...)
Because if the above holds, those balanced ixi subsquares in particular will
contain balanced subsquares too, etc.

Could make a nice subset of the correct solutions...


Angelo Wentzler
Newsgroups: sci.math
From: sbardhan@uncc.edu (Soumendu Bardhan)
Subject: Calculus Puzzle
Reply-To: sbardhan@uncc.edu
Organization: University of NC at Charlotte
Date: Fri, 18 Dec 1992 02:37:00 GMT

X + X + X + X +X.... X times = X^2
Differtiating both sides w.r.t X we get

1 + 1 + 1 + .....X times = 2X
or , X = 2X
 as X may not be Zero
1 = 2.


--Soumendu, UNCC
From: G.Joly@cs.ucl.ac.uk (Gordon Joly)
Newsgroups: sci.math
Subject: Would Pi repeat, were it expressed in a base other than 10?
Date: 14 Dec 92 13:06:06 GMT


Also, a friend asks:

``Is there any structure in an expansion of pi which will manifest itself
in any base?''

Gordon,

____

Gordon Joly      Phone  +44 71 387 7050 ext 3703      FAX  +44 71 387 1397
Internet: G.Joly@cs.ucl.ac.uk        UUCP: ...!{uunet,uknet}!ucl-cs!G.Joly
Computer Science, University College London, Gower Street, LONDON WC1E 6BT
From: alien@acheron.amigans.gen.nz (Ross Smith)
Newsgroups: sci.aeronautics
Subject: Re:  SILENT HELICOPTER
Date: 17 Dec 92 22:13:22 GMT+12
Distribution: world
Organization: Muppet Labs

In article <921215011849@avistic.demon.co.uk> lorcan@avistic.demon.co.uk (Lorcan Mongey) writes:
>In article <1992Dec6.235739.9736@athena.mit.edu> cid@athena.mit.edu
>(Derek H Cedillo) writes:
>
>> And, damn was that an impressive sight.  Id love to see the Mi-24 hind.
>> Only one bigger than the 53 series
>
>Don't you mean the Mi-26 Halo? The Hind is a helicopter gunship and
>considerably smaller than the 53.

The Mi-26 wasn't the only helicopter larger than the Stallion; so was its
predecessor, the Mi-6/10 family. The Mi-12 "Homer" was even bigger than the
Mi-26, but only three prototypes were ever built (it was basically two
modified Mi-6 engine/rotor assemblies side by side, with a huge fuselage
slung between). Some comparative data (various sources) :

Helicopter       CH-53E          Mi-6A      Mi-26T     Mi-12
                 Super Stallion  "Hook"     "Halo-A"   "Homer"
Max TO weight    33,340 kg       42,500 kg  56,000 kg  105,000 kg
Max payload      16,330 kg       12,000 kg  20,000 kg  35,380 kg
Rotor diameter   24.08 m         35.00 m    32.00 m    35.00 m (each)
Rotor blades     7               5          8          5 (each)
Fuselage length  22.35 m         33.18 m    33.73 m    37.00 m
Engines          3               2          2          4
Total power      9,798 kW        8,202 kW   16,760 kW  19,388 kW

(making the Mi-12 bigger than a Hercules!)


--
...... Ross Smith (Wanganui, NZ) ...... alien@acheron.amigans.gen.nz ......
   Mine is the ship bound for Alpha Centauri
   We must be out of our minds
   For though we are shipmates bound for tomorrow
   Everyone here's flying blind                          (Crystal Gayle)
--
From: prichard@devon.larc.nasa.gov
Newsgroups: sci.aeronautics
Subject: Re: "silent" helicopters
Date: 14 Dec 92 12:31:24
Organization: Lockheed Engineering & Sciences Co.
NNTP-Posting-Host: devon.larc.nasa.gov
In-reply-to: cm9@prism.gatech.EDU's message of 11 Dec 92 20:27:14 GMT


 cm9@prism.gatech.EDU (MCKEITHAN,CLIFFORD M.) writes:

   Devon, (aka Senior Gofer)

   The noise problem can be solved by not building noisy
   helicopters and instead building tiltrotors, right?

   Cliff McKeithan

hey, Cliff!  thats the plan.  tiltrotors have their own acoustic
peculiarities, for which my paycheck is grateful.  the bottom line is,
as usual, capital.  not only for our end (i.e. prediction method 
development, model and full-scale testing, etc.) but also to create
the market for the production vehicles.  we're now in a wobbly state;
we have existing noisy helicopters in service, and an increasing
understanding on noise reduction, but no impending design projects on
which to apply it.

Slick Willie sez he's for infrastructure spending, so let's hope
that includes rotorcraft and short-haul.  our problem is we're not
glamorous enough.  we don't have snappy acronyms and "space-camps"
and all that.  and since Congress has Nat'l Airport in their front
yard they probably don't appreciate the air transport bottlenecks
which are developing.

--
 ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
 | Devon Prichard                       I haven't lost my mind;         |
 | Senior Gofer                         its backed up on tape somewhere.|
 | Lockheed Engineering & Sciences Co.                                  |
 | prichard@devon.larc.nasa.gov                                         |
 ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||