HDTenEightyP/NetNews huggingface dataset:
From: wangl@sierra.com (Larry Wang)
Subject: Find all polygon?
Organization: Sierra Geophysics Inc.,  Kirkland, Wa
Date: Thu, 23 Jul 1992 22:38:39 GMT

    A method to find all polygons which do not contain any other points within
a polygon for graphs like the following one:


            v.....................................................v



           v.............v.....................v.................v
                        .                       .
                       .                         .
                      .                           .
                     .                             .
                    .                               .
                   v..............v..................v
                  .               .                    .
                 .                .                     .
                .                 .                      .
               .                  v.......................v.
              .                  .                         .
             v                  .                           .
                               .                             .
                              .                               .
                             .                                 .
                            v                                   .
                                                                 .
                                                                  v

v = vertex

The finished graph should like this:


         v.......................................................v
          x                                                      x
          x                       1                              x
          x                                                     x
          v..............v.....................v................v
           x            .                       .               x
           x           .                         .              x
           x   2      .            3              .      4      x
           x         .                             .            x
           x        .                               .           x
           x       v..............v..................v          x
           x      .               .                    .        x
           x     .                .         6           .       x
           x    .                 .                      .      x
           x   .                  v.......................v     x
           x  .      7           .                         .    x
            v                   .                           .   x
              x                .                            .   x
                x             .             8                .  x
                  x          .                                . x
                    x       .                                 . x
                       x   .                                   .x
                         v x x x x x xx x x x x xx x  xx x x x xv 


1, 2, ..., 8 are the polygons found.
--
	Gary Beckman            
	Unix Systems Manager
	Sierra Geophysics	
	11255 Kirkland Way
From: mapsj@gdr.bath.ac.uk (Simon Juden)
Newsgroups: sci.math
Subject: Re: An interesting limit problem.
Date: 29 Jul 92 11:56:56 GMT
Organization: School of Mathematics, University of Bath, UK

In article <1992Jul29.000223.27339@massey.ac.nz> news@massey.ac.nz (USENET News System) writes:
>In article <1992Jul28.191037.28756@gdr.bath.ac.uk>, mapsj@gdr.bath.ac.uk (Simon Juden) writes:
>> 
>> >mattm@lure.latrobe.edu.au writes:
>> 
>> [stuff deleted]
>> 
>> >Will someone please back me up, and say that no one learning
>> >Calculus should ever be allowed anywhere _NEAR_ Mathematica?
>> >(When I say 'learning Calculus' I mean the first two or three
>> >semesters)
>> 
>> I could hardly agree more. Mathematica should be viewed as a fancy calculator
>> (which, essentially, is what it is). Very good and very useful, BUT undergrads
>> HAVE to learn basic concepts and manipulative skills before they're let near
>> it. Otherwise they will never become mathematicians, but rather computer
>> operators. Also they'll never FULLY understand subtle concepts or follow harder
>> arguments used in difficult proofs if they haven't had to do things with their
>> bare hands first. Like any good similar system Mathematica can be very helpful
>> to the professional mathematician. But I believe such gadgets can also do
>> irreparable harm unless used appropriately. I also believe children should not
>> be given calculators until they can do sums without them. But doubtless these
>> views will get me flamed...
>> 
>Since flames were explicitly invited :-), I'll start the ball rolling.
>
>I believe that it is far more important to understand the meaning of
>the operations of arithmetic than to be able to work through the
>algorithms like trained monkeys without having a clue why they work.
>(I know some bright spark will ask how many monkeys I've trained to
>do long division - well, no actual monkeys, but a lot of great apes :-)).
>
>I would probably agree on something like Mathematica - but perhaps
>I'm being illogical in making a distinction.


...I seem to have started an interesting discussion. I should make it
absolutely clear that:

	 My views are my own and do NOT represent those of the University of
	 Bath School of Mathematical Sciences

That said, I agree that it is more important to understand the meaning of the
operations than carry them out like a trained monkey. The point is that when
faced with a new concept, IMHO the best way to understand it is to work through
some easy examples, and then test that understanding with some harder ones.  If
students get into the habit of thinking about things such as limits rather than
running to the nearest machine and asking it to do the problem for them they
may actually turn into mathematicians. But if all that is taught in
undergraduate mathematics courses is what buttons to push then the people that
emerge from those courses will not be mathematicians. I don't think this is
such an antedeluvian view! The problem that started this thread off was a good
example of a pretty argument that those who misuse computers would have missed
out on.

Smile! ;-)

Simon the Slightly Toasted Analyst
Newsgroups: sci.math
From: jefu@akbar.nmt.edu (Jeff Putnam)
Subject: run the hailstone backwards...
Organization: New Mexico Institute of Mining & Technology
Date: Wed, 22 Jul 1992 13:46:01 GMT


I was thinking the other day about the hailstone numbers
(or whichever name you prefer to use) and thought about running
them backwards as a programming exercise.  I wanted to
give the numbers n and m and produce the m smallest precursors
(a precursor to n is a number k, such that f(k), f(f(k)), and 
so on eventually includes n) to n _in_ _ascending_ _order_.   
That is, given (say) 5, we have 10, 20, 40... as precursors, 
and 10 has 3 as a precursor, so 3 gives us 6, 12.... (this 
branch will never get smaller) and so on.  So 5 has (at least)
3,6,10,12 as precursors

Now, each number n has at least one immediate precursor (2n)
and then all the doubles of this.  If n=3k+1, then n has
precursors 2n and k.  If n=3k+2, it only has one precursor
(2(3k+2)=3(2k+1)+1), but that precursor has two precursors,
one of which (2k+1) is less than n. 

So, to compute all the precursors we want to develop this
tree.  This doesnt give us the precursors of n in ascending
order.  If we always try the subtract-one-and-divide-by-3
subtree first, we get smaller numbers, but there is still
the possibility that by going out one of the multiply-by-2
branches we will arrive at a number that is a multiple iterate
of the 3n+1 branch.  (That is, it is 3n+1, where n is 3k+1 and
k is 3j+1 and so on.)

So, my question is, is there a way to figure out which branches
of the tree are best to explore in order to generate the
m smallest precursors to n?

--
jefu <=> Jeff Putnam - New Mexico Tech <=> jefu@nmt.edu 
"Overturn the dominant paradigm"
Newsgroups: sci.math
From: newcomb@cs.columbia.edu (Newcomb Greenleaf)
Subject: A Collatz-like problem
Organization: Columbia University Department of Computer Science
Date: Tue, 28 Jul 1992 17:29:37 GMT


In analyzing 5-state "busy beaver" candidates I
came across the following function which seems
similar to the Collatz/Ulam 3n+1 or n/2 function.
	|-
        |   5j+4   if n = 3j
f(n) = -|   5j+7   if n = 3j+1
	|   0      if n = ej+2
	|-
From any starting positive integer we generate a
sequence by applying f repeatedly.  To questions:

	1.  Does the sequence eventually arrive at
0 for any starting value?
	2.  If so, is there a bound on the length
of the sequence up to the first arrival at 0?

I have, of course, done some computer experiments
which are not concllusive.  For small starting
values here are some longest lengths found up to
then:
      0.  5
      3. 15
    748. 16
    823. 17
   1263. 21
   5278. 23
  31863. 24
  97776. 27
 121935. 28
 168048. 29
 550071. 32
1029315. 35
 
I would appreciate any solutions or advice on how
to attack this problem.

Newcomb Greenleaf
newcomb@cs.columbia.edu
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Re: Is this game determined?
Date: 31 Jul 92 20:48:33 GMT
Distribution: sci
Organization: M.I.T. Artificial Intelligence Lab.


A few respondents have suggested that the axiom schema  I proposed is
equivalent to the axiom of choice.

Can someone propose similar classes of games equivalent to each of the variants
of the axiom of  choice? For example, the axiom of choice for 2 element sets
or n element sets or the countable axiom  of choice or dependent choice?

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
Subject: Re: random triangles
From: wft@math.canterbury.ac.nz (Bill Taylor)
Date: 28 Jul 92 13:10:42 +1200
Distribution: world
Organization: Department of Mathematics, University of Canterbury
Keywords: asymptotics, acute triangles

>	What is the probability that a random triangle is acute  

I think this problem might have appeared here before. It is more elegant to
formalize the concept of a random triangle in R^2 , as that formed by three
lines whose angles are independemtly chosen from uniform[0,2pi].

This determines the (distribution of the) shape and orientation of the triangle
completely, (the size being irrelevant to the question at hand).

Then,  WOLOG, we can consider one of the 3 sides to be horizontal,
 and   WOLOG the 2nd side to have angle t (anticlockwise from x-axis) to be
                   uniform[ 0 , pi/2 ],

 and   the 3rd side to have angle  w  (anticlockwise from x-axis) to be
                   uniform[ 0 , pi ].

Then   P(acute | t) = P( w in [ pi/2 , pi/2 + t ]
                    = t/pi

                          / pi/2
                          |
thus   P(acute) =  (2/pi)*| (t/pi) dw  = 1/4  .
                          |
                          / 0


There is also a quick slick way of getting this answer:-  by considering that
the angles of the 2nd and 3rd lines (given the first is horizontal) must be
oppositely inclined, (prob 1/2) ; and given this, the angle between them can
only be half of the range of possibilities, to ensure acuteness.
Again giving  P(acute) = 1/4 .
---------------------------------------------
Bill Taylor         wft@math.canterbury.ac.nz
Newsgroups: sci.math,sci.math.num-analysis
From: rcpshdb@dutrun2.tudelft.nl (Han de Bruijn)
Subject: RE: Triangulation
Followup-To: sci.math.num-analysis
Originator: rcpshdb@dutrun2.tudelft.nl
Reply-To: rcpshdb@dutrun2.tudelft.nl (Han de Bruijn)
Organization: Delft University of Technology
Date: Fri, 31 Jul 1992 13:14:48 GMT

Summary
=======
In article <1992Jul27.064833.19391@dutrun2.tudelft.nl> I wrote:

> Throw an arbitrary number of points at random in the plane.
>
> Does there exist an algorithm that _triangulates_ such an set of points;
> i.e. generates triangles in a "sensible" way, such that every point is a 
> vertex of a triangle, and the triangles cover the whole area of points ?

Many people responded. Thanks to everybody!

- Reading now the textbook "Computational Geometry, an Introduction",
  by Franco P. Preparata and Michael Ian Shamos, 1985, Springer-Verlag.

- Made an "anonymous ftp" to  netlib@research.att.com , subdirectory "acm",
  and got algorithm 626 from the ACM Transactions on Mathematical Software,
  looked up accompanying articles in the library (but didn't save them).

- Made another "anonymous ftp" to  netlib@research.att.com ,
  and got everything from the "voronoi" triangulation subdirectory.

> I've heard there exists something like "Kolgomorov triangulation".

Nobody heard of it, of course: the beast is called a Delaunay triangulation.
(Well, allow me some nitpicking: it's also not "delaney", "Delauney", ...)

Next question:
|| ----------------------------------------------------------------------
|| Are there any generalizations (and computer programs) for the 3-D case ?
|| ----------------------------------------------------------------------

Please forgive that I don't read "sci.math" anymore. E-mail preferred.
-
* Han de Bruijn; Applications@Convex | "A little bit of Physics * No
* TUD Computing Centre; P.O. Box 354 |  would be NO idleness in * Oil
* 2600 AJ  Delft; The Netherlands.   |  Mathematics" (HdB).     * for
* E-mail: Han.deBruijn@RC.TUDelft.NL | Fax: +31 15 78 37 87 --- * Blood
From: harry@issun1.kfk.de (Harald Kucharek)
Newsgroups: sci.math
Subject: Problem: find smallest box around points in 3D
Date: 24 Jul 92 06:53:24 GMT
Reply-To: harry@issun1.kfk.de
Organization: Kernforschungszentrum Karlsruhe

I have some points in 3D space and I want to find the smallest rectangular box
which encloses these points. The orientation of the box in 3D is arbitrary (otherwise
the problem would be trivial).
Any hints, references, algorithms, code???
Thank you!
		Harald

         Harald Kucharek, Nuclear Research Center Karlsruhe, IDT
		7514 Eggenstein-Leopoldshafen, Germany
         Internet: harry@issun1.kfk.de Phone: +49 7247 825706 
Newsgroups: sci.math
From: lowrie@shear.engin.umich.edu (Robert Byron Lowrie)
Subject: Re: A puzzle!
Date: Fri, 31 Jul 92 15:10:23 EDT
Organization: University of Michigan Engineering, Ann Arbor
Keywords: Math, puzzle
Originator: lowrie@shear.engin.umich.edu


In article <1992Jul26.203418.20562@mailer.cc.fsu.edu>, rose@fsu1.cc.fsu.edu (Kermit Rose) writes:
> In article <chepan.712011867@gsusgi1.gsu.edu>, chepan@gsusgi1.gsu.edu (Parthasarathy Nambi) writes...
> > 
> > 
> > Here is something for puzzle lovers:
> > 
> > Below is a sequence of numbers, can you find the next two numbers and 
> > the general formula for generating numbers in this sequence:
> > 
> > The numbers are:
> > 
> > 4, 72, 21600, 190512000, 58090919040000,   etc 
> > 
> > 
> > If you know the answer please post a response in this group.
> > 
> > 
> > P.Nambi
> > 
> 
> 2^2, 2^3  3^2,  2^5  3^3  5^2,  2^7  3^5  5^3  7^2, etc
> 

I presumed that then,

    58090919040000 = 2^9 3^7 5^5 7^3 9^2

when in fact,

    58090919040000 =  2^10 3^7 5^4 7^3 11^2

Maybe the original posting is wrong?  Because,

    580909190400000 = 2^11 3^7 5^5 7^3 11^2

which makes more sense (the base is a sequence of primes, with the
exponents in reverse order).

Thank you Maple V.


-- 
 Rob Lowrie
 Aerospace Engineering Dept.
 University of Michigan
 lowrie@caen.engin.umich.edu
From: kubo@zariski.harvard.edu (Tal Kubo)
Newsgroups: sci.math
Subject: Re: An interesting limit problem.
Date: 26 Jul 92 19:06:26 GMT
Article-I.D.: husc3.1992Jul26.150627.14192


In article <1992Jul25.212844.1@lure.latrobe.edu.au>
mattm@lure.latrobe.edu.au writes:
>
> I think that this problem was first posed by the
> Russian mathematician Arnold. Hope you find this
>
>                sin(tan x)    -    tan(sin x)
>	lim  ----------------------------------  = ???
>	x->0 arcsin(arctan x) - arctan(arcsin x)
>

See "Huygens, Barrow, Hooke and Newton" by V.I. Arnol'd.
He gives the above limit as an example of a problem
that mathematicians today simply can't solve quickly (in
contrast to their predecessors). He remarks that the only
exception known to him, G. Faltings, proves the rule.

The book is well worth reading, by the way.
From: pt@doc.ic.ac.uk (Paul Taylor)
Newsgroups: sci.math
Subject: Re: The Schroder-Bernstein Theorem.
Keywords: fixpoint, adjunction
Date: 24 Jul 92 15:26:49 GMT
Organization: Department of Computing, Imperial College, London.

The following proof of the Schroder-Bernstein Theorem is my own,
but was inspired by that in Peter Johnstone's book "Set Theory and Logic"
(Cambridge University Press).

Y denotes the "least fixed point" of a monotone endofunction of a poset.
f^*(V) is the inverse image of a subset under a function.
f_! and f_* denote the left and right adjoints of f^* considered as a monotone
function between powersets.
In fact f_!(U)={y:some x in U.fx=y} and f_*(U)={y:all y.fx=y => x in U}.

Let f:A->B and g:B->A be injective functions.
Consider the subsets U=Y(g_!f_*) of A and V=Y(f_!g_*) of B.
(Right-to-left composition; when I say "consider", I mean you have to think
about it for a few minutes.).
The given functions f and g restrict to bijections between U and B-V
and between V and A-U.

The result depends on (and is probably equivalent to) Excluded Middle.
Xref: sparky sci.math:9530 comp.theory:1690
From: eclark@gauss.math.usf.edu. (Edwin Clark)
Newsgroups: sci.math,comp.theory
Subject: Re: dominating sets in a graph
Date: 20 Jul 92 17:53:47 GMT
Organization: Univ. of South Florida, Math Department

In article <1992Jul9.124211.1124@allegra.att.com> bhattach@allegra.att.com (Debashis Bhattacharya) writes:
>I need a brief, but reasonably complete list of references (or a pointer
>to such a list) dealing with dominating sets in a graph. I am interested
>in all that is known about the subject, esp., that found after 1974.
>
>Debashis Bhattacharya.
>bhattach@allegra.att.com


See Discrete Math., vol 86, number 1-3, Dec 1990---the entire
volume is devoted to topics on domination in graphs. If you
are interested in domination numbers of grid graphs, I have
some recent reprints.

Edwin Clark
Math. Dept.  
U of South Florida
Tampa, FL 33620-5700
eclark@math.usf.edu
From: cet1@cl.cam.ac.uk (C.E. Thompson)
Newsgroups: sci.math
Subject: Re: American mathematical hegemony
Date: 21 Jul 92 21:22:24 GMT
Reply-To: cet1@cl.cam.ac.uk (C.E. Thompson)
Organization: U of Cambridge Computer Lab, UK

In a desperate attempt to save this thread from degenerating into a
discussion of the rudeness of the British, or even a Welsh vs. English
slanging match, might we violate Usenet custom and return to the
original subject?

In article <1992Jul16.165327.2769@galois.mit.edu>, tycchow@riesz.mit.edu
(Timothy Y. Chow) writes:
|> In article <75953@ut-emx.uucp> tim@ccwf.cc.utexas.edu writes:
|> >Well, the British journal Nature this month announced that after stubbornly
|> >clinging to an archaic tradition during its 125 years of publishing it is
|> >finally succumbing to modern American terminology and redefining the
|> >word "billion" from 10^12 to 10^9 and also abandoning its use of "trillion"
|> >as a word for 10^18 except in direct quotation of others.
|> 
|> Is this really AMERICAN influence only?  Doesn't Russian follow the same
|> conventions as American English?  What about the French?

Well, the sources seem to be in some doubt here. I seem to recall that when
I was taught such things (c.1960), the two systems were distinguished as 
"American" and "Continental" (which I took to mean "French"). However, the
OED seems to be sure that French custom matches the American in making
"billion" = 10^9, "trillion" = 10^12. On the other hand, they also believe
that French "milliard" = 10^9. Is this really a case of two words for the
same number?

By the way, it is by allowing the perfectly good imported word "milliard"
to fall into disuse in English that we have allowed the Americans to win
this particular battle by default. Discussion of (inter)national economics
especially encourages one to find a single word for 10^9.

|> >Now I wonder how much longer it will take before the "centre" of a sphere
|> >becomes a "center".

No, no. Never. We shall fight them on the beaches...

Chris Thompson
Cambridge University Computing Service
JANET:    cet1@uk.ac.cam.phx
Internet: cet1@phx.cam.ac.uk
Newsgroups: sci.math
From: jnjohann@cip.informatik.uni-erlangen.de (Jan Johannsen)
Subject: Re: Stupid question about FLT
Organization: CSD., University of Erlangen
Date: Mon, 27 Jul 1992 12:18:44 GMT

cmenzel@tamsun.tamu.edu (Christopher P Menzel         ) writes:

>In article <1992Jul19.231456.21018@mailer.cc.fsu.edu> rose@fsu1.cc.fsu.edu writes:
>>I suggest that if FLT is undecidable in one model of the integers, it is 
>>undecidable is ALL models. It is no paradox that if it is undecidable, then 
>>it is true. This is because undecidable simply means unable to prove true or 
>>false. If we cannot (in principle) prove FLT false, this means that it IS 
>>NOT FALSE.  

>You seem to be saying that inability to prove the negation of a
>sentence implies that the sentence isn't false.  But, for example, we
>cannot prove (in PA) the negation of the G\"{o}del sentence for PA,
>but (reasoning in the usual way in our metatheory) it is false (in the
>natural numbers) all the same.

Of course the implication   not (provable (not A)) -> A
does not hold in general, but it holds for _universal_ sentences, 
and of course FLT is a universal sentence (or at least, if you 
define exponentiation, a \Pi_1- sentence, for which the same holds).

>>Whereas, it might be possible that no method exist to prove FLT
>>is true.  Since we say that FLT is true if it is not false, we say that if 
>>FLT is undecidable, then it is true.

>Correct me if I'm wrong, but I *think* the reason that the
>undecidability of FLT implies its truth is simply that any
>counterexample to FLT (i.e., a formula of the form a^n + b^n = c^n)
>would be provable in PA.  Hence, FLT can't be both undecidable and
>false.

Yes, and this can be generalized to any universal (or \Pi_1) sentence, since
any counterexample would be an open (or bounded) formula, and all such 
formulae are provable in PA iff they are true (in the REAL integers).

>Chris Menzel

J. Johannsen     jnjohann@immd1.informatik.uni-erlangen.de
From: kai@cyklop.nada.kth.se (Kai-Mikael J-Aro)
Newsgroups: sci.math
Subject: Buckets of water (references sought)
Date: 26 Jul 92 20:13:36 GMT
Distribution: sci
Organization: Royal Institute of Technology, Stockholm, Sweden
Originator: kai@cyklop.nada.kth.se

I have been thinking about those old puzzles where you are given two
buckets of specific volumes and have to measure up a certain,
different, volume of water in one of them.

Has anything been written on this subject?  (I can't even begin to
guess how to make a literature search.  "Look for 'bucket' and/or
'water' - whoops 45000 hits..." ;-)
-- 
Kai-Mikael Jdd-Aro	email:  kai@nada.kth.se	    "Don't win, don't lose."
IPLab	 		voice:  +46 8 790 91 05		-- Yoshigasaki-sensei
NADA, KTH		fax:    +46 8 790 09 30
S-100 44  Stockholm	telex:  812 6154 7052 SICS
SWEDEN			teletex:2401-812 6154 7052=SICS
From: nickh@CS.CMU.EDU (Nick Haines)
Newsgroups: sci.math
Subject: Re: wanted (was: Mathemantical tattoos)
Date: 22 Jul 92 18:36:28 GMT
Organization: School of Computer Science, Carnegie Mellon University
Originator: nickh@VOILA.VENARI.CS.CMU.EDU

In article <15512@star.cs.vu.nl> anil@cs.vu.nl (Sukul AR) writes:

   =
   And so God said:

   < 
     a bunch of complex integrals and differential equations, 
     which would cause a normal person to slightly faint and not gain
     conscience for an hour or so.
   >

   And there was light.
   =

The equations in question are basically Maxwell's equations (at least,
the ones I've seen are), only written out in full partial-derivatives
terms (so there are, erm, 8 (?) of them) instead of div-grad-curl
terms, in order to look more impressive (and which therefore look
substantially _less_ impressive to anyone who knows what they mean). I
think if I were to have a mathematical tattoo, it might well be
relativistic Maxwell (4 symbols in a single equation) or the basic GR
equations (which are about 6 symbols each).

Nick Haines nickh@cs.cmu.edu