HDTenEightyP/NetNews huggingface dataset:
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart Goddard)
Subject: Re:Proof of God's Existence
Organization: Rose-Hulman Institute of Technology
Date: Tue, 1 Sep 1992 18:35:36 GMT


In article <1992Sep1.215331.89956@vaxc.cc.monash.edu.au>  
kevin@vaxc.cc.monash.edu.au writes:
> Asides from limitations in the expressive power of mathematics, the  
following
> will show any proof of the ontic status of God futile.
> 1. It is possible to imagine a world, completely agreeing with the  
current one
> on all sensory data, in which God exists. 
> 2. It is possible to imagine a world, completely agreeing with the  
current one
> on all sensory data, in which God doesn't exists.
> Call a world satisfying condition 1 M, and a world satisfying 2 M'.
> Then the existence of these epistemically indistinguishable worlds  
proves that
>[...] Well, there you have it. No further comment necessary.
> Kevin Davey
> Monash University 
> Australia.

Both statements require great leaps of faith (maybe I have seen an  
unconsumed burning bush, the fact of which takes the wind entirely out  
of statement 2).  It may be possible for you to imagine a world without  
God, but that's because you don't have the data I have (my kids can  
make 12 baskets of crumbs from only one small pack of crackers!)
This is an interesting concept:  a proof whose validity depends on the  
who the reader is.

Bart Goddard
From: steiner@andy.bgsu.edu (Ray Steiner)
Subject: Transcendence question
Summary: Question about transcendental numbers.
Organization: Bowling Green State University B.G., Oh.
Date: Sun, 23 Aug 1992 20:57:31 GMT

Is there an irrational number t such that 2^t and 3^t are
both rational? Is this question still open? The answer is
yes if we just consider 2^t (2^{log_2 3} being an example)
but no if we look at 2^t, 3^t and 5^t.(This is a case
of the famous "6 exponentials theorem.") The general case
of a^t and b^t, a and b integers, is still open.
Ray Steiner
-- 
steiner@andy.bgsu.edu
Newsgroups: sci.math
From: kyee@bnlux1.bnl.gov (kenton yee)
Subject: Help! Simple constrained Integration prob
Organization: Brookhaven National Laboratory, Upton, NY 11973
Date: Sat, 29 Aug 1992 23:50:50 GMT

Is there an elegant way to do integrals like

 int dx dy dz f(x,y,z)   

  where -1 < x < 1;  -1 < y < 1;  -1 < z < 1;
    subject to the constrained that  
          -1 < x+y+z < 1   ?

  By "elegant" I mean not having to break up
  integration region into little triangles by
  hand, etc...
From: mps@sparc68.hri.com (Mark Stockley)
Newsgroups: sci.math
Subject: Polygon point enclosure
Date: 26 Aug 92 18:25:24 GMT
Reply-To: mps@hri.com
Organization: Horizon Research, Inc.

I'm looking for a method to determine if a point is enclosed
by a polygon. Any help would be greatly appreciated.

------------------------------------------------------------------------------
Mark P. Stockley    |   INET: mps@hri.com    | But I don't like Spam!!!
Horizon Research    |  Voice: (617) 466-8300 | 
1432 Main St.,      |   		     | Is the alphabet in that order
Waltham MA 02154    |    FAX: (617) 466-8323 | or is it because of that song?
------------------------------------------------------------------------------
Newsgroups: sci.math
From: takriti@engin.umich.edu (samer Takriti)
Subject: Re: linear programming HELP REQUIRED!
Date: Wed, 26 Aug 92 22:35:52 EDT
Organization: University of Michigan Engineering, Ann Arbor
Keywords: linear programming

Well, I use a software by ibm called OSL: Optimization Subroutine
Library". I have tried to solve some large LP's with it and it 
works fine (up to 1000 constraints). OSL has the ability to solve
integer programs as well as qudratic programs. I know that ibm
has a "SUN" version of their program. I use it on the IBM/6000
workstation. 
If you cannot get OSL, you may want to use some technics that
will exploit the structure of your constraint matrix.
I forgot to mention that osl can be called from any programming
language as fortran or C.
Hope this help.
-Samer
.

Newsgroups: sci.math
From: rusin@mp.cs.niu.edu (David Rusin)
Subject: Re: p prime, p divides ab => pdivides a or b
Organization: Northern Illinois University
Date: Wed, 2 Sep 1992 18:33:41 GMT

In article <Btyo8q.E63@ux1.cso.uiuc.edu> ceblair@ux1.cso.uiuc.edu (Charles Blair) writes:
>   My recollection is that a number theory course I took presented
>this as a difficult result, only proved after doing some stuff
>with the Euclidean algorithm.  Is there a proof which avoids that?

Not really (I just presented my students with this proof an hour ago!).
More prescisely, what you are proving is the equivalence of what are
really _irreducible_ elements of the ring (p <> a . b unless a or b = unit)
and _prime_ elements ( p|ab => p|a or p|b). This is not true in general rings.
Somehow you have to use something special about the natural integers.
Being a Principal Ideal Domain is good enough, and you prove that for
the integers using the Division algorithm.

(Actually I think I remember some quadratic extensions of  Z  for
which you can show no division algorithm exists but which are still
PID's. Readers?)

dave rusin@math.niu.edu

Newsgroups: sci.math
From: bhonsle@bhonsle.iss.nus.sg (Shailendra K Bhonsle)
Subject: Re: u(v^n)w prime puzzle SOLUTION
Organization: Institute of Systems Science, NUS, Singapore
Date: Mon, 24 Aug 1992 02:58:50 GMT

In article <1992Aug21.220719.16092@wri.com>, roach@bikini.wri.com (Kelly Roach) writes:
|> 
|> 
  
|>      Sum[10^(a*i+b),{i,0,n-1}] = 0 (mod p)
|> 
|> Prime number p does not divide 10 because uw has at least
|> 2 digits.  Hence
|> 
|>      10^(a*i+b) (mod p)
|> 
|> is a periodic function of i.  The period divides p-1
|> and that means that if p(p-1) | n, then each residue
|> appearing in the list
|> 
|>      10^b, 10^(a+b), ..., 10^(a*(n-1)+b)     (mod p)
|> 
|> appears a multiple of p times.  Consequently, it is
|> sufficient to let n=p(p-1) to get p | u(v^n)w.  Obviously
|> u(v^n)w > p=uw.
|> 
|> 			  QED
|> 
|> 

Is there a mistake here? what if p^2 divides 10^a-1? Since a & p are independent
consider a =x. p.(p-1) (where x is any positive integer.)

In this case each residue appearing in the list will be a multiple of p^2 and one needs to choose n=p^2 (p-1).

In general if p^i exactly divides 10^a-1 then choose n=(p^(i-1))(p-1)


Shailendra

--
From: wilson@web.ctron.com (David Wilson)
Newsgroups: sci.math
Subject: sqrt sequences
Date: 28 Aug 92 16:12:40 GMT
Reply-To: wilson@web.ctron.com (David Wilson)
Organization: Cabletron Systems INc.


    For those of you who disparage sequence completion puzzles, here
    are some sequence puzzles which pose themselves.  The first few
    digits in decimal expansions of each of the following values
    suggests the start of an integer sequence.  Can you give the
    general term for each sequence?

	1.  5-2*sqrt(6)
	2.  sqrt(51)/7
	3.  sqrt(2)/7



-- 
David W. Wilson (wilson@ctron.com)

Disclaimer: "Truth is just truth...You can't have opinions about truth."
- Peter Schikele, introduction to P.D.Q. Bach's oratorio "The Seasonings."
From: lwall@netlabs.com (Larry Wall)
Newsgroups: sci.math
Subject: Re: Solitaire games
Date: 3 Sep 92 17:07:51 GMT
Organization: NetLabs, Inc.

In article <92Sep2.171725edt.48031@neat.cs.toronto.edu> pedmonds@cs.toronto.edu ("Philip G. Edmonds") writes:
: In article <1992Sep2.204931.29320@wdl.loral.com> mab@wdl39.wdl.loral.com (Mark A Biggar) writes:
: >In article <Btyo5z.D8q@cs.psu.edu> morgan@math.psu.edu (Ilene Morgan) writes:
: >>My game with license plates is to try to find a word that contains the
: >>letters of the license plate in order, not necessarily consecutively.
: >>For example, XPV -> expressive.  My license plate used to have XPF; I never
: >>did think of one for that.
: >
: >expeditefull
: >excerptfull
: >exemplify
: >exemplification
: 
: ex post facto

Note this can be played competitively too.  The shortest word wins.

foxproof
exprof

That last one is a member of the (rather large) set of words that you
won't find in the dictionary but that everyone understands immediately.
Some may prefer to spell it with a hyphen, of course.

Larry Wall
lwall@netlabs.com
From: mueller@schaefer.math.wisc.edu (Carl Douglas Mueller)
Newsgroups: sci.math
Subject: Re: Proof of God's Existence
Date: 1 Sep 92 11:04:22 GMT
Reply-To: mueller@schaefer.UUCP (Carl Douglas Mueller)
Organization: Univ. of Wisconsin Dept. of Mathematics

In article <17ui6kINNsft@matt.ksu.ksu.edu>, bubai@matt.ksu.ksu.edu
(P.Chatterjee) writes:
> I was told by somebody that there is a mathematical proof of God's existence;
> was wondering if somebody could shed some light on the same.
>
> Thanks. Looking forward to the response.

The proof I've seen depends upon the axiom of choice.        :-)

             Carl Mueller (mueller@math.wisc.edu)
Newsgroups: sci.math
From: stephen@mont.cs.missouri.edu (Stephen Montgomery-Smith)
Subject: Springer Verlag server
Keywords: springer-verlag, server, ftp
Organization: University of Missouri
Date:  4 Sep 92 21:01:49 GMT

Hi everyone,

Does anyone know if it is possible to get the Springer-Verlag files for
submitting articles via ftp?

Thanks, Stephen Montgomery-Smith
From: shoham@ll.mit.edu (Daniel Shoham)
Newsgroups: sci.math
Subject: Lighthouse Visibility Problem
Date: 3 Sep 92 22:18:55 GMT
Organization: MIT Lincoln Laboratory

Can anyone help me with this problem:

Let
        x(k) = Normal(0,1) iidrv        where k = 1, 2, ...    

        y(0) = 0
        y(k) = a*y(k-1) + b*x(k)        where a^2 + b^2 = 1

        m(k) = [y(k) - H] / [k + L]     where H, L are known constants

        M(k) = max {m(j) | j=1..k}

I am looking for an asymptotic expression for the expectation of M(k)
for large k (as a function of H, L, and a).

For those of you who are interested, y(k) is a simulated terrain [with
correlation length of -1/ln(a) ]. H is the height of a lighthouse at a
distance L from the shore.  M(k) is the (tangent of the) minimum 
elevation angle a land observer must be at to see the lighthouse.
(Normalized units are used.)

Extra credit:
-------------
        h(k) =  H + (k+L) M(k) - y(k)
h(k) is the height above the ground one must be to see the lighthouse.
Find an asymptotic expression for the expectation of h(k).

Any hints would be appreciated

- Thanks

Dan Shoham
shoham@ll.mit.edu
Newsgroups: sci.math
From: asimov@wk223.nas.nasa.gov (Daniel A. Asimov)
Subject: Re: Calendar (NEW)
Organization: NAS, NASA Ames Research Center, Moffett Field, CA
Date: Wed, 26 Aug 92 18:28:23 GMT

In article <6xmpb6wb@csv.warwick.ac.uk> mareg@warwick.ac.uk (Dr D F Holt) writes:
>In article <2906@ucl-cs.uucp> P.Samet@cs.ucl.ac.uk (Paul Samet) writes:
>>Actually Easter is the first Sunday following the first full moon which occurs
  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>>on or after March 21 (Spring equinox), not March 20, as claimed.
>>
>
>Surely 'on or after March 21' is the same as 'after March 20'. But am I
>correct in thinking that if the full moon occurs on a Sunday then one has
>to wait for the following Sunday? So the earliest possible date for Easter
>is presumably March 22.
>
>Derek Holt.
----------------------------------------------------------------------------
Although the date of Easter is usually described this way, the
*actual* date of Easter is, I believe, based on traditional but
now outdated calculations, which once in a great while disagree with
modern, "correct" astronomical calculations.

Can anyone confirm or refute this?


--Dan Asimov
asimov@nas.nasa.gov

Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000
(415) 604-4799
From: mccolm@darwin.math.usf.edu. (Gregory McColm)
Newsgroups: sci.math
Subject: Re: You know, the integers (was: Re: Stupid question about FLT)
Date: 24 Aug 92 15:35:55 GMT
Organization: Univ. of South Florida, Math Department

In article <1992Aug16.172642.13398@sics.se> torkel@sics.se (Torkel Franzen) writes:
>In article <1992Aug11.190119.23518@ariel.ec.usf.edu> mccolm@darwin.math.usf.
>edu. (Gregory McColm) writes:
>
>   >From there, we get more problems.  Suppose that you 
>   >believe that the model of the integers exist.  Is PA 
>   >true on this model?
>
>  What is PA? My explanation of the integers is simple: the integers
>are 0, s(0), s(s(0)) and so on. Any obscurity or ambiguity that you
>find in this explanation carries over to any explanation of what is
>meant by "PA".


And what, precisely do you mean by "and so on"???  You may think 
that it is obvious what you mean, but a number of people, from 
Aristotle to Brouwer, have had doubts about the murkey depths of 
that "and so on".

===================================================================
                          |
Greg McColm               |    I see it, but I don't believe it.
Dept of Mathematics       |
Univ of S Florida         |        -----Georg Cantor
mccolm@math.usf.edu       |
From: bennett@math.ksu.edu (Andy Bennett)
Newsgroups: sci.math
Subject: Re: dividing 100 digit nos.?
Date: 26 Aug 1992 09:11:45 -0500
Organization: Dept. of Mathematics, Kansas State University
NNTP-Posting-Host: hilbert.math.ksu.edu

comptec91065@camins.camosun.bc.ca writes:

>	Can you help me locate the easiest method of dividing
>	integers of at least 100 digits (possibly up to 4300 digits) ?

Use UBASIC. This is a public domain basic developed by Yuji Kida in Japan
with full support for integers up to about 2500 digits. It also comes with
state of the art number theory algorithms already coded (for primality
testing, factoring, etc.) It used to be available on anonymous ftp from
simtel, wuarchive, etc. I already have my copy so I haven't checked lately
but I presume it is still there. 

-- 
Andrew G. Bennett         bennett@math.ksu.edu         If you count too
Dept. of Mathematics      Voice: (913) 532-6750        much you turn
Kansas State University   Fax:   (913) 532-7004        purple.  -  SARAH
Manhattan, KS 66502       STRICTLY MY OWN OPINIONS
From: dik@cwi.nl (Dik T. Winter)
Newsgroups: sci.math
Subject: Re: Solitaire games
Date: 4 Sep 92 00:41:21 GMT
Organization: CWI, Amsterdam

In article <NICKH.92Sep3143716@VOILA.VENARI.CS.CMU.EDU> nickh@CS.CMU.EDU (Nick Haines) writes:
 > I play a game with triplets of digits (such as one finds on 99% of
 > British numberplates),
Sorry.  900 out of 999 is not 99%.
-- 
dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland
home: bovenover 215, 1025 jn  amsterdam, nederland
dik@cwi.nl
Newsgroups: sci.math
From: mls@cbnewsm.cb.att.com (mike.siemon)
Subject: Re: Godel and the US constitution
Organization: AT&T
Date: Tue, 1 Sep 1992 20:35:08 GMT
Summary: nope; much easier than that

In article <1992Sep1.160045.15281@husc3.harvard.edu>,
elkies@ramanujan.harvard.edu (Noam Elkies) writes:

> In article <1992Sep1.175844.16825@nas.nasa.gov>
> asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:

> >Out of curiosity, does anyone know how Godel envisioned a
> >consitutional dictatorship possibly arising in the U.S. ???

> It would seem that all you need is 2/3 of the Senators and
> Representatives to agree on an Amendment that would make
> (say) Madonna the absolute ruler of the United States...

ummm, amendments do not become effective without ratification
by the states.  I have no idea what Goedel may have had in mind,
but he certainly witnessed essentially dictatorial power as
wielded by Roosevelt (we ran a demand economy throughout WWII.)
Lincoln also was a near dictator.  These powers are implicit
in the position of commander-in-chief during a military "emer-
gency."  A congressional declaration of war or similar bill
is sufficient (and the Congress becomes relevant again mostly
at the point of ratifying treaties, so all you need is a per-
manent emergency, say something like the containment of world
Communism...)

Now, there were severe constraints -- practical and political --
on Lincoln or Roosevelt (or LBJ or Nixon or ...) including the
potential for impeachment, but that last is about the only one
which is formalized in the Constitution -- and I suppose that
one can argue that presidential power could be used to prevent
Congress from meeting or otherwise negating the Constitutional
provision (Lincoln suspended _habeas corpus_, for example.)

In America, as in the early Principate in Rome, some *forms*
of constitutional power, such as consular elections and
deference to the Senate, may be maintained to mask the effective
irrelevancy of an institution.  Note that a president only
needs a third of the Senate to be able to block ANY legislation.

-- 
Michael L. Siemon		The Son of Man has come eating and drinking;
				and you say "Behold, a glutton and a drunkard,
mls@usl.com			a friend of tax collectors and sinners."  And
standard disclaimer		yet, Wisdom is justified by all her children.
Newsgroups: sci.math
From: lafollet@romulus (Paul Lafollete)
Subject: matrix question
Summary: looking for info about a certain class of matr4ices
Organization: University of Illinois at Urbana
Date: Thu, 27 Aug 1992 18:23:40 GMT
Keywords: matrix, inverse, polynomial


I am looking for information about matrices of the following form.

A(0,0) = M (some positive integer)

                M - 1
           ----------
           \
A(i,j) =    \             (i+j)K
            /            X              for i,j = 0..N-1
           /
          -----------
             K = 0


A is thus an NxN symmetric matrix of polymonials, each of which has
M non-zero terms (excepting the element A(0,0)).

I would like to know what is known about such beasts.  In particular,
I conjecture that A has no inverse when M < N.  Is this true? Is it
obvious?  What other interesting properties does A have?

I would guess that these are well studied objects, and so I would 
appreciate any references any of you might be able to give me
where I could start reading.  Thanks in advance.

Paul LaFollette
CIS Dept.
Temple University
lafollet@astro.ocis.temple.edu
lafollet@ws5.cis.temple.edu
Newsgroups: sci.math.research
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Ktheory question
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University Of Kentucky, Dept. of Math Sciences
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Sun, 23 Aug 1992 17:55:27 GMT

Let F be a field and L a quadratic extension of F.  Then it is 
well-known that K_2(L) can be generated by semiinvariant
symbols; that is, things of the form {a,b} where a is in F - {0} and
b is in L - {0}.

Does this fact extend to L/F of degree greater than 2?  Affirmation,
partial results and counterexamples all welcome.

Charles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu


Newsgroups: sci.math.research
From: takriti@engin.umich.edu (samer Takriti)
Subject: Geometry question
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Michigan Engineering, Ann Arbor
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 27 Aug 1992 14:36:58 GMT

I have a linearly independent set of n vectors in R^n, i.e., the 
vectors form a basis for R^n. I need to compute the content (volume)
of the intersection of the cone formed by these vectors with a 
sphere. The sphere is given using the coordinates of its center and its
radius.
Any idea?
-Samer
Newsgroups: sci.math.research
From: asimov@nas.nasa.gov (Daniel A. Asimov)
Subject: Exponential of an arbitrary mapping f: R^n -> R^n
X-Submissions-To: sci-math-research@uiuc.edu
Organization: NAS, NASA Ames Research Center, Moffett Field, CA
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 28 Aug 1992 18:12:24 GMT

One way to generalize the exponential of a matrix to arbitrary
continuous functions f: R^n -> R^n is as follows:

exp(f): R^n -> R^n via

	exp(f)(x) = x + f(x) + f(f(x))/2! + f(f(f(x)))/3! +...

It is easy to see that this does not necessarily converge for all x.

Question:  Has this version of exp(f) been defined and discussed
previously in the literature?  Can someone supply references and/or
mention some of the elementary properties (if any) of this definition?

For example, where it exists is exp(f) continuous?  If f is differentiable,
or even smooth, then what about exp(f) ?  Are there elementary conditions 
under which exp(f) is invertible?   For which g can one find a
corresponding "log," i.e., an f such that exp(f) = g ?


--Dan Asimov
asimov@nas.nasa.gov

Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000
(415) 604-4799
From: bumby@no.rutgers.edu (Richard Bumby)
Newsgroups: sci.math.research
Subject: Re: Science reporting
Date: 28 Aug 92 15:58:20 GMT
Organization: Rutgers Univ., New Brunswick, N.J.
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu


Note has been made on an error in terminology in the obituary of
Daniel Gorenstein in the New York Times.  I would have expected, in
this forum, that the first error to have been noticed would be that
the article appeared to credit group theory for proving the
impossibility of squaring the circle.  The classification of finite
simple groups doesn't need the support of irrelevant mathematical
accomplishments.  Also considering the recent front page treatment
given to "the president on the left didn't say what the president on
the right said that he said", the use of the E. T. Bell version of
Galois was somewhat inappropriate.
-- 
R. T. Bumby **  Rutgers Math ||   Amer. Math. Monthly Problems Editor
bumby@math.rutgers.edu       || P.O. Box 10971 New Brunswick, NJ08906-0971
bumby@dimacs.rutgers.edu     || Phone: [USA] 908 932 0277 * FAX 908 932 5530
Newsgroups: sci.math.research
From: fernand@acf9.nyu.edu (Chris Fernandes)
Subject: convex functions on L_1 spaces
Summary: Do strictly convex functions on closed convex and bounded set in L_1 achieve Minimum?
X-Submissions-To: sci-math-research@uiuc.edu
Organization: New York University
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Sun, 30 Aug 1992 23:39:04 GMT
Keywords: convex, L_1

I have a question regarding convex functions on L_1 spaces.

Consider the space L_1.
Let U: L_1->R  be a strictly convex function.
Let G be a closed convex and bounded set in L_1.

Is it then true that the function U achieves its minimum on the set G?

I have not been able to find this result in any reference book.  Intuitively,
 the result seems to be true, but I cannot come up with a clean proof.

I do know that the set G is compact in the weak* topology, but on L_1
the weak* and the weak do not coincide.  For example, in L_2, the set
is weakly compact and thus the minimum is achieved.

Hopefully  yours,

Indrajit, mailing from friend's account.

Newsgroups: sci.math.research
From: asimov@nas.nasa.gov (Daniel A. Asimov)
Subject: Triangulating a Region of R^3 Bounded by Triangulated Surfaces
X-Submissions-To: sci-math-research@uiuc.edu
Organization: NAS, NASA Ames Research Center, Moffett Field, CA
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Tue, 1 Sep 1992 18:55:42 GMT

Some usual definitions (just to avoid any ambiguity):

	Let k+1 points in R^n be said to be in "general position" if 
	they lie on no (k-1)-dimensional plane.

	Let a subset S of R^n be called a "k-simplex" if it is the convex 
	hull of k+1 points in R^n in general position.  
	
	The k+1 points are the "vertices" of S. 

	A "face" of S is defined as the convex hull of a subset of the vertices.

	Define a compact subset X of R^n to be "triangulated" if X is expressed 
	as the union of finitely many simplices whose pairwise intersection 
	is a common face, or empty.
Now:
Let M be the closure of a bounded open subset of 3-space, and assume that 
the boundary of M consists of a finite number of connected components N(i).  

Assume that each of these N(i) is a compact triangulated surface 
(without boundary).  Call this the "boundary triangulation." 

QUESTION:  Is it necessarily true that M can be triangulated in such 
a way that the restriction of this triangulation to the boundary of M 
is the given boundary triangulation?  

It is easy to see that this is true if M is convex, but what if it isn't?

--Dan Asimov
asimov@nas.nasa.gov

Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000
(415) 604-4799

Newsgroups: sci.math.research