HDTenEightyP/NetNews huggingface dataset:
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Subject: Summary: summation of random series
X-Submissions-To: sci-math-research@uiuc.edu
Organization: The Ohio State University, Dept. of Math.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Tue, 15 Sep 1992 13:34:28 GMT

Here is a summary of the responses received.  Thanks to:
  bishop@math.sunysb.edu (Chris Bishop)
  stephen@mont.cs.missouri.edu (Stephen Montgomery-Smith)
  drobot@sjsumcs.sjsu.edu (Vladimir Drobot)

I asked:
>
>There is a theorem, probably due to Paul Levy, stated below.  Where can
>it be found in a modern textbook?
>
>If a series of independent (mean zero, say) random variables diverges a.s.,
>then applying a summation method won't help: it will still diverge a.s.

Two references were suggested.

(1) Theorem V.8.2 in Zygmund's _Trigonometric Series_ is the special case
   of the result for Rademacher series.

(2) Theorem 1 of Chapter II in J. P. Kahane, _Some random series of
   functions_ is a generalization to series with values in Banach space.
   Kahane does not give a reference for the theorem, but for the main lemma,
   he cites a paper of Levy.


-- 
  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.research
From: koiran@ens.ens-lyon.fr (Pascal Koiran)
Subject: Re: dynamical systems and (perhaps) algebrai
Reply-To: koiran@ens.ens-lyon.fr
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Ecole Normale Superieure de Lyon
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 10 Sep 1992 18:53:08 GMT

The solution proposed by Arthur Rubin in sci.math.research is perfectly
correct.  However, I'd like to have a less degenerate exemple. One might
perhaps add a condition like

"all the variables x_1,...,x_n must occur in each P_i"

or a similar but weaker condition like 

"The set of variables {1,...,n} cannot be partitioned in two subsets I1 and
I2 such that the two subsystems (x_i)_{i in I1} and (x_i)_{i in I2} evolve
independently from each other".

The motivation behind my question is to find a dynamical property
differentiating piecewise-linear functions from polynomial, rational, or
analytic function on [0,1]^n. Any suggestion on this is welcome. For n=2,
there exist non degenerate piecewise-linear functions with infinitely many
k-cycles for every k (hence my question).

Pascal.

Newsgroups: sci.math.research
From: ctm@math.Berkeley.EDU (Curtis T. McMullen)
Subject: Re: decidability and dynamical systems
X-Submissions-To: sci-math-research@uiuc.edu
Organization: U.C. Berkeley Math. Department.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 10 Sep 1992 05:04:45 GMT

This answer is yes (it is decidable) for a large class of 
algebraic endomorphisms of varieties where everything is defined over the
rationals.  For example, let f(x) = x^2 + c where c is rational.
Define the height of a rational number p/q (where (p,q)=1) as
h(p/q) = log max(1,|p|,|q|).  Then it is easy to see that 
for x rational, h(f(x)) = 2 h(x) + O(1) (the implied constant depends on c).
This gives an a prior bound on the height of all rational points with
finite forward orbits, thus a bound on the number of such points,
and also on the size of their forward orbits.   

References:
  J. Silverman, Rational points on K3 surfaces:  A new canonical height.
Invent. math. 105 (1991), 347-373.

  G. Call and J. Silverman, Canonical heights on varieties with morphisms.
Preprint 1992.

Newsgroups: sci.math.research
From: ezli@ntu.ac.sg (Li Ziqing)
Subject: Nonlinear Diff. Equ.
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Illinois at Urbana
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 10 Sep 1992 00:51:15 GMT

Hi, there

I have a question on the existance and uniqueness of the
following nonlinear differential equation

        f(x) - C d [f'(x) h(f'(x))] /dx =g(x)

where C>0 is a constant, g(x) is a known, piecewise C^0
continuous function and h(.) is a nonlinear function satisfying

(1) h(z) is C^1 continuous for all real z
(2) h is even h(z)=h(-z),
(3) h(z) >0,
(4) h(z) < 0 for all z > 0 and
(5) z h(z) --> 0 as z --> infinity

Examples of h(z) are

        exp(-z^2/sigma), 1/(1+z^2/sigma)

where sigma>0 is a constant.

Are there any mathematicians or engineers out there who have
any ideas about the existance and uniqueness of the above equation?

Any replies are greatly appreciated.


Z. Li


Newsgroups: sci.math.research
From: rlm7638@tamsun.tamu.edu (Jack McKinney)
Subject: Group Theory Reference needed.
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Texas A&M University, College Station
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Mon, 14 Sep 1992 20:03:31 GMT

     I am looking for a reference that contains a list of all the groups
of all orders up to a given limit [i.e., a book can only be so large.]
For example:

Groups of order 1: {e}
Groups of order 2: {<a>:a^2=e} [Z_2]
Groups of order 3: {<a>:a^3=e} [Z_3]
Groups of order 4: {<a>:a^4=e} [Z_4]
                   {<a,b,c>:a^2=b^2=c^2=e} [V=Z_2xZ_2]
Groups of order 5: {<a>:a^5=e} [Z_5]
Groups of order 6: {<a>:a^6=e} [Z_6]
                   {<a,b>:a^2=e,y^3=e,xy^2=yx} [S_3]
Groups of order 7: {<a>:a^7=e} [Z_7]

ad nauseum...

        I know that there are 5 groups of order 8, 2 of order 9, etc.
I would like to see a book that [not necessarily with derivations] will
list each group of each order.
        Another thing I would like to see is a list of characters for 
a number of finite groups. (i.e. all the finite groups of some particular
order and smaller.)


+--------------------------------------------------------+--------------------+
| Martin: Have we done this before?                      | Jack McKinney      |
| Halsey: Are we doing this now?    -from Brain Dead     | jmckinney@tamu.edu |
+--------------------------------------------------------+--------------------+

Newsgroups: sci.math.research
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Subject: summation of random series
X-Submissions-To: sci-math-research@uiuc.edu
Organization: The Ohio State University, Dept. of Math.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 11 Sep 1992 13:59:24 GMT


There is a theorem, probably due to Paul Levy, stated below.  Where can
it be found in a modern textbook?

If a series of independent (mean zero, say) random variables diverges a.s.,
then applying a summation method won't help: it will still diverge a.s.
-- 
  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.research
From: broman@schroeder.nosc.mil (Vincent Broman)
Subject: Re: Better than Cauchy-Schwarz
Reply-To: broman@nosc.mil
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Naval Command Control and Ocean Surveillance Center, RDT&E Div.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Thu, 10 Sep 1992 23:25:35 GMT

let C = 1/8,
let f be L1 and L2 on [0,\infty),
and let \int_0^\infty f(x) x dx < C \int_0^\infty f(x) dx.

Then
       \int_0^C f(x) (C-x) dx >= \int_C^\infty f(x) (x-C) dx
implies with a slight amount of work
       \int_0^{2 C} f(x) dx >= \int_{2 C}^\infty f(x) dx,
meaning that the median is not more than twice the mean.

Apply Cauchy-Schwartz to f and the characteristic function on [0,2C].
Then,
       \int_0^\infty f^2 >= ( \int_0^{2 C} f )^2 / (2 C)
                         >= ( 1/2 \int_0^\infty f )^2 / (2 C)
                          = ( \int_0^\infty f )^2.

Vincent Broman,  code 572 bayside,                                  =   o     
Naval Command Control and Ocean Surveillance Center, RDT&E Div.   =  _ /- _   
San Diego, CA  92152-5000,  USA                                  =  (_)> (_)  
Internet Email: broman@nosc.mil    Fax: +1 619 553 1635   Phone: +1 619 553 1641


Newsgroups: sci.math.research
From: a_rubin@dsg4.dse.beckman.com (Arthur Rubin)
Subject: Re: decidability and dynamical systems
X-Submissions-To: sci-math-research@uiuc.edu
Organization: University of Illinois at Urbana
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Fri, 11 Sep 1992 21:52:08 GMT

In <Bu9B1J.H8E@ens-lyon.fr> koiran@ens.ens-lyon.fr (Pascal Koiran) writes:

>Hello,

>Can someone provide a solution to the following problem, or give references
>to related work in the litterature ?

>Let f:[0,1]-->[0,1] be a continuous piecewise-linear function (with a finite
>number of laps). The endpoints of the laps have rational coordinates.
>Given such an f and a rational x \in [0,1], is it decidable whether a fixed
>point is reached in finite time when f is iterated on x ?
>In other words, is it decidable whether there exists t, f^t(x)=f^{t+1}(x) ?

The collection of all such x is clearly recursively enumerable.  Also,
given a (one-tape, one-sided infinite) Turing machine T, it is clear that
one can define a recursive piecewise linear function f with a countable
number of segments, and a G of all possible tape states into [0,1] such
that f(G(state)) = G(T-successor of state), so that f reaches a
fixed point started at G(state) iff T halts starting at "state" (if you
make the convention that any production rule which leaves the entire state
fixed is replaced by a cycle back-and-forth, so that fixed points of T
correspond to halted states.)

If all slopes of segments are 1/n for (positive or negative) integer n,
then for any x, and t, x = A f^t(x) + Q, where A is an integer, and Q has
a bounded denominator.  If, in addition, f does not have an interval of
fixed points, this clearly shows the set of "eventual fixed points" is
recursive.  I believe the proof will go through even if f has an interval
of fixed points; but this still doesn't solve the general case.



--
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.

Newsgroups: sci.math.research
From: anq@maths.warwick.ac.uk (Anthony Quas)
Subject: Expanding Maps
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Mathematics Institute, University of Warwick, UK.
X-Administrivia-To: sci-math-research-request@uiuc.edu
Date: Mon, 7 Sep 1992 11:42:12 GMT

I am considering the problem of expanding maps from the circle to itself.
For f to be expanding, I mean that f is C^1 and |f'(x)| >= K >1 for all x
in S^1. Such maps may be "lifted" to the interval, where they become
piecewise expanding, once-differentiable maps of the interval, whose
branches map onto the whole interval.

If the map f is C^2 or even C^(1+\alpha) (i.e. its derivative is Hoelder
continuous), then it is known, using the theory of Lasota-Yorke and others
that the map has an Absolutely Continuous Invariant Probability Measure
(ACIPM) (with respect to Lebesgue measure) and that this measure is unique.

In the case where the map is C^1, there need not be an ACIPM, as shown
in the paper of Gora and Schmitt in Ergodic Theory and Dynamical Systems
(1988?).

I am interested in the case where the map is C^1 and preserves Lebsegue
measure. The question which I want to answer is whether this probability
measure is unique (i.e. whether in that case, Lebsegue measure is ergodic).

I have some partial results. These are the following:
For C^0 maps, expanding can be defined that all sufficiently small distances
are expanded by a factor uniformly bounded below by some K>1. One can then
ask if a C^0 expanding map of the circle which preserves Lebesgue measure
can have more than 1 ACIPM. The answer to this is yes, it may have more
than 1 ACIPM. My example has a Cantor set C of positive measure such that
f(C) is contained in C. I have shown that this cannot arise for C^1 maps.
I would be happy to show the proofs to anyone interested.

I should be extremely interested to hear of any comments or suggestions
which people may have with this problem, as I am fairly stuck with it.

Thanks in advance!

Anthony Quas                     anq@maths.warwick.ac.uk
Maths Institute
University of Warwick
Coventry CV4 7AL
ENGLAND


Newsgroups: sci.math
From: steve@hubcap.clemson.edu ("Steve" Stevenson)
Subject: Re: computable reals
Organization: Clemson University
Date: Mon, 14 Sep 1992 12:19:08 GMT


See any of Errett Bishop's works.

-- 
===============================================================================
Steve (really "D. E.") Stevenson           steve@hubcap.clemson.edu
Department of Computer Science,            (803)656-5880.mabell
Clemson University, Clemson, SC 29634-1906
From: hussein@bora.inria.fr (Hussein Yahia)
Newsgroups: sci.math
Subject: Freedman-Donaldson Theorem
Keywords: Exotic R^4, differential structures, topology
Date: 10 Sep 92 12:06:42 GMT
Organization: Institut National de Recherche en Informatique et Automatique -- Rocquencourt, France



  Hi everyone,



  I'm interested in understanding the proof of the famous Freedman-Donaldson
theorem about "fake R^4", that is the existence of exotic diffentiable 
structures on R^4. (For others R^n , n different of 4, all differentiable
structures are always diffeomorphic to the standard one). I tried to read
a book "Connections, Definite Forms, and Four-manifolds" by T. Petrie and 
J. Randall (Oxford Science Publications) but it is quite a little bit 
too difficult for me. 

Could someone give me a list of references leading to a proof of that theorem
for somebody like me who is just at the level of Volumes 1-2 of Spivak's 
Course on Differential Geometry and Hirsh's Differential Topology (Springer
Verlag) ?


   Thank you very much in advance.


   Hussein Yahia

   INRIA BP 105
   78153 Le Chesnay Cedex
   France

   E-mail: hussein@bora.inria.fr
    
Newsgroups: sci.math
From: sld@etta.auc.edu (Steven Louis Davis)
Subject: looking for reference for the Lebesgue Density Theorem
Organization: Spelman College, ATL, GA, USA
Distribution: usa
Date: Tue, 8 Sep 1992 14:28:35 GMT
X-Posted-From: etta.auc.edu
X-Posted-Through: sol.ctr.columbia.edu


If anyone out there can help I would appreciate it.  I've looked
through all of my 'standard' measure, integration, and analysis
books for this theorem:

        Let E be Lebesgue measurable.  Then except for a
        negligable set we have

                        L(E*B(r,x))     { 1, x in E
                lim     ----------   =  {
                r->0     L(B(r,x))      { 0, x not in E

        (* denotes set intersection, B(r,x) is the ball of
	radius r about x)

I'm looing for the proof that uses the Vitali Covering Theorem
using the covers {B(r,x): x in E, r<e, L(E*B(r,x)) > aL(B(r,x))}
for e>0, a<1.

************************************************************************
* Steve Davis ***************************** internet: sld@etta.auc.edu *
* Spelman College ************************* telephone: (404) 223-7626 **
* 350 Spelman Lane S.W. ******************* fax: (404) 659-8930 ********
* Atlanta, Georgia  30314 ** this space intentionally left blank--oops**
************************************************************************

-- 
************************************************************************
* Steve Davis ***************************** internet: sld@etta.auc.edu *
* Spelman College ************************* telephone: (404) 223-7626 **
* 350 Spelman Lane S.W. ******************* fax: (404) 659-8930 ********
Newsgroups: sci.math
From: astrod@kentaurus.dftsrv.gsfc.nasa.gov (AstroD Developer)
Subject: least squares fit question
Keywords: l1, l2
Organization: Goddard Space Flight Center
Date: Tue, 8 Sep 1992 20:39:24 GMT

Can anyone provide me with a basic description or even a reference to the  
l1 and l2 techniques for least squares fitting. Please responde to my  
e-mail address (kent@kentaurus.gsfc.nasa.gov) unless you think this is of  
general interest to the group. Thanks in advance!

-Kent Blackburn
kent@kentaurus.gsfc.nasa.gov
Newsgroups: sci.math
From: karl@ima.isc.com (Karl Heuer)
Subject: Re: Chess Problem
Organization: Interactive Systems, Cambridge, MA 02138-5302
Date: Sat, 12 Sep 1992 17:45:45 GMT

Here's a more advanced chessboard question.

A white king, a black king, and a white pawn are randomly placed on an NxN
chessboard.  (Independent, uniform distributions.)  What is the limit, as
N -> infinity, of the probability that the position is a win for white?

(Note that it doesn't matter what you do about collisions or illegal
positions, since they occur with probability zero in the limit.)

Karl Heuer   karl@ima.isc.com   uunet!ima!karl
From: t9014186@phillip.edu.au
Newsgroups: sci.math
Subject: Fast Fourier Transform
Date: 14 Sep 92 16:18:15 GMT
Organization: RMIT (Bundoora Campus)

Does anybody know where I can find, or does anybody have, a source listing of
how to perform a Fast Fourier Transform ??

A listing in C would be preferable but not essential.



-- 
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
=-= Steven Corral                                                       =-=
=-=                                                                     =-=
=-= T9014186@phillip.edu.au                                             =-=
=-= scorral@arcadia.mc.phillip.edu.au                                   =-=
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
From: mccolm@darwin.math.usf.edu. (Gregory McColm)
Newsgroups: sci.math
Subject: Re: Prime conjecture
Date: 4 Sep 92 19:46:30 GMT
Organization: Univ. of South Florida, Math Department

In article <17dg0nINNo1j@hilbert.math.ksu.edu> bennett@math.ksu.edu (Andy Bennett) writes:
>mccolm@darwin.math.usf.edu. (Gregory McColm) writes:
>
>>The "Twin primes conjecture" goes back to ancient Greece:
>
>What is a reference for this. I went looking once and couldn't find a good
>reference for when the Twin primes conjecture was first made.
>
>Thanks
>
>Andy B.
>
P

I had heard that the twin primes conjecture goes 
back to ancient Greece in a number theory course.
I just looked in my study, and none of the history 
books mention it.  Davies & Hersch's Mathematical 
Experience calls it a major problem, but doesn't 
mention its history.  Ivar Paterson's [sic?] 
Mathematical Tourist says that many mathematicians 
have been working on it in the last 100 years.

Several people have told me that it was a Greek 
problem, and that's what I thought, too (one would 
think that surely Erastosthenes would have noticed 
the problem) but that may be a myth.  There are many 
myths about, eg, the tale that the 4-color problem 
is an ancient cartographer's problem, when in 
fact the oldest references known are about a 100 
years old.  Anyone got any old references to the 
problem, at least so far as the Renaissance?

-----Greg McColm
From: vm0h+@andrew.cmu.edu (Vincent J. Matsko)
Newsgroups: sci.math
Subject: Re: Tiling sphere by triangles (Re: 3 space terahedron-packing)
Date: 13 Sep 92 11:17:29 GMT
Article-I.D.: andrew.AegtD9O00Vp4EF8l8t
	<BuHpJr.Frv@acsu.buffalo.edu>
Organization: Doctoral student, Mathematics, Carnegie Mellon, Pittsburgh, PA

One other method of tiling the sphere with conruent triangles is given
any Archimedean solid, let the sphere be divided by all planes of
symmetry for that solid.  I think this will do.

For a few references, try R. Buckminster Fuller's "Synergetics" (I and
II), and Magnus Wenninger's "Spherical Models".  I'm sure Coxeter also
wrote something about such tilings.

Vince Matsko
Newsgroups: sci.math
From: victor@watson.ibm.com (Victor Miller)
Subject: Re: What's going on here ???
Date: Fri, 11 Sep 1992 14:05:52 GMT
Reply-To: victor@watson.ibm.com
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Organization: IBM, T.J. Watson Research Center

>>>>> On 11 Sep 92 21:46:59 +1200, wft@math.canterbury.ac.nz (Bill Taylor) said:


Bill> The following rather silly problem cropped up in our department just now.

Bill> Evaluate    S = 0! - 1! + 2! - 3! + 4! - ....

Bill> (yes, I know it's divergent, but blame Euler, not me.)

.... Details omitted

Bill> So what's going on here ????

Bill> Two crazy solutions to a crazy problem giving the same answer.   Why ?

Bill> --------------------------------------------------------------------------
Bill>             Bill Taylor              wft@math.canterbury.ac.nz
Bill> --------------------------------------------------------------------------
Bill>  MATH: necessary consequences of arbitrary axioms about meaningless things.
Bill> --------------------------------------------------------------------------

Bill, I heard Nick Katz (nmkatz@pucc.princeton.edu) give a lovely talk
on this and other related sums.  It seems that Euler "really knew what
he was doing".  The values of these sums are related to p-padic
modular forms.  This talk was quite a number of years ago (over 15),
and I don't remember any more details.

		Victor
--
		Victor S. Miller
		Bitnet: VICTOR at WATSON
		Internet: victor@watson.ibm.com
		IBM, TJ Watson Research Center
		"Great artists steal; lesser artists borrow" Igor Stravinsky
Newsgroups: sci.math
From: sasrdt@shewhart.unx.sas.com (Randall D. Tobias)
Subject: Re: measures of the `size' of infinite sets
Originator: sasrdt@shewhart.unx.sas.com
Date: Wed, 9 Sep 1992 19:50:56 GMT
Organization: (none)


In article <1992Sep9.170045.1617@cs.rose-hulman.edu>, brock@NeXTwork.Rose-Hulman.Edu (Bradley W. Brock) writes:
|>
|> 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.

What's the density of the set of prime powers?  Ie. how many Galois
fields are there?

-- 

Randy Tobias          SAS Institute Inc.     sasrdt@unx.sas.com
(919) 677-8000 x7933  SAS Campus Dr.         72450.2545@compuserve.com
(919) 677-8123 (Fax)  Cary, NC   27512-8000  norat@aol.com

 ... just my $(-exp(2*sqrt(-1)*arcos(0))/(((2**(2 + 1)) - 1)**2 + 1)).
From: kriman@acsu.buffalo.edu (Alfred M. Kriman)
Newsgroups: sci.math
Subject: Re: Chess Problem
Date: 14 Sep 92 04:17:27 GMT
Organization: UB

In article <1992Sep12.222402.14408@nmt.edu> jmarlan@titan.nmt.edu
(Jon Marlan) issues a challenge:
>  FOLLOW-UP QUESTION FOR EXTRA CREDIT:
>  Determine the odds for doing the same with eight bishops!  ;-)
>
>In article <BuGA8t.DL8@cmptrc.lonestar.org> carter@cmptrc.lonestar.org
(Carter Bennett) writes:
>I'll give this one a try.  
>
>Let B(i) = # of available "safe" places for i'th bishop
>
>B(1) = 64 
>B(2) = 64-8 = 56
> .
> .
> .

It's not so simple.  The number of safe squares depends not only on the
number of bishops previously placed (safely), but also on their locations.
B(2) as given is correct only if the first bishop is placed at a corner.
Newsgroups: sci.math
From: mvarmstr@eos.ncsu.edu (MARK VERNON ARMSTRONG)
Subject: Wibold of Cambray
Originator: mvarmstr@c00471-224wi.eos.ncsu.edu
Reply-To: mvarmstr@eos.ncsu.edu (MARK VERNON ARMSTRONG)
Organization: North Carolina State University, Project Eos
Date: Tue, 15 Sep 1992 15:35:18 GMT


   This may not belong in this category, but for the lack of a better category,
here it goes.

   Recently, while doing some mathematical research, I ran upon a name;
specifically Wibold (or Wibald), bishop of Cambray.  The article stated that
this priest used dice for some theological reason but left it at that.  After
exhaustive searches, I have been unable to fine any other references to this
elusive bishop.

   If anyone can come up with any information on this man, historical and/or 
mathematical, your assistance will be greatly appreciated.