HDTenEightyP/NetNews huggingface dataset:
From: bern@Uni-Trier.DE (Jochen Bern)
Subject: Re: A REAL 3-sided coin
Originator: bern@kleopatra
Organization: Theor. CS, FB IV / CS, Univ. of Trier, Germany (Internet TI.Uni-Trier.DE)
Date: Thu, 12 Nov 1992 14:29:36 GMT

In <1992Nov11.172703.2931@vela.acs.oakland.edu> phkahler@vela.acs.oakland.edu ( Paul H. Kahler) writes:
>1) Start with an equilateral right cylinder.
>2) Eliminate the possibility of it landing on end by:
>    a) tapering the ends to a point (a 3-sided football)
>    b) rounding the ends
>3) For each side A=1,2,3 put A face down and write A on the bottom
>   of the other 2 sides.

Just for Everybody's Information: I've been concerned about EXISTING non-cubic
Dices when I tried to design a Board Game. I went into a Fantasy Games Shop
and asked them about the Dices they offer (I knew that they offered some).
They offered me Dices with 4, 8, 10, 12 and 20 Sides. The 10-sided one was a
straight Generalization of the (8-sided) Double Pyramid; All others were
Platonic Bodies. In Addition to this, they told me that there is a 100-sided
(!) Monster, looking quite ball-like, but they weren't able so far to get it.

To take up Pauls Proposal, you can create fair Dices with ANY Number of Sides
by creating a Cylinder (sufficiently long, pointed, or rounded) whose Base
is a regular n-Polygon. If you don't like Cylinders, you can simulate many
many Numbers of Sides by taking several of the abovementioned Dices and
calculating the total Result from their individual Results. This includes
"identifying" Sets of Sides of a single one, too.

OK, you may be more interested in theoretic Approaches. In that Case, here's
a Brain-Teaser for you: Supposed that I'm stuck with non-platonic Bodies as
Dices. They may be not fair, since there are Things like Air Influence,
different Distances of Sides from the Gravicentre, Sides with equal Area but
different Shapes etc. involved. Question: IS IT POSSIBLE TO CREATE A FAIR
n-SIDED RANDOMIZER BY STARTING WITH A m-SIDED BODY (m>>n, no fair m-sided
Randomizer) AND LABELING ITS SIDES APPROPRIATELY?

Have terrific Brainstorms,
								J. Bern
-- 
 /  \  I hate NN rejecting .sigs >4 lines. Even though *I* set up this one. /\
/ J. \ EMail: bern@[TI.]Uni-Trier.DE / ham: DD0KZ  / More Infos on me from /  \
\Bern/ X.400 Mail: S=BERN;P=Uni-Trier;A=dbp;C=de  /   X.400 Directory, see \  /
 \  /  Zurmaiener Str. 98-100, D-W-5500 Trier    /     X.29 # 45050230303.  \/
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: a first year grad student freaks out.
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Wed, 11 Nov 92 22:37:22 GMT


>In article <92314.170255RVESTERM@vma.cc.nd.edu> <RVESTERM@vma.cc.nd.edu> writes:
>>i'm a first year grad student.  i can do most of the homework assigned
>>to me.  i can pass tests i have to take.  i can usually understand
>>proofs of theorems that we're studying, given some thought.  i think
>>that with a lot of work, i can pass my orals.
>
>>however, what's the deal with this thesis thing? what happens if you
>>simply cannot prove whatever your advisor assigned?

You think *you've* got it bad!  I'm a mathematics professor with nobody
to assign me things to prove!  So when I come up with an idea I have
*no* idea at first whether it can be done at all.  At least you have an
advisor, who is supposed to choose problems for you that can be done!

In other words - you are beginning to face up to what life as a
researcher is like.  Sometimes fun, sometimes terrifying.

Becoming an academic has many stages, none of which prepares you
adequately for the next.  For example, in math: in high school you may
think you are good at math if you are good at calculating.  Then in
college you find out that this is not what being a (pure) mathematician is
primarily about - it's about proving things.  In college you may think
you are good at math if you good at doing proofs for homework.  Then in
grad school you find out that this is not what being a mathematician is
about - in your thesis you try to prove things that might or might not
turn out to be true, and might be too hard.  After you finishes your
thesis you might think you are good at math, if your thesis was good.
But then you find out that to be a mathematician you have to choose your
*own* research direction, which involves spotting topics that are "ripe"
for research, figuring out what you need to learn to tackle them, etc..
(Here I am completely leaving out all the *political* skills one must
develop, which are also crucial.)

That's why I'm glad that starting in high school I started trying to
come up with math topics to do research on.  One has to face the unknown
eventually if one is going to do research, so one might as well get used
to it as early as possible (even if ones first research projects are a
little silly).
Newsgroups: sci.math
From: uds@trace.eng.wayne.edu (Seetamraju Udaybhaskar)
Subject: ......  roots of a FINITE fourier series ......
Reply-To: uds@trace.eng.wayne.edu (Seetamraju Udaybhaskar)
Organization: Wayne State University, Detroit
Distribution:  world
Date: Mon, 9 Nov 1992 20:48:50 GMT


given a TRUNCATED (finite) trignometric fourier series

            --- m                              
   F(m) =   \            a    cos ( i w x  +  phi  ) 
            /             i                      i   
            --- i = 0                          


where :: phi_i is the initial phase of the i-th harmonic.   a_i will be real.

The LHS F(m) is a function of x.  Is there a general method (algorithmically
also will be great) to solve the equation

		F(m)(x) = 0.    For finite but reasonable m (say m < 50)...

i.e, to find the roots of the above series...

A very important peice of information :  THE ACTUAL FUNCTION IS NOT KNOWN.
THE FOURIER SERIES IS constructed from DATA OBTAINED BY EXPERIMENTATION


Seetamraju Udaya Bhaskar Sarma
(email : seetam @ ece7 . eng . wayne . edu)

Organization: Carnegie Mellon, Pittsburgh, PA
Newsgroups: sci.math
Date: Fri,  6 Nov 1992 18:16:32 -0500 
From: "Jonathan R. Ferro" <jf41+@andrew.cmu.edu>
Subject: Re: feynman story probably not true.

RVESTERM@vma.cc.nd.edu writes:
> a little while ago, somebody posted a story to this effect: for a
> certain physics exam at caltech, students were allowed to use any
> reference material that they could carry in to the room.  one
> enterprising guy supposedly carried richard feynman in.

I believe that this is confusing two other stories: (1) Students are
allowed to bring in anything they can carry; student carries in _grad
student_ and (2) Take-home physics exam lists "Allowed references:
Halliday & Resnick, Feynman, etc."; student consults Feynman the
professor instead of Feynman the textbook; Feynman says "Yep, it
certainly does say that you can use me.  Whaddya wanna know?"

I have my doubts about the truth of either story.

-- Jon Ferro               Einsprachigkeit ist heilbar
From: kibler@turing.ICS.UCI.EDU (Dennis Kibler)
Newsgroups: sci.math
Subject: Re: definition of topological space
Date: 5 Nov 92 17:02:59 GMT
Article-I.D.: Paris.9211050900.aa22079


 The definition of a topological space is very abstract, although
even less intuitive definition are possible. (see definition
based on ultrafilters).

 What's the point? Generality, simplicity, and understanding.

Usually after studying real-value continuous functions of 1-variable
one begins to notice certain regularites. For example the
image of a interval under a continuous function is another interval or
the image of a a closed interval is an other closed interval.
You may wonder if these are general properties and if so how
general. Topological spaces are very general but sufficiently
specific so that you can define continuous functions as well
as notions of connectedness and compactness. This generality
strips away the irrelevant detail making proofs easier and
more elegant. They provide a way to abstractly describe the
regularities observed for the more familiar realms of multivariate
continuous functions.
Newsgroups: sci.math
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Subject: Re: a first year grad student freaks out.
Organization: Purdue University Statistics Department
Date: Wed, 11 Nov 1992 14:06:12 GMT

In article <92314.170255RVESTERM@vma.cc.nd.edu> <RVESTERM@vma.cc.nd.edu> writes:
>i'm a first year grad student.  i can do most of the homework assigned
>to me.  i can pass tests i have to take.  i can usually understand
>proofs of theorems that we're studying, given some thought.  i think
>that with a lot of work, i can pass my orals.

>however, what's the deal with this thesis thing? what happens if you
>simply cannot prove whatever your advisor assigned?

Research is like that.  It may be that you will have to start over.  It
may be that what you can prove is enough for a dissertation.  It may be
that someone announces the result before you do and your work is not
accepted as original.  All of these have happened.

At most schools you formally need an advisor, but rarely is this true in
the strict case.  Some schools do not even require this.  
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@snap.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!snap.stat!hrubin(UUCP)
From: hdev@dutiaj.tudelft.nl (Hans de Vreught)
Newsgroups: sci.math
Subject: Re: Relatives with Crackpot Proofs
Date: 11 Nov 92 08:51:46 GMT

goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard) writes:

>In article <2105@celia.UUCP> keith@celia.UUCP (Keith Goldfarb) writes:
>> Does anybody have any good suggestions about how to deal with
>> crackpot "proof"s from relatives and friends?  > 

>This is considered horribly rude behavior when the expert is a 
>medical doctor.  If your relative is an MD or a plummer, say, be sure  
>and get some free work out of him in return.  

I doubt if an MD would ask such a question: they *know* how boring such
questions can be, since they are always asked to give a diagnoze for free.
Maybe, it will work if you charge him what your boss asked for you if he / she
gives you a task to solve for a client. (I've seen this working for a student
which asked to lecturer to explain something of ANOTHER subject. He said, well
that would be $150 per hour normally, but since you're a student I will do it
for just $50 per hour. The student decided not to go into that deal...)

But that won't work for relatives. Then every thing must be done for free.
If it is a relative on which you aren't very fond of, just stall things
"because you're *soooo* busy". After a couple of months the relative will
likely drip off.

But a relative which is close to you, try what Bart Goddard does: give an
apert wrong answer. Most people will understand that you don't want to do it.
But the real pitbulls will never give up... I'll guess biting the bullet is
the quickest way to get rid off such animal. Say he / she is "right", after
you've quickly peeked over the "proof" (first law of debate: "Never argue with
a fool - People might not know the difference"). In most cases the relative
will return to "normal" life. Even if he would sent it in to journal (not
likely), it will be rejected and then you can say "I never knew that I could
make such a clear mistake, not seeing that error. Sorry, it must have been my
day off...".

>At family reunions, I am always called on to do such difficult math as
>counting heads and 2-digit multiplication.  I always lie.  The best way  

This sounds very familiar: what do they think you do for living (well, don't
answer: I don't like nightmares)?

Many relatives think you find every thing on the subject you graduated in
easy and interesting. In most cases there are several topics in which you're
not very good and several parts of the subject you graduate in *really* turns
you off.
--
Hans de Vreught                          | John von Neumann:
hdev@dutiaa.tudelft.nl                   | Young man, in mathematics
Delft University of Technology (TWI-ThI) | you don't understand things,
The Netherlands                          | you just get used to them.
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Re: Axioms of set theory, infinity and R. Rucker
Date: 11 Nov 92 07:47:51 GMT
Article-I.D.: camelot.ARA.92Nov11024751
Organization: M.I.T. Artificial Intelligence Lab.

What is the reference to this recent work of Matiyasevich and Jones?

Also, I've never understood what a supercompact cardinal is. Would you
like to explain the concept?

Allan Adler
ara@altdorf.ai.mit.edu
From: sdunbar@nde.unl.edu (steven dunbar)
Newsgroups: sci.math
Subject: Re: group theory for HS students
Date: 8 Nov 1992 19:10:24 GMT
Organization: University of Nebraska--Lincoln	
Distribution: sci
NNTP-Posting-Host: nde.unl.edu


Here's a data point.  My daughter is in the eighth week of 7th grade.  She 
is in an "honors" math class of about 30 kids.  They all know the basic 
concepts of operation, inverse, and identity in general and with specific 
application to the cyclic groups and at least the permutation group on 3 
elements, along with a couple of other examples.  They have not yet called 
these a group or in the case of two operation on Z mod n, a ring, but they 
do recognize when they have what the book calls a uni-fold system ( a 
group) and a bi-fold system, ( a ring).  I am waiting for the introduction 
of these names.  Right now, the book they are in is explicitly titled 
"Intuitive Ideas".  It's part of a comprehensive series designed for grades
7-10.  I don't have the series title or the authors handy, but it was 
developed at Southern Illinois University, at least in part.

- Steve Dunbar
From: choy@skorpio.usask.ca (I am a terminator.)
Newsgroups: sci.math
Subject: Re: Most important event in the history of math
Date: 7 Nov 92 00:15:09 GMT
Article-I.D.: access.1992Nov7.001509.16784
Organization: University of Saskatchewan, Saskatoon, Canada

In article <zlsiida.331@fs1.mcc.ac.uk>, zlsiida@fs1.mcc.ac.uk (dave budd) writes:
|> Clearly, the most important event in the history of math was Mattel's 
|> withdrawal of the 'math class is tough' Barbie
 
Math class is tough.
Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Relatives with Crackpot Proofs
Organization: Computer Science Department,  Stanford University.
Date: Mon, 9 Nov 1992 23:29:28 GMT

In article <2105@celia.UUCP> celia!keith@usc.edu (Keith Goldfarb) writes:
>Does anybody have any good suggestions about how to deal with
>crackpot "proof"s from relatives and friends?  A relative of
>mine cornered me at a party recently and gave me a copy of
>his "proof" of FLT.

Have them buy you lunch, at which they explain the proof.  If you can
see the error don't point it out until they've paid the bill.  If you
can't, advise them to write it up as a paper.  Either way you get a
free lunch, and the probability of having a real paper to deal with
should be reasonably low.
-- 
Vaughan Pratt
Newsgroups: sci.math
From: clarke@acme.ucf.edu (Thomas Clarke)
Subject: Re: Bill Clinton and Complex Analysis : -)
Organization: University of Central Florida
Date: Mon, 9 Nov 1992 13:48:09 GMT

I heard on a local NPR station that a local politician was disappointed
when he rode from the airport with Bill Clinton but didn't get to
talk to him very much.  The now Pres-elect was busy helping with
some of Chelsea's algebra problems.

At least he hasn't forgotten everything :-)  Does this mean he's
better at math than Hilary?
--
Thomas Clarke
Institute for Simulation and Training, University of Central FL
12424 Research Parkway, Suite 300, Orlando, FL 32826
(407)658-5030, FAX: (407)658-5059, clarke@acme.ucf.edu
From: afm@trillian (Andreas Mueller)
Subject: Re: Help wanted in integration.
Organization: University of Heidelberg, Germany
Date: Mon, 9 Nov 92 10:41:13 GMT

UKJW@DKAUNI2.BITNET ("Christoph Schlenker") writes:
: Hello,
:
: I have just typed your integral into a math-prg and the solution
: of it is just    0.
<stuff deleted>
: I hope thats right...                                 Christoph
It cannot possibly be right: the integrand is a function >=0,
so the integral cannot vanish unless the integrand is identically
zero, which it is obviously not.
                                Andreas Mueller

---------------------------------------------------------
Andreas Mueller         afm@vogon.mathi.uni-heidelberg.de
Mathematisches Institut
Im Neuenheimer Feld 288
W - 6900 Heidelberg 1
---------------------------------------------------------
From: nas_ps@jsc.nasa.gov (Pradip R. Shah)
Newsgroups: sci.math
Subject: Sum of Numbers
Date: 12 Nov 92 21:49:36 GMT
Article-I.D.: aio.1992Nov12.214936.15458
Reply-To: nas_ps@jsc.nasa.gov
Organization: G.E. Government Services

I hope this is not a FAQ.  I have posted the same question on rec.puzzles.
Given numbers from 1 to 16, arrange them on a 4 by 4 - magic square such that
when added them diagonally, horizontally, and vertically would yield the same
number.  Is there any algorithm do this problem ? The solution may not be 
unique.  Can we use the solution from a simultaneous equations ?

I posted this earlier (today) and I found empty mail - hence I am posting again.
Thanks.

Pradip Shah    General Electric
Xref: sparky sci.math:14612 sci.physics:18457 sci.astro:11786 sci.bio:4085 sci.chem:4483 misc.education:4197
From: bruck@mtha.usc.edu (Ronald Bruck)
Newsgroups: sci.math
Subject: Re: symbolic derivation of polynomial roots
Date: 11 Nov 1992 16:55:04 -0800
Organization: University of Southern California, Los Angeles, CA
NNTP-Posting-Host: mtha.usc.edu

In article <1834@spam.ua.oz> ahanysz@spam.ua.oz (Alexander Hanysz) writes:
>In article <5412@daily-planet.concordia.ca> mckay@alcor.concordia.ca (John McKay) writes:
>>
>>My understanding is that the roots of ANY polynomial in Q[x] 
>>can be expressed in terms of radicals. What is the trick?
>>You may need infinitely many of them.
>
>Well, if you're going to be like that then you don't even need radicals!
>Any real number can be expressed in terms of integers and arithmetic
>operations.  You just need infinitely many of them.  It does seem to
>trivialise the issue somewhat.
>
>								Alex.
>

I think this misses the point.  As I understand the question (although
I don't know the answer), he's asking whether there is some closed-form,
though possibly infinite in extent, formulation of the roots in terms of
the coefficients of the polynomial.  For example, it might mix continued
fractions with expressions like $\sqrt{a_0 + \sqrt{a_1 + \dots$, where
the $a_i$ have explicit expressions in terms of the coefficients.  It's
this dependence on the coefficients which makes the example of "every real
has an expansion into an infinite decimal" spurious.

He's asking a serious question, and if his formulation of it is a little
vague, ***that is the nature of all research problems***, until the
canonizers have reduced it to Definition 2.1.7 of Section 3.2, after which
I cease to be interested.

I'm curious as to the answer.  Is there an interesting formulation?  

--Ron Bruck
bruck@mtha.usc.edu preferred


Newsgroups: sci.math
From: victor@watson.ibm.com (Victor Miller)
Subject: Re: Extended Fermat primes
Date: Thu, 12 Nov 1992 14:45:23 GMT
Reply-To: victor@watson.ibm.com
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
	<1992Nov8.004737.13519@Princeton.EDU> <BxKLzE.Bu9@cs.columbia.edu>
Organization: IBM, T.J. Watson Research Center

>>>>> On Wed, 11 Nov 1992 21:21:13 GMT, kasdan@cs.columbia.edu (John Kasdan) said:

John> In article <1992Nov8.004737.13519@Princeton.EDU> tao@fine.princeton.edu (Terry Tao) writes:
Terry> 
Terry> ....   And it is highly likely that there are infinitely many primes
Terry> of the form n^4 + 1, n^8 + 1, etc. on the grounds that any polynomial which
Terry> is not factorizable should give infinitely many primes.  (Is there a name
Terry> for this conjecture? if you know it could you email me?)
Terry> 

John> I doubt that there is a name for the conjecture in that form, because
John> it is obviously false.  Consider x^2 + x + 2.

John, There is actually a conjecture like this.  I don't remember what
it is called in general.  Obviously, it needs to be stated in a
modified form: the polynomial x^2+x+2 is always divisible by 2 at
integer values, so consider (1/2)(x^2+x+2).  The generalization is as
follows:

Let (x;n) = x(x-1)...(x-n+1)/n!.  Then show that a polynomial with
rational coefficients takes on integer values at integer values of
it's argument if and only if it is an integral linear combination of
the (x;n).  In your case, your polynomial was: 2 (x;2) + 2(x;1) +
2(x;0).

A more usual conjecture has to do with generalizing arithmetic
progressions:
If f(x) is an irreducible polynomial over Q, with no fixed divisor
(i.e. the gcd of the coefficients in the expansion into (x;j) is 1),
then there are infinitely many primes of the form f(x).

Unfortunately, this is unknown for any polynomial above first degree!

Terry> 	Terry 

John> /JK

--
		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: ledwards@leland.Stanford.EDU (Laurence James Edwards)
Subject: Re: definition of topological space
Organization: DSG, Stanford University, CA 94305, USA
Date: Fri, 6 Nov 92 09:46:25 GMT

In article <1dbm2eINN7gr@function.mps.ohio-state.edu>, edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:
|> In article <1992Nov5.033835.5180@leland.Stanford.EDU> ledwards@leland.Stanford.EDU (Laurence James Edwards) writes:
|> [...]
|> 
|> Some math educators say that we should begin with the abstract (like the
|> above) and later specialize to the concrete.  Obviously, that approach is
|> not good for Mr. Edwards.
|> 
|> The definition above should come only after many, many examples have been
|> studied.  At that point, the purpose of the definition may be more
|> apparent.

Actually, I don't mind the abstraction as long as its accompanied with some
explanation and motivation of the ideas leading up to it. This motivation
doesn't necessarily have to take the form of examples but can be more in the
way of a historical account of the evolving thought processes that led up to
the abstraction. Either way works for me.

Normally, one would get this kind of context (I would hope) in a class. I was
just trying to learn enough about this subject so that I could understand the
main ideas of an intriguing paper I ran across. I was just using a couple of
math dictionaries which don't provide a lot of context.

Larry Edwards
From: mld900@anusf.anu.edu.au (Murray Dow)
Newsgroups: sci.math
Subject: Re: Simple Diff Eq
Date: 9 Nov 1992 22:18:21 GMT
Organization: ANU Supercomputer Facility
Distribution: world
Reply-To: mld900@anusf.anu.edu.au
NNTP-Posting-Host: 150.203.5.3
Originator: mld900@asterix


In article <13390031@hpspdla.spd.HP.COM>, ric@hpspdla.spd.HP.COM (Ric Peregrino) writes:
|> 
|> Hello sci.math,
|> 
|> I've come by a simple differential equation that I'm interested in:
|> 
|> df(x)/dx - 1/f(x) = 0
|> 
Use d/dx(f^2) = 2fdf/dx to get
f=+-sqrt(2x+c)
-- 
Murray Dow                         GPO Box 4 Canberra ACT 2601 Australia
Supercomputer Facility             Phone: +61 6 2495028
Australian National University     Fax:   +61 6 2473425
mld900@anusf.anu.edu.au