HDTenEightyP/NetNews huggingface dataset:
From: news@massey.ac.nz (USENET News System)
Subject: Re: Three-sided coin
Organization: Massey University
Date: Tue, 10 Nov 92 20:47:33 GMT

In article <5413@daily-planet.concordia.ca>, mckay@alcor.concordia.ca (John McKay) writes:
> 
> 
> "How thick should a coin be to have equal (=1/3) probability
>  of landing on its head,tail,or edge?"
> 
> Surprisingly, making "reasonable" assumptions, this can be
> done in your head.
> 
I doubt it. Any asymmetrical object will be affected by air resistance
in a fairly predictable way, so the probability will depend on how far
the coin falls. One can hope that the bounce will be unpredictable, but
that depends on the surface the coin falls on and was not specified in
the problem. If you want to throw a randomising device, you'd better
stick to Platonic solids.
Newsgroups: sci.math,sci.physics
From: gmortens@rodan.acs.syr.edu (Gerald E Mortensen)
Subject: Re: Three-sided coin
Organization: Syracuse University, Syracuse, NY
Date: Thu, 12 Nov 92 13:43:19 EST

>>>> von Neumann was asked, when about to enter a taxi,
>>>>
>>>>"How thick should a coin be to have equal (=1/3) probability
>>>> of landing on its head,tail,or edge?"

it seems to me that this problem is less difficult conceptually than
several other responders indicate.  it seems to me that the problem
can be formulated fairly simply, although actually doing the work seems
excessively tedious!

1st of all, its certainly not true that in the case of a soft landing
the side that lands "down" stays down. consider a long thin rectangular
solid. if the axis of the solid is less than 45 degrees from the ground
normal you could consider
the end face to be down, but the solid will certainly fall over most of
the time.

my view of the problem is that:
1. the only random variable is the angle between the coin face outward
normal and the ground outward normal.
2. the soft landing assumption is fair (otherwise you've got to consider
the bounce dynamics... yuck)
3.if the coin lands at angle 0 or 90 it will stick on the face or edge 
respectively. otherwise, a "corner" hits first. 
4. draw a plane through the contact point, normal to the ground and normal
to the plane defined by the ground and coin normals.
5. the coin will topple onto a face iff the forces (due to gravity
acting on the coin mass) on the face side 
outweigh the forces on the edge side of the plane.

this could easily be carried out by computer simulation.

am i all wet? naive? brilliant, handsome, and talented?

////////////////////////////////////////////////////////////////////////
Gerald E. Mortensen (aka Jay)                    Syracuse Research Corp.
Research Engineer                                Merrill Lane
(315)426-3269 -- gmortens@mailbox.syr.edu        Syracuse, NY 13210
////////////////////////////////////////////////////////////////////////
Newsgroups: sci.math
From: "Christoph Schlenker" <UKJW@DKAUNI2.BITNET>
Subject: normal divisor  -  example
Organization: University of Karlsruhe, Germany
Date: Fri, 6 Nov 1992 13:42:41 GMT

Hi,

anyone out there who knows a (simple) (drawable) example of a normal
subgroup that shows the difference to other subgroups?
Need help.                                            Christoph
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Newsgroups: sci.math
Subject: Re: Curvature of a Line in Space
Date: 5 Nov 92 03:06:11 GMT
Distribution: usa
Organization: Computer Science Department,  Stanford University.

In article <1992Nov5.014717.9834@nas.nasa.gov> asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:
>In article <1992Nov3.002252.8053@shell.shell.com> morton@yukon (Scott Morton) writes:
>	[...]
>>
>>The curvature vector is the second derivative of the position vector
>>with repect to the parameter t; the magnitude of the curvature vector
>>is simply called the curvature.
>----------------------------------------------------------------------
>
>Um, not exactly.  The curvature vector can be defined as the second
>derivative of the position vector *with respect to arclength*.
>Then, the magnitude of this vector is the curvature.
>With respect to an arbitrary parametrization, you will not in general
>get the same thing.

Sounds like a culture clash.  In differential geometry t (sometimes s)
is conventionally arc length, and the curve can be uniquely specified
up to an isometry by its curvature and torsion each as a function of
the real-valued parameter t.  This representation has not proved
convenient in computer graphics, where it is preferred to take t to be
an independent parameter and to define the curve to be a suitable (e.g.
cubic polynomial or rational) map of the real line (the parameter space
indexed by t) into R^3 (R^2 for 2D graphics).

-- 
Vaughan Pratt				There's no truth in logic, son.
Newsgroups: sci.math
From: gen5061@husky1.stmarys.ca
Subject: Linear Algebra
Organization: St. Mary's University, Halifax, N.S., Canada
Date: Fri, 6 Nov 1992 15:23:36 GMT

Can anyone suggest some good Linear Algeba software, preferably shareware.

Thanks in advance.

-- 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|    Paul Cyr send e-mail to           | All comments are my own and if you    |
|                                      | don't like them, don't pay attention. |
|                                      |***************************************|
|   GEN5061@HUSKY1.STMARYS.CA          | Bellows      Damphousse       Muller  |
|                                      |                                       |
|                                      |             What a line!!             |
|                                      |              Go Habs Go!              |
|                                      |                                       |
| Why do today what you can put off till tomorrow.                             |
|			-unknown			                       |
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Newsgroups: sci.math
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: What is a knot?
Organization: Computer Science Department,  Stanford University.
Date: Tue, 10 Nov 1992 05:51:04 GMT

In article <1992Nov10.033122.10598@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>Perhaps they weren't very well educated.  Actually this is the sort of
>thing I hoped Pratt would bounce back with when I teased him about folks
>who can't tie their shoelaces until it is explained in
>category-theoretic terms.

I couldn't tie my shoe-laces until the back-and-forth argument was
explained to me.  :-)

Two trivia concerning this post: (i) A-->B *is* a concrete category
(one from which there exists a faithful functor to Set); (ii) (rather
more work) it is the only category with that many or fewer arrows
containing such a noniso.  (The one-object case is the hard part.)
-- 
Vaughan Pratt
Newsgroups: sci.math
From: gsmith@clio.uucp (Eugen W. Schmidt)
Subject: Re: Univariate polynomial equations and the FAQ
Organization: IWR, University of Heidelberg, Germany
Date: Fri, 6 Nov 92 18:45:27 GMT

In article <1d72mnINNq2p@mozz.unh.edu> dvf@kepler.unh.edu (David V Feldman) writes:

>Fix an integer m.  Let K be the extension of Q obtained by adjoining
>all roots of all polynomials of the form
>       n     m    
>	  x + a x + ... a
>		   m         0

>where the coefficients are rational.

This sounds like the algebraic closure of Q, Q-bar.

  Let s(m) be the smallest degree of a 
>polynomial with rational coefficients which does not have any root in K.
>So s(0)=5, by Galois theory.  What is known about the function s(m)?

This is false for Q-bar.  If your original field extension was the
maximal solvable extension in Q-bar, then we could try to figure out
the answer to your question, if we could figure out the question,
which I still can't do!


-- 
   Eugen W. Schmidt/Der Brahms Gang/IWR/Ruprecht-Karls University 
               gsmith@kalliope.iwr.uni-heidelberg.de
Xref: sparky sci.math:14779 sci.physics:18704
From: ask@ucscb.UCSC.EDU (Andrew Stanford Klingler)
Newsgroups: sci.math,sci.physics
Subject: Re: Three-sided coin
Date: 11 Nov 1992 21:17:48 GMT
Organization: University of California; Santa Cruz
NNTP-Posting-Host: ucscb.ucsc.edu


In article <1992Nov11.061630.22658@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>limits).  The dynamics counts.
>
>>Note that this would make the surface area of the edge \sqrt{2} times the
>>surface area of each face, contradicting my original guess that the area
>>determined the likelihood... I stick with the solid angle approach, though.
>
>Solid angle seems right in the limit of a tossed coin that
>achieves a random orientation and then floats down through honey, i.e.
>gently, so that it's bound to land on the side that is "pointing down".
>But clearly this is not how an actual tossed coin works.  
>
>I think this is a job for experimentalists.
>
>
Actually, I don't even think this is riight in the theoretical limit.
Coins "flip nicely" because they're nearly two-dimensional symmetric objects.
If I remember my mechanics correctly, the only stable rotations are about the
inertial axes with the highest and lowest moments.  In this case that means
the "vertical" axis and any "horizontal" axis.  I don't recall how to
compute the angular trajectory of an object with an arbitrary initial
orientation and spin, but the general answer will not be proportional times
for proportional solid angles.  If the coin is "nicely flipped" it should
be proportional times for proportional pure angles, giving a "floating
through honey" solution h=d.  But as you say, this is far from relevant
to a real throw.


Newsgroups: sci.math
From: sichase@csa1.lbl.gov (SCOTT I CHASE)
Newsgroups: sci.math
Subject: Re: What can we have for an educational system?
Followup-To: sci.math
Date: 13 Nov 1992 09:16 PST
Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA
Distribution: world
NNTP-Posting-Host: 128.3.254.196
News-Software: VAX/VMS VNEWS 1.41    

In article <26302@optima.cs.arizona.edu>, lal@cs.arizona.edu (The Morning Sun) writes...
> 
>Having Ph.D's teach in public schools is not going to help.
>A Person with a PhD, has done research in a particular area
>which is probably totally irrevelant to his teaching.

Two comments:

(1) My experience in high school was the the few teachers with advanced
degrees were the best teachers.  I had a calculus teacher who had been a
Stanford postdoc - he modeled galactic dynamics for a living before 
heading the math department at my high school.  He understood exactly 
how the math we were learning would be used by us in later life.  I 
also had a chemistry teacher who was working on a M.S. in instrumentation - 
he was designing better spectrographs.  Both of these guys were terrific.

(2) Anyone who claims that research experience is irrelevant to teaching
ability hasn't had the opportunity to see the kind of education you can 
get from top-notch researchers.  As an MIT undergrad, and now a Berkeley
grad student, I have learned more from practicing researchers than I could
ever have learned in the same courses from teaching professionals.  
The best students and advisors know this - that's why the best research
universities attract the best students - you get the best education from
people who are working in the field, not from the teaching professionals.

-Scott
--------------------
Scott I. Chase			"It is not a simple life to be a single cell,
SICHASE@CSA2.LBL.GOV		 although I have no right to say so, having
				 been a single cell so long ago myself that I 
				 have no memory at all of that stage of my 
				 life." - Lewis Thomas
Organization: Penn State University
Date: Fri, 13 Nov 1992 14:53:45 EST
From: <BAV2@psuvm.psu.edu>
Newsgroups: sci.math
Subject: Packing of balls of different radii

Could anybody give me reference(s) on the following problem:

There are spheres of two different radii (r1 & r2). A fraction of spheres
of radius r1 is fixed. What is _maximal_ packing ratio (i.e. maximal
volume fraction occupied by spheres that do not penetrate) in 3D space?
What is the packing ratio for a _random_ close packing? How it behaves
at r1<<r2 ?

Thanks a lot

-Boris Veytsman <bav2@psuvm.psu.edu>
From: dbc@ecs.soton.ac.uk (Bryan Carpenter)
Newsgroups: sci.math
Subject: Re: FREE-ENERGY TECHNOLOGY
Date: 9 Nov 92 17:18:54 GMT

In <1992Nov4.183509.2117@cnsvax.uwec.edu> mcelwre@cnsvax.uwec.edu writes:



>     Mathematics will be needed to ENGINEER the hardware described below:

>            
>                            FREE-ENERGY TECHNOLOGY
>                       by Robert E. McElwaine, Physicist
>          
>               Ninety to a hundred years ago, everybody "knew" that a 
>          heavier-than-air machine could not possibly fly.  It would 
>          violate the "laws" of physics.   All of the "experts" and 
>          "authorities" said so. 
>          
>               For example, Simon Newcomb declared in 1901:  "The 
>          demonstration that no possible combination of known 
>          substances, known forms of machinery and known forms of 
>          force, can be united in a practical machine by which man 
>          shall fly long distances through the air, seems to the writer 
>          as complete as it is possible for the demonstration of any 
>          physical fact to be." 
>          
>               Fortunately, a few SMART people such as the Wright 
>          Brothers did NOT accept such pronouncements as the final 
>          word.  Now we take airplanes for granted, (except when they 
>          crash). 
>          
>               Today, orthodox physicists and other "scientists" are 
>          saying similar things against several kinds of 'Free Energy' 
>          Technologies, using negative terms such as "pseudo-science" 
>          and "perpetual motion", and citing so-called "laws" which 
>          assert that "energy cannot be created or destroyed" ("1st law 
>          of thermodynamics") and "there is always a decrease in useful 
>          energy" ("2nd law of thermodynamics").  The physicists do not 
>          know how to do certain things, so they ARROGANTLY declare 
>          that those things cannot be done.  Such PRINCIPLES OF 
>          IMPOTENCE are COMMON in orthodox modern "science" and help to 
>          cover up INCONSISTENCIES and CONTRADICTIONS in orthodox 
>          modern theories. 
>          
 
On the other hand, if you spent much time around a university physics
department at the time when Pons and Fleischmann first made their
claims, you must have been surprised by how seriously people were
prepared to take cold fusion when it first came out.  And there was a
surprisingly large diversion of experimental effort into trying to
reproduce what seemed like (and turned out to be) a far-fetched idea.

Who was Simon Newcomb, anyway?
 
Bryan
From: israel@unixg.ubc.ca (Robert B. Israel)
Newsgroups: sci.math
Subject: Re: Relatives with Crackpot Proofs
Date: 12 Nov 92 17:44:25 GMT
Organization: The University of British Columbia
NNTP-Posting-Host: unixg.ubc.ca

In <92315.144432RVESTERM@vma.cc.nd.edu> <RVESTERM@vma.cc.nd.edu> writes:

>why don't you just tell him where his proof went wrong? sheesh.

>just say, "this step here is wrong, because blah blah blah."
>you don't have to be derisive about it, and tell the guy how
>dumb his proof is.  just tell him why it's wrong.

>also, pretending that it's right, or that you don't see a mistake,
>could be even worse.  if you do that, then he sends his "proof" off
>to a bunch of people he doesn't know; thus, a bunch of people who
>may very well have no qualms in saying, "this is the stupidest piece
>of garbage i've ever seen."

>jeez, come on.  do you really need other people's advice in order
>to be honest?

>bob vesterman.

One problem with this approach is that it's unlikely to be effective very
long.  With very high probability, he will come back to you in a week or
so with the mistake "fixed".  Since the "fix" introduces several more
errors, this could be the start of a never-ending process.  And be assured,
he won't get tired of the process and go away, because he's getting
what he interprets as "positive reinforcement" from you.

My suggestion would be to persuade him that he needs more mathematical
background in order to present his "very interesting" ideas in a more
effective way.  Then provide him with the most difficult mathematics
text you can find, and tell him to come back when he's mastered it.
I don't know if this will work.  He might actually learn something,
so it won't be a total waste.
-- 
Robert Israel                            israel@math.ubc.ca
Department of Mathematics             or israel@unixg.ubc.ca
University of British Columbia
Vancouver, BC, Canada V6T 1Y4
Xref: sparky sci.math:14807 sci.physics:18730 sci.astro:11892 sci.bio:4104 sci.chem:4528 misc.education:4254
From: waohe@uniwa.uwa.edu.au (WA Office of Higher Education)
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Subject: Re: 2-dimensional grading system (was Re: What can one do for the bright?)
Date: 12 Nov 1992 09:35:26 +0800
Organization: The University of Western Australia
NNTP-Posting-Host: uniwa.uwa.edu.au
X-Newsreader: Tin 1.1 PL5

Onar Aam (onar@hsr.no) wrote:
: 
: >In article <1992Nov5.070342.6288@hsr.no>, onar@hsr.no (Onar Aam) writes:
: >
: >|> What the hell are you guys talking about?(!) This is EXACTLY why I proposed the
: >|> 2D grading system in the first place. With today's grading system you only get
: >|> one grade which includes both effort and grasp. With this system the employer
: >|> wouldn't know whether his employee has brains or not. With a 2D system, however,
: >|> the employer gets that vital information. 
: >
: >What are YOU talking about? The question that was being addressed is WHY WOULD
: >ANYBODY CARE ABOUT THE EFFORT PUT IN CLASSES? It is additonally unclear whether
: >A's would go to those people who put in the least effort, or if you would give
: >A's to the people who are dumb and couldn't learn it in twice the time that other
: >people could, but gave up a social life so they could get an A on the academic
: >part.
: >
: >Jason W. Solinsky
: 
: Are you an employer? I find that very unlikely. Employers are in most cases
: interested in people who are willing to work, not in some brilliant-but-lazy guy.
: Someone with a grade: effort=A , understanding=C is probably VERY much wanted
: by an employer. 
: 
: 
: 
: Onar.
:    
Oops!
Of course you are right Onar if the name of the game in education is
to prepare quality employees, and there is some importance in that.

Still, some time ago, I noticed that if I should live for the average
Australian male life-span, that I'm counting down my time, and I notice
that being a beaut employee isn't what I want to have spent my gift
of life on.  
Similarly, there are a lot of things more important to me than 
maximizing the GDP!  What's wrong with happiness, fulfilment, and
celebration (of nothing in particular)?  Does this have anything to 
do with education?
Does it have anything to do with how we grade each other?

Jeff 
Newsgroups: sci.math
From: brick@ucdmath.ucdavis.edu (Stephen Brick)
Newsgroups: sci.math
Subject: from an ad
Date: 5 Nov 92 21:39:47 GMT
Distribution: usa
Organization: Math department, UC Davis

Recently I posted an article here which turned out to be a FAQ.
I offer my apologies for doing so. Here is a little something
to make up for my faq sin.

In the April 18, 1986 edition of the San Francisco Chronicle,
an ad for the video store "Adam's Video Sales" contained the
following:

	Show that

		xgx^{-1}gx^{-1}gxgx^{-1}gx = 1

		where g^2=1 and g \ne 1

	has no solution over the group Z_2 and
	get your choice of a free telephone or
	AM/FM radio with headphones.

A few words of explanation are in order. The group Z_2
is the cyclic group of order two (here with non-trivial
element g). The equation having a solution *over* Z_2 means
that Z_2 is a subgroup of a bigger group that contains
some element x which satisfies the above equation. (Of
course, the problem is to show that no such element x
exists in *any* group containing Z_2 as a subgroup.)

The store was owned by someone with an advanced degree
in engineering. Each week he would include an applied
math problem and give out a free telephone or radio
to anyone who solved the problem (I got the feeling 
that he enjoyed talking math with the people who came
in with solutions). Of course, the offer is no longer
valid. In fact, the store went out of business (changed
ownership ?) a number of years ago.

I was wondering if there have been any other promotions
connected with mathematics. (Also, feel free to try
to solve the problem.)

Btw, the equation is an example due to Roger Lyndon.

----------------------------------------------------
Steve Brick
Dept of Mathematics
UC-Davis
Davis, CA 95616

brick@ucdmath.ucdavis.edu
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
From: solman@athena.mit.edu (Jason W Solinsky)
Subject: Re: 2-dimensional grading system (was Re: What can one do for the bright?)
Organization: Massachusetts Institute of Technology
Date: Sun, 8 Nov 1992 07:17:56 GMT

In article <1992Nov3.091430.4135@hsr.no>, onar@hsr.no (Onar Aam) writes:

|> As a current student (Electrical Engineering if you're curious AND a  
|> National Merit Finalist (read: Seimifinalist with "formalities" done  
|> NOT! - but that's a different argument I'm perfectly willing to let  
|> slide)

Well I'm not. Please DO read National Merit Finalist as National Merit
Semifinalist with formalities. The difference between the two is that
semifinalists are chosen objectively and finalists are all semi-finalists
who fit the stereotypes that the organizers have in mind for the nation's
brightest individuals. This cut of 5% of all semifinalists is highly
subjective and effectively meritless.

Jason W. Solinsky
National Merit Finalist
Newsgroups: sci.math