HDTenEightyP/NetNews huggingface dataset:
From: leyfre@McRCIM.McGill.EDU (Frederic Leymarie)
Newsgroups: sci.math
Subject: Re: Michael Spivak (Publish or Perish)
Date: 5 Nov 92 16:41:47 GMT
Organization: McGill Research Centre for Intelligent Machines


In article <Bx8xz4.67L.1@cs.cmu.edu>, sundar+@cs.cmu.edu
 (Sundar Vallinayagam) writes:

|> I too am interested in getting hold of Spivak's text-book on
|> Calculus.  Any info to this end would be much appreciated.

Try:

	Publish or Perish, Inc.
	3701 W. Alabama, Suite 450-130
	PO Box 27703-130
	Houston, TX 77027
	U.S.A.

Ask for the 2nd edition (1980) of "Calculus" by Spivak.
-- 
Frederic Leymarie -- leyfre@mcrcim.mcgill.edu
McGill University, Electrical Eng. Dept., McRCIM,    |	Tel.: (514) 398-8236
3480 University St., Montreal, QC, CANADA, H3A 2A7.  |	FAX:  (514) 398-7348
Newsgroups: sci.math,sci.physics
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Three-sided coin
Organization: Computer Science Department,  Stanford University.
Date: Fri, 13 Nov 1992 06:53:40 GMT

In article <1992Nov12.134111.3793@schaefer.math.wisc.edu> mueller@schaefer.UUCP (Carl Douglas Mueller) writes:
>Consider the coin as being carved out of a sphere
>(the edges of the top and bottom of the coin are on the surface of the sphere
>and stuff is carved away to leave the coin (two chunks of sphere removed by
>slicing along the faces of the coin -- and a sort of belt which is then 
>removed by slicing along the outer edge of the coin).  The answer is given
>by finding the thickness that makes the surface areas (ON THE SPHERE) of these
>three chunks of sphere equal.  The answer is:
>
>The thickness should be the diameter divided by the square root of 8.
>(That is, the thickness is to be about 35.4% of the diameter.)

For this reasoning to be valid the axis of rotation would have to be
uniformly distributed on a sphere enclosing the coin.  Under typical
launching conditions I question whether it is as likely for that axis
to be normal to (the face of) the coin as lying along a specified line
in the plane of the coin.

In fact a regular flip should ensure the latter, at least at the moment
of launching.

The coin is a gyroscope while in flight, but presumably it can nutate
(its axis precess).  Can a vertical impulse applied to a single point
of a coin lying flat induce nutation?  I'd guess not.  What about two
unequal vertical impulses each applied at a point?  I can't think of an
elementary argument for either side, though I'd sort of guess it
could.

===
To change the topic back to what I vaguely recall to be one of the
earlier questions, namely can you build a fair die with n sides, I just
now recall a paper by our own Joe Keller in I think AMM two or three
years ago on just this topic.  Joe gave a very comprehensive theory of
fair dice.

Here's Joe's simplest construction of a fair n-sided die for n >= 5.
Cylindrify (prismify) a regular n-agon.  The n sides have equal
probalities p, and the top and bottom have equal probabilities q.  For
thin enough dice q<p, for thick enough, p<q, whence there exists a
thickness in between where p=q.

For 2 <= n <= 4 one can solve the problem for 2n or 3n and take pairs
or triples of sides as denoting the same outcome.  (And for n=4 there
is also the simplex.)
-- 
Vaughan Pratt	  		A fallacy is worth a thousand steps.
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Who are our best mathematicians?
Organization: MIT Department of Mathematics, Cambridge, LA
Date: Fri, 6 Nov 92 03:11:26 GMT

In article <92310.121654KGHDB@ASUACAD.BITNET> Hans DeBano <KGHDB@ASUACAD.BITNET> writes:

>Actually, it's been awhile since I've seen anything substantive from Gauss.
>Is he on sabbatical this year?

Mathematicians generally burn out when they are over 150 years old.
Gauss is an exception, however; he is here visiting U. C. Riverside, but
he has adopted a pseudonym since he is sick of proving yet another
"Gauss's theorem," inventing yet another "Gaussian," or finding another
"Gauss law."
From: palais@binah.cc.brandeis.edu
Newsgroups: sci.math
Subject: Re: Michael Spivak
Date: 5 Nov 92 15:08:33 GMT
Reply-To: palais@binah.cc.brandeis.edu
Organization: Brandeis University

A number of people have asked how to order Spivak's "Calculus".
It is published by his own company, Publish or Perish Inc.
The address and phone number, and Spivak's email address follow.
  Michael D. Spivak      
1200 McDuffie  
Houston, TX 77019  
713  524 5515 
Publish or Perish Inc.
3701 West Alabama 450-130
Houston, TX,   77027
713  524  5515 
IN%"spivak@rice.edu"    
FAX:  713 523 6743
Xref: sparky sci.math:14543 misc.education:4169
From: burtt@comet.nscl.msu.edu (BRIAN BURTT)
Newsgroups: sci.math,misc.education
Subject: Re: Is Math Hard?
Date: 6 Nov 92 22:49:00 GMT
Organization: NSCL Michigan State University
News-Software: VAX/VMS VNEWS 1.41

(In response to Mr. Parson's comments on home education...)
In my particular circumstance, which I think reflects that of some other 
people out there:
	As of about fifth or sixth grade, I was quite of ahead of my 
mother (my single parent, who BTW graduated high school and has almost
two years of college behind her) in knowledge of science, math, and history,
and by the time I reached high school in most other academic subjects.
She wanted to "home educate" me, letting me teach myself, which I have 
always done quite well.  Of course, the local school district was not
at all interested in letting this happen.  (They weren't concerned about
the quality of my education, because I was already far past what they
could teach me in classes that, for example, sixth graders were taught
at a second grade level.  They wanted to be sure they continued to get 
the money from the state of Michigan that they were granted for each 
enrolled student.  These are statements of officials and teachers of 
the school district.)
	The only thing I remember learning from my first five years
is arithmetic.  Almost everything else I knew years before it was 
taught in school.
	Having failed at the home education route, my mother tried to
get me enrolled in a gifted program in a local school district.  They
were quite happy to have me, but it took TWO AND A HALF YEARS before
this particular school district was willing to give up its state funds
for me and let me go on my way.
	Have others had similar problems in moving elementary 
school students to more appropriate situations, or was I just 
particularly unlucky?

--Brian Burtt
Undergraduate major in physics and mathematics
Michigan State University
burtt@lynch.nscl.msu.edu
From: rgep@emu.pmms.cam.ac.uk (Richard Pinch)
Newsgroups: sci.math
Subject: Re: definition of topological space
Summary: Definition of continuity in terms of closed sets works just as well
Keywords: Topology; Open sets; Continuity; Closed sets
Date: 6 Nov 92 10:12:58 GMT
Organization: Department of Pure Mathematics, University of Cambridge

In article <1992Nov6.092037.7676@leland.Stanford.EDU> ledwards@leland.Stanford.EDU (Laurence James Edwards) writes:
>[...]
>In defining continuity what is the advantage of using open sets vs. closed sets,
>i.e. why not say:
>
> |x-x'| <= e => |f(x) - f(x')| <= d
>
>and similarly:
>
> Y closed => f*(Y) closed
>
No reason, except maybe historical.  It works just as well.

Richard Pinch
Date: Monday, 9 Nov 1992 16:58:08 EST
From: <RVESTERM@vma.cc.nd.edu>
Newsgroups: sci.math
Subject: Re: 4x4 matrix

forget about the "formula" to invert a 4x4 matrix, as opposed to the
"formula" to invert a 3x3 matrix, or whatever.  a much easier way to
invert a square matrix of any size (say nxn) is the following:

1) using elementary row operations, reduce the matrix in question
   to the nxn identity matrix.

2) use the same elementary row operations, in the same order, on
   the nxn identity matrix.

the resulting matrix will be the inverse of the matrix you started
with.

bob vesterman.


Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Mercator Projection
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Tue, 10 Nov 92 03:10:43 GMT

In article <1992Nov8.214329.27209@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>In article <israel.721212129@unixg.ubc.ca> israel@unixg.ubc.ca (Robert B. Israel) writes:
>>In <a34uTB4w165w@netlink.cts.com> kfree@netlink.cts.com (Kenneth Freeman) writes:
>>
>>>My Mercator projection goes 'up' to only 84 degrees, ~the northern
>>>tip of the classically huge Greenland. I'd like to know three things.
>>>1) For a given area, what is its apparent increase in size for a 
>>>given latitude? I.e., what is the rate of increase the closer you
>>>get a pole (and infinity)?
>>
>>At latitude t, linear dimensions are multiplied by sec(t), so areas are
>>multiplied by sec^2(t).
>
>Turns out if you try to calculate this using the 1986 Encyclopedia
>Britannica you get sec^3(t).  The reason is that EB defines the
>Mercator Projection to be the result of projecting the globe from its
>center onto the cylinder tangent to the equator.  If this were true the
>vertical direction would scale not by sec(t) but by the derivative of
>tan(t), namely sec^2(t).

Okay, great, so I'm not utterly out of it.  But if lengths scale by
sec^2(t) then areas scale by sec^4(t), not sec^3(t) -- by conformality,
as you note.

>1.  What is the weakest condition required in addition to conformality
>to uniquely determine the Mercator projection up to dilatation?

This is a nice question.  Given two conformal maps from the sphere with
north and south pole removed to the cylinder, we can compose one with the
inverse of the other to get a conformal map from the sphere minus 2
points to itself.  What are the choices?  I just see a 2-parameter group
of these, a subgroup of SU(1,1) (which acts as conformal transformations
of S^2) - but could there be more that don't extend to S^2?  Over in
"Mercator projection space" (= the cylinder) this 2-parameter group
corresponds to north-south translations and east-west rotations.  No
dilations arise in my way of formulating the problem because I am taking
the range of the Mercator projection to be the cylinder, which admits no
dilations.
From: kosowsky@phoneme.harvard.edu (Jeffrey J. Kosowsky)
Newsgroups: sci.math
Subject: Re: Bozos Synonymous
Date: 13 Nov 92 18:31:02 GMT
Article-I.D.: phoneme.KOSOWSKY.92Nov13133102
	<1992Nov13.121426.13419@wraxall.inmos.co.uk>
Organization: Harvard Robotics Lab, Harvard University

In article <1992Nov13.121426.13419@wraxall.inmos.co.uk> cath@dyrham.inmos.co.uk (Catherine Barnaby) writes:
>   Crop circles are not new, they have been noted way back, but
>   are only "trendy" recently. They are also a lot more common
>   than they used to be. There is a physicist who has done a lot
>   of work on them, and believes them to be due to the effects of
>   wind. There are lots of people who wander round with dousing 
>   rods twitching, and others who feel the energies and colours
>   (not sure of the collective here). There are also a 
>   number of people who go round faking them, and farmers who
>   make quite a bit of money charging #1 a person to go into 
>   their field if it has one. 
>

Talking about making money from "crop circles"...
Here at Harvard, I have seen numerous posters plastered on bulletin
boards throughout the campus advertising the following:

				Crop Circle
			  Lecture / Slide Show
			 with George Wingfield
			Director, Field Research
		Center for Crop Circle Studies, Somerset England

The event is *not* being held on camput but rather at a local church.
Furthermore, they are *charging* 10 dollars a ticket!

Who is this most Bozo of Bozos who can command 10 dollars for the
chance to hear him drivel psycho-pseudo-science. Also what is this
so-called "Center for Crop Circle Studies?" 
Do they have any openings for post-docs or for junior faculty tenure
track positions? :.)


Jeff Kosowsky
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
From: mkrogers@unix.amherst.edu (MICHAEL K ROGERS)
Newsgroups: sci.math
Subject: Re: FREE-ENERGY TECHNOLOGY
Date: 5 Nov 92 15:41:11 GMT
Organization: Amherst College
X-Newsreader: TIN [version 1.1 PL6]

mcelwre@cnsvax.uwec.edu wrote:
:             
:                             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. 
:           
:           [...]
:           
:                Fortunately, a few SMART people such as the Wright 
:           Brothers did NOT accept such pronouncements as the final 
:           word....

Perhaps they had heavier-than-air birds in their neighborhood.
Newsgroups: sci.math
From: frank@Cookie.secapl.com (Frank Adams)
Subject: Re: A REAL 3-sided coin
Date: Thu, 12 Nov 1992 20:13:50 GMT
Organization: Security APL, Inc.

In article <bern.721578576@kleopatra> bern@Uni-Trier.DE (Jochen Bern) writes:
>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.

The 100-sided "dice" available are just spheres with 100 flat "indentations"
spread roughly evenly around the surface.  It is not at all clear that they
really give each result with the same probability.  I wouldn't use them.
Xref: sparky sci.math:14739 sci.physics:18643 sci.astro:11850 sci.bio:4098 sci.chem:4510 misc.education:4236
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Subject: Re: Is Math Hard?
From: marder@agri.huji.ac.il
Date: 10 Nov 92 09:37:51 IST
 <00721013472@elgamy.uucp.taronga.com> <BxB3B6.417@mentor.cc.purdue.edu> <1992Nov7.184203.1496@allegra.att.com>
Distribution: world
Organization: The Hebrew University of Jerusalem - Faculty of Agriculture

In article <1992Nov7.184203.1496@allegra.att.com>, rfc@allegra.att.com (Robert F. Casey) writes:
[ . . . ]

> One time I visited a friend who had a young kid, about 4 to 5 years old,
> and the kid was learning to count and such.  My friend asked questions
> like "How many hands do you have? feet? noses?  Could be memorized responses
> for answers, so I asked "How many tails do you have?"  kid:"Ahhh...
> none! zero!"  He had to think a little for that one, probably noone ever
> asked that question before.  Then "How many fingers?  Thumbs?"  "OK,
> how many fingers do you have that are not thumbs?"  kid: "Ahh.. 10?"
> looks at hands "no, ahhh.. 1,2,3,4,5,6,7,8 eight."  Another wierd
> question!
That reminds me the time that I asked my 3-year-old daughter how many legs
we have in our family.  She couldn't answer until my wife came out of the
shower! (3 years later this is still a family joke).  Actually, I am
constantly surprised about my daughter's (now 6) capacity for abstraction.
The other day while I was lying down, she wanted to play noughts and
crosses (tic-tac-toe).  Instead of opening my eyes, I suggested we play by
grid references (A1, B2, C3 etc.).  She has learned the concept of grid
references before, but what really surprised me was that she was clearly
quite able to play the game without any visual aid!
  Unfortunately, I am not a math teacher, but this incident taught me an
excellent way to test kids for their grasp of grid co-ordinates!

--
                                 '      Jonathan B. Marder
Internet: MARDER@AGRI.HUJI.AC.IL |      Department of Agricultural Botany
Bitnet:   MARDER@HUJIAGRI        | /\/  The Hebrew University of Jerusalem
Phone:    (08 or +9728) 481918   |/  \  Faculty of Agriculture
Fax:      (08 or +9728) 467763   /      P.O.Box 12, Rehovot 76100, ISRAEL
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math
Subject: Gauss (was: Erdos number
Date: 13 Nov 1992 15:44:47 -0500
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu


>Here's another question I've always wondered about:  what is Gauss's Erdos
>number?
>
>It certainly makes sense to ask such a question, since coauthorship can
>extend into the past as well as the future.  The answer might be trivial,
>because it is my __impression__ that coauthorship was rare until relatively
>recently.  Does anyone know offhand whether Gauss ever coauthored a paper?
>(For that matter, where can one find a list of his publications?  Relatively
>short, given his motto.)

His collected works, apparently 12 volumes, although some of the "volumes"
are bound in more than one physical book.

Gauss, Carl Friedrich,  1777-1855.
  Carl Friedrich Gauss Werke ... Herausgegeben von der K. Gesellschaft der
Wissenschaften zu G?ottingen.  [G?ottingen,  Gedruckt in der Dieterichschen
Universit?atsdruckerei (W.F. Kaestner)]  1870-19  v.  tables, diagrs.  28 x 23
cm.




-- 
  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)
From: torbenm@diku.dk (Torben AEgidius Mogensen)
Newsgroups: sci.math
Subject: Re: To express Q(x)/P(x) into continued fraction
Date: 5 Nov 92 13:14:33 GMT
Organization: Department of Computer Science, U of Copenhagen

jchen@sct.gu.edu.au (Jinghong CHEN) writes:


>Suppose there are two n-th order polynomials Q(x) and P(x), how can we
>express Q(x)/P(x) into a continued fraction, i.e.

>      Q(x)             a0
>     ------ = ----------------------
>      P(x)                a1
>               x + -----------------
>                                an
>                    x + ... + ------
>                               x + a

Normally, a continued fraction has the form

a0 + 1
    ------------
    a1 + 1
	--------
	a2 + 1
	    ----
	    ...
	      --
	      an

where the ai are polynomia in x.

We need not even assume that P and Q have the same order. I assume
that you are familiar with the standard polynomial division algorithm,
and is able to find the quotient and remainder polynomia. That is,
find K(x) and R(x), such that

	Q(x)/P(x) = K(x) + R(x)/P(x)

where R has a strictly lower order than P.

K(x) is the first term (a0) of the continued fraction. The remaining
terms are found by letting a1,... be the continued fraction of
P(x)/R(x).

Example:

consider Q(x)=2x^3+x^2-3x+1, P(x)=x^3-2x^2-x-4

By normal division we get

K(x) = 2, R(x) = 5x^2-x+9

so a0 = 2. Now we try P(x)/R(x), ad get

K'(x) = (1/5)x+(11/25), R'(x) = (-1/5)x-199/25

so a1 = (1/5)x+(11/25). Doing R(x)/R'(x) we get

K''(x) = -25x+1000, R''(x) = 3969

Now we only need to do R'(x)/R''(x) = (-1/19845)x-199/92400

Thus our complete continued fraction is

	Q(x)	    1
	---- = 2 + ------------------------------------------------
	P(x)	   (1/5)x+(11/25) + 1
				   --------------------------------
				   -25x+1000 + 1
					      ---------------------
					      (-1/19845)x-199/92400


All but the first term is guaranteed to have an order of at least 1.
All quotients of polynomia have finite continud fractions, with n+1
terms (a0,...,an), where n is the order of the polynomium. I think all
C-infinity functions can be written as a (possibly infinite) continous
fraction.

	Torben Mogensen (torbenm@diku.dk)

P.S.
There is probably a method for constructing a fraction of the form you
memtioned.
From: dchatterjee@kuhub.cc.ukans.edu
Newsgroups: sci.math
Subject: Re: What is catastrophe theory?
Date: 11 Nov 92 21:39:05 CST
Organization: University of Kansas Academic Computing Services

In article <1992Nov11.180552.14797@progress.com>, neil@progress.COM (Neil Galarneau) writes:
> I have heard of something called catastrophe theory.
> 
> I am looking for recommendations on articles/books (in English!) readable by a
> non-math major.
> 
> 
> Thanks!
> 
> Neil
> neil@progress.com

 To answer this question, I would suggest ask John Baez. My two penny opinion
 is that catastrophe theory is "something" very advanced in mathematics - 1st
 conceived by Zeeman - followed by Tim Poston and others. Most recently, in
 England, Michael V.Berry is doing work in catastrophe theory. 

 A catastrophe is something like caustics in optics. Evaluation of the e.m
 field at such locations, at  very high frequencies, requires computation
 of integrals that have confluence of severally coincident saddle-points.
 Berry's recent and very useful work is focussed in this area.

 But, then attempting to explain catastrophe theory physically, is probably
 not possible other than citing a few well-known examples, IMO.

 - dc
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: FREE-MONEY TECHNOLOGY
Date: 5 Nov 92 21:04:01 GMT
Article-I.D.: master.1dc281INNj4q
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Organization: Computer Science Department at Rose-Hulman
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu



         FREE-MONEY TECHNOLOGY

They laughed at the Wright Brothers. They laughed at Dr. Joyce  
Brothers. They laughed at the Smothers Brothers.  But WHERE DID IT GET  
THEM?

I am on the verge of inventing a maching which prints money.  For a  
small investment, any impoverished family could purchace one of my  
machines and be SUDDENLY WEALTHY.  The new type of science I have  
discovered allows me to exploit never-before-known principles of  
economics so that the printing of my specially treated money DOES NOT  
CAUSE RUN-AWAY INFLATION!!!  The secret is the newly discovered  
"SILVERMAN" principle which makes this problem TRIVIAL to solve.  My  
new machine (a "clinton-o-matic") will enable the most down and out  
street bum to afford the best in health care and still have enough to  
stay soundly drunk for the rest of his life.  

The last few bugs are being worked out NOW.  Success is imminent.   
Quickly turn all your grant money over to me, so I can finish my  
research before I am denied tenure by this short-sighted, earth-bound  
administration.

Send small bills via FAX or e-mail to

			GOD-CO
			c/o Bart GODdard
			At the obvious place.

Barbie is a hard wood duck, God exists in this universe and you're all
against me.


PS :-)
Organization: School of Computer Science, Carnegie Mellon, Pittsburgh, PA
Newsgroups: sci.math
Date: Wed, 11 Nov 1992 23:41:01 -0500 
From: Andrew Lewis Tepper <at15+@andrew.cmu.edu>
Subject: Polygon Coloring

  I know that there must be a fast algorithm for coloring irregular
polygons, but I can't seem to figure it out. I did come up with a slow
algorithm (unimplemented, and unproven) which is as follows:

Call the vertices in the polygon V0,V1,...,Vn where V0==Vn
For each point P in the rectangle that encloses the polygon:
  List the angles formed by Vx \ P \ Vx+1 for 0<=x<=n. Express
  all angles in the range -PI < angle < PI. (If angle==PI, it's
  a boundary point.)
Add the list of numbers. If they add to 0, the point is outside the
polygon. Otherwise it's inside.

Certainly there are optimizations; the easiest would be to plot the
polygon, run the algorithm for one point, and do a seed fill for the
rest. Is there a more elegant/faster algorithm than this? I want to do
high speed graphics with this...

Andy