HDTenEightyP/NetNews huggingface dataset:
Newsgroups: sci.math,sci.physics
Subject: Vectors Question
From: <A54SI@CUNYVM.BITNET>
Date: Monday, 25 Jan 1993 22:31:36 EST
Organization: City University of New York/ University Computer Center

I'm reading Principles of Electrodynamics by Schwartz. In it he discusses
 two types of vectors, polar (where the components negate under pure
 reflective transformation) and axial (where the components are invariant
 for pure reflective transformations).

Either my thinking is wrong or he contradicts himself :

Let us set c = a cross b. In my mind, if a and b are both polar or they are
 both axial then c is axial. I do this by picturing reflections performed on
 the vectors, and I am fairly certain of this result. If we try to cross two
 vectors of different types, then the c vectors before and after the
 reflection (c and c') differ in magnitude as well as direction and so
 I feel that it's impossible to cross different type vectors. Be that as it
 it may you won't get a polar vector by crossing a polar with and axial
 (Unless my mental pictures are totally wrong.)

From Coulomb's law he gets that force is a polar vector. Fine.

Now from magnetism we know that force F = qv cross B. Velocity v is polar.
 He's already assumed that charge q is scalar (totally invariant). From all
 this he thinks this tells us that B is axial!

So my question is, how is he crossing a polar with an axial and getting a
 polar vector??
-------
CHARLES HOPE   A54SI@CUNYVM   A54SI@CUNYVM.CUNY.EDU
GOVERNMENT BY REPORTERS...MEDIA-OCRACY.
From: bennett@math.ksu.edu (Andy Bennett)
Newsgroups: sci.math
Subject: Re: Ancient Number Systems (Was: why is pi irrational)
Date: 24 Jan 1993 00:14:27 -0600
Organization: Dept. of Mathematics, Kansas State University
NNTP-Posting-Host: hilbert.math.ksu.edu

fc03@ns1.cc.lehigh.edu (Frederick W. Chapman) writes:
>I've heard that letters of the Hebrew alphabet all have numerical
>equivalents, which were used in ancient scriptures as the basis of a number
>system.  I would be interested in knowing more about this, since it must
>surely qualify as a very early example of a number system.  Doesn't some
>ambiguity occasionally arise as to whether a given string of characters
>should be interpreted as a word or as a numerical quantity?  
>Didn't classical Greek also assign numerical values to the letters of the
>alphabet and employ a similar number system?  (For example, there is a New
>Testament passage that speaks of "the *number* of his name" in reference to
>the anti-Christ.)

Classical Greek used the letters of the Greek alphabet for numbers.
alpha = 1
beta = 2
gamma = 3
delta = 4
epsilon = 5
digamma = 6
zeta = 7
eta = 8
theta = 9
iota = 10
kappa = 20
...
sampi = 900

You may have noticed digamma and sampi in the above list. They, along with
qoph, dropped out of the Greek alphabet after it was borrowed from the
Phoenicians because the Greeks didn't need them for the language, but they
kept them for the number system where they were useful. Numbers bigger than
1000 start with alpha again. In modern texts of classical greek, diacritical
marks are used to distinguish between alpha 1 and alpha 1000 and also between
letters that make up a number as opposed to a word. I don't know for sure
if such marks appear in the actual classical texts (though my guess would
be not). Since both Hebrew and Greek borrowed their alphabets from the
Phoenicians and both used the letters for numbers, I would suspect that
the idea originated with the Phoenicians, but I've never been curious enough
to do a literature search and find out. As far as being among the oldest
number systems, the Babylonians had a place value system (base 60) with
a fair knowledge of algebra by 1800BC, well before the Greeks adopt their
alphabet (I'm not sure about dates on the Hebrews or Phoenicians). Denise
Schmandt-Besserat has done a lot of work on the origins of the Babylonian
system tracing it back to 8000BC (though in such a primitive form at that
date that I wouldn't call it a number system and neither would she). She 
wrote an article for Scientific American some 10-15 years ago that gives
a nice overview without requiring much background.

-- 
Andrew G. Bennett         bennett@math.ksu.edu         If you count too
Dept. of Mathematics      Voice: (913) 532-6750        much you turn
Kansas State University   Fax:   (913) 532-7004        purple.  -  SARAH
Manhattan, KS 66502       STRICTLY MY OWN OPINIONS                    
Newsgroups: sci.math
From: kwhyte@arcana.uchicago.edu (Kevin Whyte)
Subject: Re: request for info on game theory
Organization: Dept. of Mathematics, U. of Chicago
Date: Mon, 25 Jan 1993 20:06:59 GMT

In article <1993Jan23.212705.287@ctsx.celtech.com> davidd@ctsx.celtech.com (davidd) writes:
>
>Hello, I'm a new reader to this news group and was wondering if
>anyone could offer any advice. For some years now I've had
>various ideas for a computer/board game. In a nutshell, (in the
>computer version) you would play against a autonomous agent. (no,
>not a shoot them up thing) Anyway I was talking to a friend over
>lunch the other day and was babbling incoherently about some of
>my ideas and she was wondering what game theory books I had
>studied or used. I hadn't. I didn't really know anything about game theory
>as such so I thought I'd better look into it. If anyone could
>offer any recommondations, I'd appreciate it. Hmmm, just a
>thought, perhaps should I be looking for any relevent AI
>book...??? Thanks for your time and help.
>
>David


   You might try "Winning Ways" by Berlekamp, Conway, and Guy.  You
want to be somewhat careful, as "game theory" has a very precise meaning.
The games studied in "Winning Ways" are akin to Chess, Go, TicTacToe, etc.
(i.e. deterministic, finite, perfect information).  "Game theory" studies
probabilistic strategies for games without perfect information, but with
perfect understanding of all the outcomes: i.e. games which would be
trivial if you knew what your opponent was going to do.  

  Kevin


We are faced with the very real possibility that "digital" and 
"manual" will be used as antonyms.
Newsgroups: sci.math
From: wft@math.canterbury.ac.nz (Bill Taylor)
Subject: Re: Bishop against God
Organization: Department of Mathematics, University of Canterbury
Date: Thu, 21 Jan 1993 23:16:28 GMT

|> 	                         If God has mathematics
|> 	of his own that needs to be done, let him do it
|> 	himself."
|> 
|> 			-- Bishop

I've always thought this was a fun quote !

This is from Bishop's "Foundations of Constructive Analysis", a very sound
and solid attempt to re-present *undergraduate* mathematics from a strictly
constructivist point of view; surely a worthwhile endeavor.

I seem to recall that Bishop (or his supporters) claim that his approach is
in some sense a *minimalist* constructivist attitude, as distinct from
"classical" Brouwerian intuitionism, or Russian constructivism, both of
which make extra assumptions or introduce concepts unacceptable to either
orthodox math or Bishop's minimalism.

Bishop claims that all his results would be acceptable to *all* three other
viewpoints; orthodox, Brouwerian, Russian.

This is probably true, but he sprinkles remarks (like the jewell above)
throughout his text, that suggest his basic viewpoint is quite otherwise.


Here is another provocative anti-orthodox opinion, (page 26),

"Since nothing is true unless and until it has been proved...."


And here is an anti-intuistionist pearl...

"In Brouwer's case there seems to have been a nagging suspicion that unless he
personally intervened to prevent it the continuum would turn out to be discrete" 

Award winning !!

------------------------------------------------------------------------------
              Bill Taylor              wft@math.canterbury.ac.nz
------------------------------------------------------------------------------
             It's a Kleene machine...  ("Penny Lane", the Beatles)

                      Kleeneness is next to Godelness.
------------------------------------------------------------------------------
Newsgroups: sci.math,sci.math.symbolic
From: hdev@dutiai.tudelft.nl (Hans de Vreught)
Subject: Re: Which CAS have BA's in math?
Organization: Delft University of Technology
Distribution: sci
Date: Fri, 22 Jan 1993 11:51:17 GMT

rivin@SAIL.Stanford.EDU (Igor Rivin) writes:

>(b) Major point: Their work is very interesting, but if you did your
>exams with as much help as their system (or any theorem proving
>system, for that matter) gets, you would get kicked out of school
>pronto for plagiarism.

Not entirely true: plagiarism is the use of text *without* permission of the
authors. You can't plagiarise with permission. Fraud is the more likely reason
why they would be ousted.

--
Hans de Vreught                          | John von Neumann:
hdev@dutiba.twi.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.
Newsgroups: sci.math
From: davidd@ctsx.celtech.com (davidd)
Subject: request for info on game theory
Date: Sat, 23 Jan 1993 21:27:05 GMT
Organization: Cellular Technical Services, Seattle


Hello, I'm a new reader to this news group and was wondering if
anyone could offer any advice. For some years now I've had
various ideas for a computer/board game. In a nutshell, (in the
computer version) you would play against a autonomous agent. (no,
not a shoot them up thing) Anyway I was talking to a friend over
lunch the other day and was babbling incoherently about some of
my ideas and she was wondering what game theory books I had
studied or used. I hadn't. I didn't really know anything about game theory
as such so I thought I'd better look into it. If anyone could
offer any recommondations, I'd appreciate it. Hmmm, just a
thought, perhaps should I be looking for any relevent AI
book...??? Thanks for your time and help.

David

-- 
    ___   ____   ____    David Doll                   |
   /       /    /___     Cellular Technical Services  | davidd@celtech.com
  /___    /    ____/     2401 4th Ave., Suite 808     |         -or-
                         Seattle, WA 98121            |   uunet!ctsx!davidd
From: dezan@enstb.enst-bretagne.fr (Catherine Dezan)
Newsgroups: sci.math
Subject: looking for an algorithm
Keywords: geometry
Date: 26 Jan 93 11:17:47 GMT
Reply-To: dezan@enstb.enst-bretagne.fr
Organization: Ecole Nationale Superieure des Telecommunications de Bretagne, Brest  FRANCE

I am looking for an algorithm which can separate n convex polyhedral domains
(each one from others) with a minimal number of hyperplans.
Does such an algorithm exist?
What about its complexity?

I thank you very much in advance for any information.

Catherine Dezan.

email: dezan@enstb.enst-bretagne.fr
From: system@kalki33.lakes.trenton.sc.us (Kalki Dasa)
Newsgroups: sci.math
Subject: Re: Bishop against God
Date: Thu, 21 Jan 93 19:42:01 EST
Organization: Kalki's Infoline BBS, Aiken, SC, USA

solan@smaug.uio.no (Svein Olav G. Nyberg) writes:

> I found the following beautiful quote:
> 
>        "Mathematics belong to man, not to God. We are not
> 	interested in the proiperties of the positive
> 	integers that have no describtive meaning for man.
> 	When a man proves a positive integer to exist, he
> 	should show how to find it. If God has mathematics
> 	of his own that needs to be done, let him do it
> 	himself."

Beautiful to some, but self-contradictory to me:

 "Mathematics belong to man, not to God."

 followed by

 "If God has mathematics of His own..."

Well, which is it?

Sincerely,
Kalki Dasa


       ---------------------------------------------------------
      |                Don't forget to chant:                   |
      |                                                         |
      |  Hare Krishna Hare Krishna, Krishna Krishna Hare Hare   |
      |       Hare Rama Hare Rama, Rama Rama Hare Hare          |
      |                                                         |
      |    Kalki's Infoline BBS Aiken, South Carolina, USA      |
      |           (kalki@kalki33.lakes.trenton.sc.us)           |
       ---------------------------------------------------------
From: scavo@cie.uoregon.edu (Tom Scavo)
Newsgroups: sci.math
Subject: Re: Plotting Graphs
Date: 27 Jan 1993 08:26:03 GMT
Organization: University of Oregon Campus Information Exchange
Distribution: world
NNTP-Posting-Host: cie.uoregon.edu

In article <1k3faeINNl3t@urmel.informatik.rwth-aachen.de> Josef Goettgens <jg@techmech.itme.rwth-aachen.de> writes:
>Does anybody know about programs that layout and plot graphs and run
>on small machines (e.g. Mac)?

If what you want is typeset-quality PostScript images for inclusion
in, say, a LaTeX document, then try PSMathGraphsII by Mary Ann Soft-
ware (P.O. Box 6252, San Rafael, CA, 94903-0252).  Costs $80 I think,
and worth every penny...

-- 
Tom Scavo
scavo@cie.uoregon.edu
Newsgroups: sci.math
From: orourke@sophia.smith.edu (Joseph O'Rourke)
Subject: Re: pyramid volume
Organization: Smith College, Northampton, MA, US
Date: Fri, 22 Jan 1993 20:17:30 GMT

In article <1993Jan21.173423.11339@sophia.smith.edu> I wrote:
>[...] a unit-height triangular prism, the convex hull of 
>		000, 100, 010, 
>		001, 101, 011,
>where "000" means "(0,0,0)" etc.  [...]
>Now partition the prism into three right tetrahedra, the hulls of
>		T1: 000, 100, 010, 001;
>		T2: 001, 101, 011, 100;
>		T3: 000, 001, 011, 100.
>[...]	Since these three are congruent, each has volume V/3.
	                      ^^^^^^^^^
Nick Haines (nickh@cmu.edu) pointed out to me that these are *not*
congruent, although they all have congruent bases and the same height.
Thus one needs the fact that two tetrahedra with congruent bases
and the same height have the same volume.  Euclid establishes a
stronger version of this in XII.5.
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: linear algebra problem
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Sun, 24 Jan 93 02:58:31 GMT

Someone once told me about the solution to the following problem.
Given two finite-dimensional vector spaces (over the complex numbers,
say) X and Y, classify all *pairs* of linear maps S,T: X -> Y up
to transformations of the pair (S,T) -> (gSh, gTh) where g and h are
invertible linear transformations of Y and X respectively.  Does
anyone recall the history of this problem and what its solution is?
From: wilson@web.ctron.com (David Wilson)
Newsgroups: sci.math
Subject: Re: Question about Prime Numbers
Date: 25 Jan 93 14:14:54 GMT
Reply-To: wilson@web.ctron.com (David Wilson)
Organization: Cabletron Systems INc.
Originator: wilson@web


    The problem is to find large integers x such that every positive-
    length prefix of the base-10 representation of x is the base-10
    representation of a prime number.

    It turns out that there are five 8-digit numbers satisfying the
    conditions.  They are 73939133, 59393339, 37337999, 29399999, and
    23399339.  No larger numbers satisfy the conditions.

    If we accept 1 as prime, then the 10-digit numbers 1979339339 and
    1979339333 are the largest satisfying the conditions.  If we lift
    the primality condition altogether on the first digit, then these
    two numbers are still the largest satisfying the conditions.

    If we lift the primality restriction on the first two digits, then
    x = 4099339193933, alone among 13-digit numbers.  If we lift the
    primality restriction on the first three digits, then x =
    1009993997993 suffices as well.

				----<>----   

    As a teaser, if we replace "prime number" with "sum of two squares"
    in the original problem, it becomes much less tractable.


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

Disclaimer: "Truth is just truth...You can't have opinions about truth."
- Peter Schikele, introduction to P.D.Q. Bach's oratorio "The Seasonings."
From: kim_sh@jhunix.hcf.jhu.edu (Sung Hyun Kim)
Newsgroups: sci.math
Subject: Re: request for info on game theory
Date: 25 Jan 1993 11:10:57 -0500
Organization: Homewood Academic Computing, Johns Hopkins University, Baltimore, Md, USA
NNTP-Posting-Host: jhunix.hcf.jhu.edu

In article <1993Jan23.212705.287@ctsx.celtech.com> davidd@ctsx.celtech.com (davidd) writes:
>
>Hello, I'm a new reader to this news group and was wondering if
>anyone could offer any advice. For some years now I've had
>various ideas for a computer/board game. In a nutshell, (in the
>

Since I am not sure whether you know what *game* means in general in game
theory, I would recommend a very elementary book..
 Dixit and Nalebuff, Thinking Strategically.  This is very recent book and
not very mathematical, but gives enough *strategic* flavor.
Also you may want to look up some game theory books from computer science or
mathematics..

>    ___   ____   ____    David Doll                   |
>   /       /    /___     Cellular Technical Services  | davidd@celtech.com

-- 
 Sung Hyun Kim    kim_sh@jhunix.hcf.jhu.edu : Economics, Johns Hopkins U.
From: mckay@alcor.concordia.ca (John McKay)
Newsgroups: sci.math
Subject: > Fields Medallists ...
Date: 26 Jan 93 12:20:09 GMT
Organization: Concordia University, Montreal, Quebec
Originator: mckay@alcor.concordia.ca


Bott studied Electrical Engineering at McGill then went to Cornell.
Harold Davenport supervised both Roth and Alan Baker. They both got
their Fields medals for work in the same area - diophantine approximation.
Roth proved that there are only finitely many rational numbers p/q
such that abs(a - p/q) < 1/(q^(2+epsilon)) for a = algebraic of degree
n > 2 and arbitrarily small epsilon > 0.
Baker gave lower bounds for linear forms in logarithms of algebraic
numbers. This is applicable to many diophantine equations. He proved
that there are effectively computable numbers bounding the size of
solutions to many diophantine problems: one example easy to comprehend
is: Can we extend the sequence 1,3,8,120 of non-zero integers such that
the product of any two members of the sequence is one less than a square?
Baker stated, and others verified, that his method was practicable and
could be used with a computer to find all solutions.
From: gore@pepper.rutgers.edu (Bittu)
Newsgroups: sci.math
Subject: Re: Matrices (problem)
Keywords: Rank
Date: 26 Jan 93 17:43:26 GMT
Organization: Recreation Center, Busch Campus

In article <1993Jan25.154208.16365@CSD-NewsHost.Stanford.EDU* rivin@SAIL.Stanford.EDU (Igor Rivin) writes:

* In article <Jan.24.22.14.31.1993.13572@inferno.rutgers.edu* gore@inferno.rutgers.edu (Bittu) writes:
* >A simple question about the rank of a special matrix (this is not a
* >homework problem; I already know a solution, want something better).
* >In fact, this was probably on the Math Olympiad a few years ago.
* >
* >Let A be a matrix with the following properties:
* >
* >1. A is 2n+1 x 2n+1 for a positive integer n.
* >
* >2. A has 0's on the diagonal.
* >
* >3. The remaining entries are either 1's or -1's.
* >
* >4. Every row has exactly n 1's and n -1's.
* >
* >We want to show that the rank of this matrix is 2n (over complex
* >numbers, say). Clearly the rank is <= 2n (all columns sum to the zero
* >vector). 
* 
* It is not clear that the below is any more elegant than the GF[2]
* solution, but here goes (m=2n+1):
* 
* (a) The question is equivalent to showing that the null-space of A is
* generated by the vector (1, ... ,1)
* 
* (b) Which is equivalent to showing that there is no null-vector v of
* A, such that the sum of elements of v adds up to 0.
* 
* (c) suppose there is such a vector V -- it is easy to see that it must
* also be a null vector of the matrix B which has 0s on the main
* diagonal, and 1s elsewhere (do it row by row).

This is not clear to me. If the entries of V add up to 0, then BV = -V
and not 0 as you mention. If the entries of V are v(1),v(2),...,v(2n+1) 
then the product of the ith row of B with V would be 
v(1) + v(2) + ... + v(i-1) + v(i+1) + ... + v(2n+1) = -v(i). Therefore
BV =/= 0.

--Bittu

* (d) B = -I(m) + J(m), where J has all ones. J(m) vanishes on the
* orthogonal complement of the vector w=(1, ... ,1), and multiplies w by
* m. hence the eigenvalues of B are (n-1, -1, ..., -1), hence it is
* non-singular, hence V is the 0 vector, hence w is the only null-vector
* of A, hence A has rank m-1 = 2n.
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: New electronic math journal (Was: Re: sci.math.* groups)
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Mon, 25 Jan 93 17:54:26 GMT

Carol Hutchins writes:
>sitarama@cps.msu.edu (Kocherlakota Sitarama) writes:
>
>>Okay, after getting lot of thoughts on sci.math.*, I think, I got
>>a good solution. Let us take the top, say 6, math journals and give a 
>>news group which coveres more or less what the journal covers.
>
> 	Please let me know once you come to a consensus
>on which 6 are the "top math journals".

I.e., never.  On a slightly related note...

The future, long delayed, finally seems to be coming.  There is a new math
journal, the Ulam Quarterly, that is available FREE online in either
AMS-TeX or Postscript form.  This wonderful idea is due to the math
department of Palm Beach Atlantic College, with support from the
University of Florida.  Kind of ironic how such a smart move is being
made, not by the hidebound Ivy League schools, but this school I'd never
heard of.   (Sorry, Palm Beach Atlantic College!  I've heard of you
now!)  "The first two issues include a significant and unpublished work
of N. Jacobson and an interpreation of Grothendieck's prenotes for EGA V
on Bertini type theorems.  The Ulam Quarterly is available using
anonymous FTP from math.ufl.edu or goliath.pbac.edu in the directory
pub/ulam/volume1.  For more information contact Piotr Blass,
blass@goliath.pbac.edu."  

I hope this journal is received enthusiastically and I hope everyone
helps popularize this kind of journal, which may put pressure on paper
journals to reduce their prices.


Newsgroups: sci.math,sci.math.num-analysis
From: dsacher@ravel.udel.edu (Dick Sacher)
Subject: Geometer's Sketchpad
Followup-To:  sci.math
Summary: Looking for Geometer's Sketchpad
Keywords:  software Geometer's Sketchpad
Organization: University of Delaware
Date: Fri, 22 Jan 1993 22:06:21 GMT


Does anyone have any information on the program Geometer's Sketchpad,,
such as how to obtain a copy?   Thanks for your help.

	Dick Sacher (dsacher@sloth.cns.udel.edu)
	University of Delaware
Newsgroups: sci.math
From: orourke@sophia.smith.edu (Joseph O'Rourke)
Subject: Re: pyramid volume
Organization: Smith College, Northampton, MA, US
Date: Thu, 21 Jan 1993 17:34:23 GMT

In article <1993Jan21.140402.25519@mr.med.ge.com> carl@crazyman.med.ge.com (Carl Crawford) writes:
>
>how do show that the volume of a pyramid is 
>
>	1/3 * area of base * altitude 
>	
>without using calculus?

Nice question!  Although I don't have an answer, I would like to
make an observation:  three identical tetrahedra pack half a cube.
	Take the unit cube 
		0 <= x <= 1
		0 <= y <= 1
		0 <= z <= 1
and intersect it with the halfspace x+y <= 1.  The result is a 
unit-height triangular prism, the convex hull of 
		000, 100, 010, 
		001, 101, 011,
where "000" means "(0,0,0)" etc.  Suppose you believe the volume of
this is V = A * h = A, where A is the base area and h=1 the height.
Now partition the prism into three right tetrahedra, the hulls of
		T1: 000, 100, 010, 001;
		T2: 001, 101, 011, 100;
		T3: 000, 001, 011, 100.
T1 has base A on the plane z=0, and height 1;
T2 has base A on the plane z=1, and height 1;
T3 has base A on the plane x=0, and height 1.
	Since these three are congruent, each has volume V/3.
I looked for this construction in several books without luck.