HDTenEightyP/NetNews huggingface dataset:
From: dbush@csugrad.cs.vt.edu (David Bush)
Newsgroups: sci.math
Subject: the uniqueness of 11,356
Summary: The infinite z-list has only one ending in a 6.
Keywords: number theory z-list
Date: 12 Oct 92 17:48:00 GMT
Organization: Virginia Tech Computer Science Dept, Blacksburg, VA


   Here's a curious sidepath in number theory, based on an
old "problematical recreations" puzzle from Litton Industries.
In the game "subtract-a-square," a natural number is written
down and two players alternate moves. A move consists of
subtracting a nonzero square from the current value, producing
a new current value for the other player. You may not subtract
more than the current value. The player who reaches 0 wins.
For example, 1 is a winning value because having this value on
your move means you can win the game. In fact, from 1 you can
win in 1 move by subtracting 1. 2, on the other hand, is a
"zugzwang value," or z-value, because no matter what move you
make, your opponent will be left with a winning value. In fact
the only legal move from 2 is to subtract 1 leaving 1 for the 
other player. Every natural number is either a winning value
or a z-value, but never both. Zugzwang is a chess term
indicating a position wherein the obligation to move is a
disadvantage. The z-list, or the set of all z-values, can be
generated by these production rules:

  1. 0 is the first z-value. (This simplifies matters.)
  2. Given that you have a list of all z-values less than n,
     n is a winning
     value IF AND ONLY IF it is greater than some z-value on
                          the list by a nonzero square.
           OTHERWISE, n must be a z-value.

    Out of all the over 180,000 z-values less than 40 million,
ONLY ONE z-value ends in a 6: 11,356. Z-values that end in 1,
3, or 8 are also few and far between. I suspect the set of
all z-values that = 1(mod 5) or 3(mod 5) is finite. Perhaps
this has something to do with the fact that both 5 and 10 can
be expressed as the sum of 2 different squares. A cursory
statistical analysis of the distribution of z-values with
respect to other modulus bases seems to corroborate this.
Modulus bases 13 and 17, which can also be expressed as the
sum of 2 different squares, show some uneven distribution, but
nothing as severe as bases that are multiples of 5. Other
bases, which are neither the sum of 2 different squares nor
multiples of such a base, show remarkably even distribution.
   The set of z-pairs, or z-values that differ by 2, appears
to be infinite. The largest such pair found so far is
39,955,435 and 39,955,437. The z-list itself must be infinite,
since assuming there exists some greatest z-value G leads to
a contradiction when you consider that G^2 + G + 1 must be a
z-value.
   There are plenty of directions to go from here; for example
there are related games "subtract-a-cube," "subtract-a-power"
etc. One could abandon the restriction that the generation
rules be based on any game at all. Regrettably, my only access
to the net is through a monitor, so I cannot send my software
or data. Thanks for your time.  :)
From: jxh@math.ksu.edu (James C. Hu)
Newsgroups: sci.math
Subject: Re: Mattel on women
Keywords: Targetting females once again.
Date: 13 Oct 92 10:17:15 GMT
Article-I.D.: hilbert.1bfasbINNft9
Organization: Dept. of Mathematics, Kansas State University
NNTP-Posting-Host: hilbert.math.ksu.edu

crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
>    Inanimate objects are greatly overrated 'role models'.  Usually,
>    what mommy or daddy say and do are much more important.

I don't think anyone disagrees with this sentiment.  However,
stereotypes get reinforced, and this is a bad thing.  I think a child
should be encouraged to learn.  Having your doll tell you "Math is
hard" is not a very encouraging sentiment.  It certainly doesn't help
foster a desire to learn math.
-- 
James C. Hu (jxh@math.ksu.edu), 1804 Denholm Dr., Manhattan, KS 66502
I speak for me, the whole me, and nothing but for me.  So help me me.
Newsgroups: sci.math
From: wjh@cbnewsl.cb.att.com (william.j.hery)
Subject: Re: Well-known people who majored in math (other than mathematicians)
Organization: AT&T
Distribution: na
Date: Tue, 13 Oct 1992 22:24:57 GMT

>	Some time ago on this group there was a discussion of well-known 
>people who had some kind of math background but weren't known as 
>mathematicians.

>Clifford Brown, 50's jazz trumpeter.

He was a maht major at Delaware, but did not complete his bachelor's
degree, opting for professional music instead.

Chico Freema, a current jazz saxophonist, did a similar thing at Northwestern

>David Dinkins, mayor of New York.

Interesting--can anyone give more information on this: what level degree,
from what school? And the jazz<-->math connection show up, since his son-in-law
is jazz vibraphonist Jay Hoggard (OK, that's pretty irrelevant here)

>Tom Lehrer, songwriter-parodist. Ph.D. in Math. at Harvard

I believe he's a mathematician first and a songwriter-parodist second

Add:

Art Garfunkel, folk-rock inger. BS math CUNY?

Bill Hery
From: smith@gramian.harvard.edu (Steven Smith)
Newsgroups: sci.math
Subject: Re: Another GRE question for you folks
Date: 12 Oct 92 19:12:47 GMT
Organization: Harvard Robotics Lab, Harvard University

nin15b66@merrimack.edu writes:

> This one came from a sample GRE test.
> 
> It is one where you have to choose A if the one on the left is
> greater, B if the one on the right is greater, C if they are equal
> or D if it can't be determined.
> 
> Column A                             Column B
> 4 + 2*the square root of 2           2 + 4*the square root of 2
> 
> The answer they gave is B.
> 
> I disagreed though, and before I go embarrassing myself with a
> nasty letter to ETS, I wanted to check with the experts on the
> subject.

Did the test really say ``the square root of 2,'' or did it use a
surd, i.e.,       _
                \/2 ?

By convention, the surd notation denotes the positive real root of a
positive number.  If the ETS used a surd, their answer is correct, and
they can avoid yet another damaging article on the front page of the
Wall Street Journal.

If they said ``the square root of 2'' or ``2^(1/2),'' they are
referring to a number x such that x^2 = 2, and the correct answer is D
by the reasons you stated.

Steven Smith
From: mkrogers@unix.amherst.edu (MICHAEL K ROGERS)
Newsgroups: sci.math
Subject: Re: Finite field software?
Date: 13 Oct 92 15:06:54 GMT
Distribution: na
Organization: Amherst College
X-Newsreader: TIN [version 1.1 PL6]

william.j.hery (wjh@cbnewsl.cb.att.com) wrote:
: Does anyone know of software (C or C++ routines would be fine) for
: doing calculations in finite fields. Particularly needed are routines
: for polynomials (manipulation, finding irreducibles, finding primitve
: roots, etc.) over fintite fields, including "polynomials of polinomials"
: i. e.,  polynomials over an extention field which is itself a field of
: polynomials modulo an irreducible polynomial over the prime field.
: 
: Public domain software preferred, but not required.

I believe Pari will do this.  It is available from math.ucla.edu
via anonymous ftp.  It consists of both a library and a programmable
calculator.

	-mike rogers
	mkr@cs.amherst.edu
From: smith@gramian.harvard.edu (Steven Smith)
Newsgroups: sci.math
Subject: Re: Another GRE question for you folks
Date: 16 Oct 92 15:30:10 GMT
Article-I.D.: gramian.SMITH.92Oct16103010
	<SMITH.92Oct12141247@gramian.harvard.edu>,<1992Oct12.221420.19382@galois.mit.edu>
	<1992Oct15.195539.11357@news.cs.brandeis.edu>
Organization: Harvard Robotics Lab, Harvard University

travis@binah.cc.brandeis.edu (Leopold Travis) writes:
> (John C. Baez) writes:
> >smith@gramian.harvard.edu
> >(Steven Smith) writes:
> >
> >>Did the test really say ``the square root of 2,'' or did it use a
> >>surd, i.e.,       _
> >>                \/2 ?
> >>
> >>By convention, the surd notation denotes the positive real root of a
> >>positive number.  If the ETS used a surd, their answer is correct, and
> >>they can avoid yet another damaging article on the front page of the
> >>Wall Street Journal.
> >>
> >>If they said ``the square root of 2'' or ``2^(1/2),'' they are
> >>referring to a number x such that x^2 = 2, and the correct answer is D
> >>by the reasons you stated.
> >
> >Surely if they say THE square root of 2 they are hinting that they believe
> >there is a unique one, i.e., that they are forgetting the negative one.
> 
> Absolutely.  If they were referring to some number x such that x^2=2,
> they would have said _a_ square root of 2.

I thought of this before posting, but it seemed too pedantic to
mention . . .  Anyway, the answer is still D (not enough information)
because it requires guessing the branch ETS desires (of course the
choice of the positive root seems likely, but is not necessary).

Steven Smith
From: hougen@focus.csl.uiuc.edu (Darrell Roy Hougen)
Newsgroups: sci.math
Subject: Re: Do you know ?
Date: 17 Oct 92 02:55:34 GMT
Article-I.D.: roundup.1bnvb6INNdv3
Organization: Center for Reliable and High-Performance Computing, University of Illinois at Urbana-Champaign
NNTP-Posting-Host: focus.csl.uiuc.edu

f(x) = {0 if x is rational
       {1 if x is irrational

Darrell
Newsgroups: sci.math
From: kavuri@lips1.ecn.purdue.edu (Surya N Kavuri )
Subject: Probably you know the probability ;-)
Organization: Purdue University Engineering Computer Network
Date: Wed, 14 Oct 1992 19:38:02 GMT

  I am given a "rod" of fixed length l. I took a hammer and
  broke it into three parts.

   (a) what is the probability that they form a triangle ?
   (b) what is the probability that they form an isoceles triangle ?

 
   Surya Kavuri


Newsgroups: sci.math
From: ilan@leland.Stanford.EDU (ilan vardi)
Subject: Re: Even pseudoprimes up to 10^12
Keywords: Pseudoprime
Organization: DSG, Stanford University, CA 94305, USA
Date: Fri, 16 Oct 92 20:58:27 GMT

In article <1992Oct16.142400.13541@infodev.cam.ac.uk> rgep@emu.pmms.cam.ac.uk (Richard Pinch) writes:
>Even pseudoprimes up to 10^12
>
>The list of pseudoprimes up to 10^12 which I announced in June
>were those satisfying 2^N-1 == 1 modulo N.  Some people use
>the definition 2^N == 2 modulo N, which allows the possiblity
>of even N.

How about square pseudoprimes? My favorites are 1093^2 and 3511^2.

-ilan
From: kaufman@eecs.nwu.edu (Michael L. Kaufman)
Newsgroups: sci.math
Subject: Here's a program to compute pi quickly
Date: 16 Oct 92 15:39:42 GMT
Article-I.D.: eecs.1992Oct16.153942.28398
Organization: EECS Department, Northwestern University

Since I asked the question in the first place, I thought I would post an
answer. I found this in David Wells's book _The Penguin Dictionary of
Curious and Intersting Numbers_. (The book by the way is quite interesting,
although I have found a few mistakes in it.) The method, goes like this:

#include <math.h>
main()
{
	float x,y,a,b,c;
	int ch = 1;

	a = x = 1.0;
	c = 0.25;
	b = 1 / sqrt(2);


	while(ch != 'q')
	{
		y = a;
		a = (a + b) / 2.0;
		b = sqrt(b * y);
		c = c - x * (a - y) * (a - y);
		x = 2.0 * x;
	
		printf("%10g\n", (a + b) * (a + b) / (4 * c));
		ch = getchar();
	}
}



Each pass through the loop doubles the number of digits you have.

Anyhow, thanks to the people who helped me, and I hope this helps someone else.

Michael

-- 
Michael Kaufman | I've seen things you people wouldn't believe. Attack ships on
 kaufman        | fire off the shoulder of Orion. I watched C-beams glitter in
  @eecs.nwu.edu | the dark near the Tannhauser gate. All those moments will be
                | lost in time - like tears in rain. Time to die.     Roy Batty 
Xref: sparky sci.math:13347 sci.physics:16678
From: mrw9e@kelvin.seas.Virginia.EDU (Michael Robert Williams)
Newsgroups: sci.math,sci.physics
Subject: Re: "The Universe of MOTION" (crackpot index)
Date: 16 Oct 92 21:29:17 GMT
Organization: University of Virginia


How about a crackpot recognition manual? Every week or month, the top 20
crackpot indices could be posted in a sort of "Jane's Crackpot Digest"
format, and then we could write little routines to kill articles from
people who have a crackpot rating higher than our crackpot tolerance
threshold.
In Real Life:Mike Williams     | Perpetual Grad Student

e-mail      :mrw9e@virginia.edu|   - It's not just a job, it's an indenture
---------------------------------------------------------------------------
The probability of something happening is inversely proportional
to its desirability
Newsgroups: sci.math,sci.physics
From: scip1061@nuscc.nus.sg (Marc Paul Jozef)
Subject: Re: How do you draw a straight line?
Organization: National University of Singapore
Date: Mon, 12 Oct 1992 08:31:28 GMT

jbaez@riesz.mit.edu (John C. Baez) writes:
: In article <1992Oct8.115013.2533@nuscc.nus.sg> scip1061@nuscc.nus.sg (Marc Paul Jozef) writes:
: >
: > The spacetime metric of GR defines geodesics
: >in spacetime. A string or a rod or whatever
: >define world*sheets* in spacetime; `straightness'
: >of a line has nothing to do with geodesics of GR.
: 
: While it's true that over time a rod covers a 2-dimensional surface
: in spacetime, the closest thing there is to a straight (spacelike) line
: in GR is a spacelike geodesic.
: 
:

    So what? 
    The correspondence may be `close', but it can
    never be precise (except in static spacetimes
    which have a unique timelike Killing-field,
    so that there is a unique 3+1 splitting of
    spacetime).
From: matmcinn@nuscc.nus.sg (Mcinnes B T (Dr))
Subject: Re: STRUCTURE OF TIME and God
Organization: National University of Singapore
Date: Fri, 9 Oct 1992 07:03:05 GMT

goddard@NeXTwork.Rose-Hulman.Edu (Bart Goddard) writes:
: Say, guys, you can (and do) insult us theists all you want,

	Thanks.

Newsgroups: sci.math
From: holmes@opal.idbsu.edu (Randall Holmes)
Subject: Re: help with recursive functions
Organization: Boise State University
Date: Thu, 8 Oct 1992 18:34:08 GMT

In article <1b074cINN4fu@usenet.INS.CWRU.Edu> cxm7@po.CWRU.Edu (Colin Mclarty) writes:
>
>	I'd like some help with partial recursive functions which
>do not extend to (total) recursive ones.  I can prove there is no
>effective routine for extending all partials to total recursive
>functions, but I do not see how to prove there are particular
>partial recursive functions that do not extend to recursive.  Are
>there typical methods from proving this in particular cases?
>
>Colin McLarty

Easy example:  the function which, given the code for a Turing
machine, simulates its operation and outputs the number of steps it
takes to halt if it does halt.  If this function could be extended to
a total recurisive function, it could be used immediately to solve the
halting problem.


-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu
From: wilson@web.ctron.com
Newsgroups: sci.math
Subject: Re: How do you draw a straight line?
Date: 7 Oct 92 17:17:03 GMT
Reply-To: wilson@web.ctron.com ()
Organization: Cabletron Systems INc.




    Let SPACE be Euclidean 3-space.

    Let PAPER be a plane in SPACE.

    Let INSTRUMENT be a set of points with the following restrictions:

	1.  Every point of INSTRUMENT is restricted to SPACE.

	2.  Any point of INSTRUMENT may be restricted to PAPER.

	3.  INSTRUMENT contains a point PENCIL which is restricted to
	    PAPER.

	4.  Any point of INSTRUMENT which is restricted to PAPER
	    may be held constant.

	5.  The Euclidean distance between any two points of INSTRUMENT
	    may be held constant.

	6.  The measure of the angle formed by any three points of
	    INSTRUMENT may be held constant.

    The locus of PENCIL is called the figure drawn by INSTRUMENT.


    Now let INSTRUMENT = { C, P, D }, where

	1.  INSTRUMENT is a subset of SPACE.

	2.  C and D are in PAPER.

	3.  PENCIL = D.

	4.  C is constant.

	5.  The distances CP and DP are constant.

	6.  The angle CPD is constant.

    We recognize this instrument as a compass with compass point C,
    pivot point P, and drawing point D, and conclude that it draws a
    circle or point.


    A straightedge or similar template does not qualify as an
    INSTRUMENT by the above definition.  Is there an INSTRUMENT, as
    defined above, which draws a line segment?  I remember reading that
    such an INSTRUMENT indeed exists.  If it does, then it
    theoretically draws line segments with the same degree of
    confidence as a compass draws circles.


-- 
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: brnstnd@nyu.edu (D. J. Bernstein)
Newsgroups: sci.math
Subject: Re: Why is slope denoted by m?
Date: 11 Oct 92 02:17:07 GMT
Organization: IR

In article <1992Oct7.181405.18957@unlinfo.unl.edu> kwright@hoss.unl.edu (Kevin Wright) writes:
> We use Z for the integers because of the German 'Zahlen' and we have
> F for a closed set because of the French 'Ferme' and we have R for rings 
> because of the English word 'ring.'  

No. According to Harvey Cohn (Advanced Number Theory, page 49), ``ring''
is a contraction of ``Zahlring,'' a German word introduced by Hilbert.
One might argue about the closeness of German ``ring'' and English
``ring,'' but the history of ``ring'' is not what you say.

---Dan
From: schectr@ucunix.san.uc.edu (ROBB SCHECTER)
Newsgroups: sci.math
Subject: Info needed on graphing calculators
Date: 8 Oct 92 01:23:53 GMT
Organization: University of Cincinnati

Hello everyone...I thought I might get some informed opinions on
   the plethora of graphing calculatoers out there.  Good experiences?
   Bad?

I am about to buy the -expensive- HP 48sx.  I've got one of HP's older
   RPN models, and I love it.   This is the main reason I think Im
   going to get HP again.  Also I think the HP48s and 48sx are the
   only two RPN ones out there.

Im a Computer Science major picking up math as a double major...is this
   a good investment?

	 Thanks for the responses.

-- 
---------------------------------------------------------------------------
Robb Shecter        University of Cincinnati      schectr@ucunix.san.uc.edu
                                                  ^^^^^^^
                 My university cannot spell my name...
Xref: sparky sci.math:13198 rec.music.classical:14281
From: roger@crux.Princeton.EDU (Roger Lustig)
Newsgroups: sci.math,rec.music.classical
Subject: Re: P.Glass and math? [Re: famous non-mathematicians who majored in math]
Date: 14 Oct 92 19:31:57 GMT
Reply-To: roger@astro.princeton.edu (Roger Lustig)
Organization: Princeton University
Originator: news@nimaster

In article <1bhqnnINN77v@calvin.usc.edu> alves@calvin.usc.edu (William Alves) writes:
>In article <1992Oct13.223043.16366@husc3.harvard.edu> elkies@ramanujan.harvard.edu (Noam Elkies) writes:
>>In article <1992Oct13.202553.7542@aio.jsc.nasa.gov>
>>>I believe Phillip Glass (the American Composer) has a background in 
>>>mathematics.  Can someone verify this?

>I don't think Glass ever majored in math. However, Steve Reich's undergrad
>degree is in Philosophy.

[Glass *did* major in math at U of Chi, graduating in 1956.  But I
already went over this...]  

>>Meanwhile I note that music theorist David Lewin and serial composer
>>Milton Babbitt got their undergraduate degrees in mathematics, and
>>math figures prominently in their work.
[...]
>Milton Babbitt finally received his doctorate in math from Princeton -
>several decades late. 

Um, that would make *two* doctorates he received recently from Princeton.
Three, really, if you count the honorary Doctorate of Humane Letters.
But serially, folks, the doctorate he recently received was in *music*.
He never studied math at Princeton, though he taught some during the 
war.

>They had originally rejected his dissertation,
>which I believe concerned serial theory in music. The Princeton pundits
>now say that the dissertation was too far ahead of its time to have
>been appreciated when he wrote it. 

No, the pundits *always* said that.  Departmental politics had far 
more to do with it.

>I suspect, too, that they don't
>want to have a famous man and academician harboring any ill will 
>towards them.

As if Milton cared!  C'mon, you must not know the guy.  I mean, after,
what, 53 years in the department?  He still comes in every day; what
would a Ph.D. change about anything?

The degree was presented to him as an utter surprise, at the end of
a lunch with the current dept. chairman and dean; they just started addressing
him as Dr. Babbitt...

Roger
Newsgroups: sci.math
From: kaufman@eecs.nwu.edu (Michael L. Kaufman)
Subject: Looking for fast methods of computing PI
Organization: EECS Department, Northwestern University
Date: Tue, 13 Oct 1992 02:58:20 GMT

I read an article a few years ago in some magazine (I think it was Discover)
that talked about two people who had come up with a fast way of computing PI.
The magazine didn't give the method and I lost it before I could write the
author. As I recall, it involved using some intermediate values in computing
more digits, and more intermediate values. (I might be misremembering this.)
Anyhow, any helppl on the subject would be appreciated.

Thanks, Michael


-- 
Michael Kaufman | I've seen things you people wouldn't believe. Attack ships on
 kaufman        | fire off the shoulder of Orion. I watched C-beams glitter in
  @eecs.nwu.edu | the dark near the Tannhauser gate. All those moments will be
                | lost in time - like tears in rain. Time to die.     Roy Batty
From: rwc124@rsphy1.anu.edu.au (Roderick Vance)
Newsgroups: sci.math
Subject: Eigenvalue Problem
Date: 12 Oct 92 09:44:52 GMT
Reply-To: rwc124@rsphy1.anu.edu.au (Roderick Vance)
Organization: Optical Sciences Centre, Australian National University
NNTP-Posting-Host: 150.203.15.51

My question concerns the eigenvalue equation:

 (del^2 + k^2 n(x,y)^2) psi = beta^2 psi

where psi is a function of the rectangular co-ordinates (x,y)
      del^2 is the two dimensional Laplacian d2/dx2 + d2/dy2
and   beta is the real eigenvalue.

This equation is gotten from the three dimensional Helmholtz 
equation when we assume a three dimensional solution of the form

   psi(x,y) exp(-i beta z)

My question is: when can there be two or more linearly independent
solutions psi1(x,y), psi2(x,y), ...  corresponding to the SAME 
eigenvalue. 

More generally - if psi  belongs to a linear (Hilbert) space and
L is a linear operator mapping the space into (or onto) itself, then
when can there be two linearly independent solutions to

 L psi = beta^2 psi

and what properties must L have so that there can be two or more
eigenvectors?

Trivial Example: The 3x3 matrix 

k0 k1 k1
k1 k0 k1
k1 k1 k0

has two linearly independent eigenvectors

-1
0
1

and

-1
1
0

that correspond to the eigenvalue k0 - k1.

 

I'd be most greatful for hints/thoughts about the above.

Many thanks in advance


Roderick Vance
Optical Sciences Centre
Australian National  University
Xref: sparky sci.math:13146 rec.music.classical:14217