HDTenEightyP/NetNews huggingface dataset:
From: mrw9e@kelvin.seas.Virginia.EDU (Michael Robert Williams)
Subject: Re: Orbital motion question
Organization: University of Virginia
Date: Mon, 14 Dec 1992 17:30:03 GMT

In article <1ggfesINN29q@access.usask.ca> choy@skorpio.usask.ca (I am a terminator.) writes:
>
>Let the vector r be the position of a mass m orbiting in a plane around
>another mass M (which doesn't move) at the origin. The mass m is
>accelerated such that
>
>   2
>  d r     KMm
>m --- = - ---- r
>    2        2
>  dt      |r|
>                                           r
>                                         d---
>                                          |r|
>What is the scalar product of r/|r| and ------ ?
>                                          dt
>
>If m moved in an elliptical path, can the scalar product be zero?
>

The scalar product of r/|r| and d(r/|r|)/dt is called sigma, and is 
always zero for a circular orbit, but has different values for each point
on an elliptical, parabolic or hyperbolic orbit. sigma is equal to 
zero at the peri- and apo-apsis of any orbit, regardless of type. If
you divide sigma by the magnitudes of r/|r| and d(r/|r|)/dt, you get
the cosine of a quantity called the flight path angle.


In Real Life:Mike Williams     | Perpetual Grad Student
e-mail      :mrw9e@virginia.edu|   - It's not just a job, it's an indenture
---------------------------------------------------------------------------
Incompetence plus incompetence equals incompetence.
Xref: sparky sci.math:16743 comp.edu:2186 misc.education:5158
From: bh@anarres.CS.Berkeley.EDU (Brian Harvey)
Newsgroups: sci.math,comp.edu,misc.education
Subject: Re: Education crisis (was RE: how much math...)
Date: 12 Dec 1992 00:33:27 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: anarres.cs.berkeley.edu

I said:
|It doesn't have to be all-or-nothing, either.  I'd say that high school is
|an intermediate stage, in which there are a *few* specific curriculum areas
|that are important (and math is one of them), but also there should be
                     ^^^^^^^^^^^^^^^^^^^^^^^
|plenty of time allowed for students to pursue their own interests.
| [...]      I think
|it's important that high school kids learn to read and write, for example,
|but it wouldn't be the end of the world if they mostly just read and write
|science fiction, or horse stories, or whatever turns them on.  Especially if
|their teachers can unearth a few examples of really good writing within the
|genre.

hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>So this kid who has only read science fiction, etc., now finds himself as
>a high school student, or later, wanting to get into physics or chemistry
>or astronomy.  There are years of fundamentals to be made up before this
>can be done.  There is even the question of whether the mental abilities
>involved in precise thinking are gone.
>
>So do we write this guy off as a permanent mathematical illiterate?  It is
>doubtful that he will be willing to spend at least two years learning basic
>high school mathematics before doing anything significant in a field of
>science.  


Geez, are you deliberately misunderstanding me, or what???

I said that the math curriculum is important.  I agreed with you about
the importance of formal reasoning and precise thinking.

Then I said that high school is full of a lot of stuff that *isn't* so
important.  _Ivanhoe_ in 7th grade.  _Hamlet_ in 10th grade.  I think
that even high school chemistry is not so crucial -- when I was an MIT
freshman they taught us chemistry as if we'd never seen any before.

I suggested that if a kid happens to get very interested in something,
as often happens (my example was computer programming, but it could
be _Hamlet_, too), it would be better to ease up on all the thousands
of silly things schools teach kids and leave some space for a serious
commitment to whatever the field of interest might be, while still
having a *small* core curriculum that we want to make sure everyone learns.

I suggested that reading and writing should be in the core curriculum,
but not reading or writing anything in particular.

I believe that if you had actually read my message before flaming about
it, you would see that I am on your side.
From: bandi@mega.cs.umn.edu (Vijay)
Newsgroups: sci.math
Subject: Pi - arbitrary precition..
Date: 20 Dec 92 20:59:12 GMT
Organization: University of Minnesota


Hi,

	I am loking for a working program fr computing Pi to arbitrary
precition. I need more than the algo ( I've never programmed for arbitrary
precitions);
	Also, if anybody out there has a parallel implementation, i'd be
happy to have it.
	Any books in this direction would be helpful.
Thanks.
-vijay
[bandi@cs.umn.edu]
Newsgroups: sci.math,rec.puzzles,alt.usage.english
From: amorgan@Xenon.Stanford.EDU (Crunchy Frog)
Subject: Re: Naming Large Numbers
Organization: Computer Science Department, Stanford University.
            <Dec.15.05.12.50.1992.13518@romulus.rutgers.edu>
            <1992Dec15.162324.28405@dartvax.dartmouth.edu>
Date: Wed, 16 Dec 1992 01:07:33 GMT

In article <1992Dec15.162324.28405@dartvax.dartmouth.edu> 
  J.Theodore.Schuerzinger@dartmouth.edu (J. Theodore Schuerzinger) writes:
>In article <Dec.15.05.12.50.1992.13518@romulus.rutgers.edu>
>clong@romulus.rutgers.edu (Chris Long) writes:
>
>>   The largest number given is millitwoillimillionillion, which
>>   can't be written down in standard notation.
>
>Why can't it be written down in standard notation?  Unless it's
>irrational or transcendental, one should be able to write it down.

In theory yes, in practice no.  Let me invent a notation.  a&b means

a^a^a^a ...... ^a
\               /
     b times

I submit that writing 10^100 & 10^100 is slightly tricky in standard
notation.  I believe Don Knuth invented something called arrow
notation to describe really *huge* numbers like Skewes number.

Consider another case.  Let triangle x be x^x.  Let square x be
triangle triangle ..... x.  Let circle x be square square ..... x
\   x times     /                            \   x times     /

circle 2 is a *large* number.  It can't be written with standard
notation.  circle 10 is beyond the mind-pummling huge and moves into
the brain squooshingly gigantic.  Let us then pause to consider
circle 10^100 & circle 10^100 which I modestly suggest be called
frog's number.

What I have always found... humbling is the word I want I guess
is that however large these numbers may be, they aren't a patch on
infinity.  Even frog's number is *nothing* compared with some
of the *really* big numbers out there.

>--Ted Schuerzinger

C Frog
From: pehanna@vnet.ibm.com (Phil Hanna)
Date: Mon, 14 Dec 92 11:59:46 EST
Newsgroups: sci.math
Subject:  Base Pi

>>  Base pi? No joking?
>>
>>  Well, what are the first 5 digits of what we normally
>>  call "5" in this base?
>>
>>  Solan

5 = 11.22012... in base pi, since 5 is approximately equal to

    1(pi**1) + 1(pi**0) + 2(pi**(-1)) + 2(pi**(-2)) + 0(pi**(-3))
                        + 1(pi**(-4)) + 2(pi**(-5)) + ...

Phil Hanna
pehanna@vnet.ibm.com
Newsgroups: sci.math
From: gay@selkirk.sfu.ca (Ian D. Gay)
Subject: Re: Master Mind:A question.
Keywords: Master Mind Game
Organization: Simon Fraser University, Burnaby, B.C., Canada
Date: Mon, 14 Dec 1992 18:39:35 GMT

jimgar@scorch.apana.org.au (Jim Garner) writes:

>evant@coos.dartmouth.edu (Evan E. Thomas) writes:

>|My question regards the game "MasterMind" where 4 pegs are chosen (from an
>[deletions]
>|You would be told that 1 color is exactly right and that two others are in
>|the solution.  You have exactly 10 guesses to find the solution.  Is there
>|an algorithm that will insure victory?

>There is an optimal strategy that has been published. It is very long
>and divided into cases, so I wouldn't call it an algorithm. But it
>certainly can be done in less than 10 guesses every time. All I
>remember is that your first guess should contain 2 colours only, 2
>pegs of each.

Having played a lot of Mastermind with my kids, I am of the opinion 
that the 5-peg version can usually be solved in 6 guesses; presumably 
the 4-peg version should require less. Sorry, I don't know an 
algorithm, but I recommend starting with two completely random 
guesses, then reasoning about the results.
From: koc@rize.ECE.ORST.EDU (Cetin Kaya Koc)
Newsgroups: sci.math
Subject: Re: What is the number
Date: 17 Dec 92 19:56:57 GMT
Article-I.D.: flop.1gqm29INN9f
Organization: College of Engineering, Oregon State University
NNTP-Posting-Host: rize.ece.orst.edu

>    Whose sum of the factorials of the digits is the number itself

1, 145, 40585
Newsgroups: sci.math
From: solan@smauguio.no (Svein Olav G. Nyberg)
Subject: Easy problem from linear algebra
Keywords: Matrix, determinant
Reply-To: solan@smauguio.no (Svein Olav G. Nyberg)
Organization: University of Oslo, Norway
Date: Fri, 18 Dec 1992 19:18:04 GMT

I have a small problem. There are these matrixes A_k, the 
index k running over the natural numbers, and for each
matrix
            |  a     b  |
            |           |
     A_k =  |           |
            |  c     d  |

a>c ,  d>b,  all entries are positive. Obtain B_k by switching
a with c and b with d. Now let C_k = A_1 * A_2 *...* A_(k-1) * B_k,
D_k = C_k \times\theta^(k-1), and let  D = C_1 + C_2 + .....  
Are there any values of \theta where the determinant of E = I - D
equals zero, and if there are constraints to this, what are they?

Thanks,
       Solan
Newsgroups: sci.math
From: brumleve@iboga (Dan Brumleve)
Subject: Re: Philosophy of Pi
Organization: University of Illinois at Urbana
Date: Fri, 18 Dec 1992 15:40:19 GMT

dat92oma@ludat.lth.se (Ola Martensson) writes:

>A friend and I discussed if you can find any integer anywhere
>in the expansion of PI?

>1415 , 92 etc is obvious BUT can you really find ALL integer
>even unlimited ones???

>-----------------------+----------------------------------------
>Ola Mrtensson         | Department of Computer Science
>dat92oma@ludat.lth.se  | University of Lund
>-----------------------+----------------------------------------
>Life is wasted on the living.
>- Zaphod Beeblebrox IV


Hmm...  I'd think that you would be able to find any integer in an irrational
number.  Not sure though.

-Dan
From: lenny@hobbs.hunt.inmet.com (Lenny Goodman)
Newsgroups: sci.math
Subject: Suggestions Wanted for Math Books
Date: 20 Dec 92 22:45:37 GMT
Organization: Intermetrics, Inc.

I found out in college that math textbooks weren't my cup of tea, 
but I find that mass market books such as Ivars Peterson's "Mathematical
Tourist" and "Islands of Truth" were not technical enough.  Does anyone
have any suggestions for books that are between these two positions in 
level of difficulty.  My main interests are topology, differential geometry,
algebra, and computation theory.  Actually, most any area will be OK 
except for probability, statistics, and numerical analysis.  Thanks.

  -- Len Goodman
Newsgroups: sci.math,sci.physics,sci.bio,sci.chem,misc.education
From: brian@quake.sylmar.ca.us (Brian K. Yoder)
Subject: Re: TIME HAS INERTIA - BASS JEALOUS AND INSECURE-ABIAN VALIDATED
Organization: Quake Public Access
Date: Sun, 13 Dec 1992 23:33:03 GMT


I think that before anyone even addresses this incredible claim (that "Time
Has Inertia") they have to explain how something which is not an entity (time)
can have properties.  Any definition of time I can think of (even ones I
very much disagree with) define time as something other than an entity.
If you claim that your definition of time is something new, that it IS an
entity, then you need to have some means by which to prove this.  What do you
think would constitute evidence of this amazing claim?

A similar problem exists for physicists who consider light to be a wave (or
a wave and something else too).  Waving is something an entity does, not a
thing in itself.  There can no more be a wave traveling through space than
there can be a room with some "jumping" going on outside of any entities which
are doing the jumping.

I think these kinds of problems both arise from physicists getting too tied up
with their equations to remember that they apply to things in the real world.

--Brian
From: baez@ucrmath.ucr.edu (john baez)
Newsgroups: sci.math
Subject: more math puzzles
Date: 11 Dec 92 21:23:37 GMT
Organization: University of California, Riverside

1)  Which famous mathematician wrote "The introduction of numbers as
coordinates... is an act of violence"?

2)  Which famous mathematician wrote "Topology is precisely that branch of 
mathematics that permits the passage from local to global"? 

3)  Prove that the tangent bundle of the long line is nontrivial.

The answers to the above 3 are in Hirsch's "Differential Topology."  (Topologists 
on the net will be delighted to learn that I finally obtained this book and
will stop pestering them with questions whose answers are in it.)  

For extra credit, an obvious spinoff of 3) that I don't know the answer to:

4)  Classify line bundles over the long line.
Newsgroups: sci.math.symbolic
From: comeaude@newton.ccs.tuns.ca (Daniel E Comeau)
Subject: Mathcad 3.1 4 Windows
Summary: Documentation? 
Date: Wed, 16 Dec 1992 04:07:13 GMT
Distribution: na
Organization: Technical University of Nova Scotia, Halifax, N.S.
Keywords: MCAD Mathcad books

	Hi there.  I was just wondering if anybody could suggest any books whichare available for use with MathCad 3.1 for Windows.  I have checked the local   computer book stores and they don't know of any.  Thanks.

				Dan

Xref: sparky sci.math.symbolic:3314 sci.math:17204 alt.uu.math.misc:25
From: dak@kaa.informatik.rwth-aachen.de (David Kastrup)
Newsgroups: sci.math.symbolic,sci.math,alt.uu.math.misc
Subject: Re: SIMTEL-20 symbolic mathmatica software
Date: 19 Dec 92 09:45:44 GMT
Organization: Rechnerbetrieb Informatik - RWTH Aachen
Distribution: world
NNTP-Posting-Host: kaa.informatik.rwth-aachen.de

I'd say that symbmath is, in a crippled version not even having sine
and cosine, is freely available on the net (as shareware), but not
freely usable (shareware, you see!), is rekking pretty much like
commercial use to me.

On the other hand, seen in this light, every distribution of crippleware,
or even shareware, constitutes a commercial use of the net.

Strictly correct would be only the posting of programs which are freely
usable for certain users (private users, non-commercial use, something
like that). Most shareware may be tested a limited time.
Distribution of such shareware is akin to an advertisement of available
services, distribution of demos and crippleware even more so.

How to cope? I mean, what constitutes commercial use if not distributing
advertisements and free samples of not completely functional equivalents?
What more must one do to qualify as a commercial user?
The only difference I see to "commercial" use is that "commercial users"
would maybe not distribute any test material. But this is definitely
a deciding line drawn by hsareware authors only.

The only other intervening rationale would be that the distribution
of shareware should have some means, and the net is an obvious one.
But then this should be restricted to shareware. I think crippleware
distribution is really as commercial as things can get.

I for myself got the crippleware version of symbmath and was not even
able to decide whether this software could be of any use to me because
it was even lacking trigonomical functions (this was, of course, the
"shareware" version). So buying the software in a sufficiently working
version would have been in my case buying the cat in the sack, not
shareware at all. I solved my special problem with an own program,
and up to now do not know if sm could probably have done it.
From: fc03@ns1.cc.lehigh.edu (Frederick W. Chapman)
Newsgroups: sci.math.symbolic
Subject: Quadratic Form Calculations in Maple
Date: 11 Dec 92 18:27:25 GMT
Organization: Lehigh University

Let Q be a quadratic form on an finite-dimensional real vector space V, and
let B be the matrix of Q with respect to some basis of V.  By a sequence of
elementary row and column operations, the real symmetric matrix B can be
reduced to a diagonal matrix D that is congruent to B; i.e., D = P B P',
where P = E_m E_{m-1} ... E_1, and the E_i's are matrices corresponding to
the sequence of elementary row operations.  The number of non-zero diagonal
entries of D is the rank of quadratic form Q, and the number of positive
diagonal entries minus the number of negative diagonal entries is the
signature of Q.


QUESTION:

Has anyone written a Maple function or package to compute the rank and
signature of a real quadratic form?  For a real symmetric matrix with
numeric entries, it should be a fairly simple matter to code the algorithm
using Maple's built-in routines for elementary row and column operations;
however, I'd prefer not to reinvent the wheel!


Thanks,

Frederick W. Chapman
Senior User Consultant
Lehigh University Computing Center
-- 
 
o ------------------------------------------------------------------------- o
|  Frederick W. Chapman, User Services, Computing Center, Lehigh University |
|    Campus Phone:  8-3218     Preferred E-mail Address:  fc03@Lehigh.Edu   | 
o ------------------------------------------------------------------------- o
| The day after the day after tomorrow is the last day before the rest of   |
| our country's future a week from the day before the day before yesterday! |
Newsgroups: sci.math.symbolic
From: eddie@laslett.SLAC.Stanford.EDU (Xintian Eddie Lin)
Subject: Re: Obtaining x-y data from a plot
Organization: Stanford Linear Accelerator Center
Date: Sat, 12 Dec 1992 09:11:00 GMT


   Hello,
   I was wondering, if in Mathematica of Maple there is a way to use a cursor
   to pick a point off the screen and obtain it's exact x-y value.

In the notebook interface, if you press down command key, the cursor position
will read off the x-y coordinates.

	Eddie Lin
--
======================================================================
#                   Balance Principle:   Gain For Lose               #
======================================================================
From: jmp1@ns1.cc.lehigh.edu (JEFFREY MICHAEL PARSONS)
Newsgroups: sci.math.symbolic
Subject: Help with user defined functions in Maple.
Date: 17 Dec 92 06:07:55 GMT
Organization: Lehigh University

I tried defining a function in Maple V r1.1 like this:

f := proc(x)  if x<0 then -1 else 1 fi;  end;

I could then type f(3) or f(-100) and get the correct result.  The problem is
that I can't integrate it, etc.  I always get:

Error, (in f) cannot evaluate boolean.

Is there a better way to be doing this kind of thing?

Thanks.
-- 
Newsgroups: sci.math.symbolic
From: drclark@daisy.uwaterloo.ca (David R. Clark)
Subject: Re: Help with user defined functions in Maple.
Organization: University of Waterloo, Waterloo, Ontario, Canada
Date: Thu, 17 Dec 1992 15:37:09 GMT

jmp1@ns1.cc.lehigh.edu (JEFFREY MICHAEL PARSONS) writes:

   From: jmp1@ns1.cc.lehigh.edu (JEFFREY MICHAEL PARSONS)
   Subject: Help with user defined functions in Maple.

   I tried defining a function in Maple V r1.1 like this:

   f := proc(x)  if x<0 then -1 else 1 fi;  end;

   I could then type f(3) or f(-100) and get the correct result.  The
   problem is that I can't integrate it, etc.  I always get:

   Error, (in f) cannot evaluate boolean.

   Is there a better way to be doing this kind of thing?

   Thanks.
   -- 

The procedure you have written does not allow for the possibility that
the parameter may be an expression that cannot be compared to zero.

The procedure can be better defined as:

f := proc(x)  if not type(x,numeric) then 'procname(x)'
              elif x<0 then -1
              else 1 fi;
     end;

When supplied with a non-numeric parameter this new function returns
without evaluating.  It can be numerically integrated, plotted, 
and manipulated in Maple.  Allowing symbolic integration of user defined
functions is a much more difficult question.

You can also work with your original function by using the Maple
quote operator to disable evaluation of the expressions, e.g.:

> f := proc(x)  if  x<0 then -1 else 1 fi;  end;

f := proc(x) if x < 0 then -1 else 1 fi end

> evalf(Int('f(x)',x=-1..1));

                                       0

Newsgroups: sci.math.symbolic
From: bagchi@eecs.umich.edu (Ranjan Drzzzzt!  Bagchi)
Subject: dumb maple question -- differential equations
Organization: Recreational Creationists, Inc.
Date: Wed, 16 Dec 1992 23:40:06 GMT

Hi folk --

	I'm playing (for lack of a better word) with a system of
ODE's, and having fed them to maple for a numeric solution, I'd like
to do something with this solution.

    |\^/|     Maple V Release 2 (University of Michigan)
._|\|   |/|_. Copyright (c) 1981-1992 by the University of Waterloo.
 \  MAPLE  /  All rights reserved. MAPLE is a registered trademark of
 <____ ____>  Waterloo Maple Software.
      |       Type ? for help.
> sys := {
> f> (v1(        diff(v1(t),t) = a1*v1(t) - b1*v1(t)*pr(t),
>         diff(v2(t),t) = a2*v2(t) - b2*v2(t)*pr(t),
>         diff(pr(t),t) = -c*pr(t) + d * pr(t) * v1(t) + e *pr(t)*v2(t)
> };

                    d
          sys := {---- v1(t) = a1 v1(t) - b1 v1(t) pr(t),
                   dt

                d
              ---- v2(t) = a2 v2(t) - b2 v2(t) pr(t),
               dt

                d
              ---- pr(t) = - c pr(t) + d pr(t) v1(t) + e pr(t) v2(t)}
               dt

> params := {a1 = 1, b1 = .3,a2 = 2, b2 = .6, c = 3, d = .7, e = .5};

      params := {a1 = 1, b1 = .3, a2 = 2, b2 = .6, c = 3, d = .7, e = .5}

>
 union sysinit);

>  :> = dsolve(eqns,{v1(t),vsysinit := { v1(0) = 5, v2(0) = 5, pr(0) = 4};

                  sysinit := {v1(0) = 5, v2(0) = 5, pr(0) = 4}

>
> eqns := subs(params,sys union sysinit);

                                            d
eqns := {v1(0) = 5, v2(0) = 5, pr(0) = 4, ---- v1(t) = v1(t) - .3 v1(t) pr(t),
                                           dt

      d
    ---- v2(t) = 2 v2(t) - .6 v2(t) pr(t),
     dt

      d
    ---- pr(t) = - 3 pr(t) + .7 v1(t) pr(t) + .5 v2(t) pr(t)}
     dt

>
> pv := dsolve(eqns,{v1(t),v2(t),pr(t)},numeric);
bytes used=302868, alloc=262096, time=0.72
bytes used=309476, alloc=262096, time=0.78
pv := proc(t) `dsolve/numeric/result2`(t,895108,[1,1,1]) end

>> pv(1);

    {t = 1., v1(t) = 1.599162730, pr(t) = 5.059208376, v2(t) = .5114643376}


----------- end of session ------------

There are several things I'd like to do with this data which 
I haven't had much luck with:

1)  I'd like to break v1(t), v2(t), pr(t) into separate functions.  While
this sounds trivial, the only way I've been able to do it is with 

V1 proc(t) op(2,op(2,pv(t))) end;

which looks fairly inelegant.

2)  I'd like to collect a large (say 10000 point) array of data from each
of the functions.  Any attempt at this has taken what seems to be
an unbearably long time.  I've been using a do loop and putting data
in each array bucket.

3) I'd like to plot these derived function.  In the V1 I defined above, 
I get the following errors:

> plot(V1,0..10);
bytes used=1491904, alloc=1048384, time=5.58
Error, (in f) wrong number (or type) of parameters in function type;


help??

	-rj
--
Ranjan Bagchi					       Ranjan.Bagchi@umich.edu
oo   oooo  o oo   ooo oo oo   oo       o o  oooo ooo o       o        oooooooo
From: huhr@formentera.uni-paderborn.de (Holger Uhr)
Newsgroups: sci.math.symbolic
Subject: Re: Obtaining x-y data from a plot
Date: 15 Dec 1992 16:13:43 +0100
Organization: Universitaet Paderborn, Germany
Distribution: world
NNTP-Posting-Host: formentera.uni-paderborn.de
X-Newsreader: TIN [version 1.1 PL7]

naomir1@vms.huji.ac.il wrote:
: Hello,
: I was wondering, if in Mathematica of Maple there is a way to use a cursor
: to pick a point off the screen and obtain it's exact x-y value.
: 
: Just wondering
: Naomi
: 

With the notebook-interface of Mathematica on my NeXT, I can
Command-click into a plot to get the x-y value.
On other platforms this should work in a similar way.

Greetings,

Holger Uhr

-- 
|   Holger Uhr  ***   Engernweg 32  ***  W-4790 Paderborn   ***   Germany   |
|E-Mail: huhr@uni-paderborn.de                            Phone: 05251-58950|
|How to become immortal: Read this signature tomorrow and follow its advice.|
Newsgroups: sci.math.symbolic