HDTenEightyP/NetNews huggingface dataset:
Newsgroups: sci.math
Subject: Re:  Fermat's Last Theorem
From: pete@bignode.equinox.gen.nz (Pete Moore)
Date: 14 Apr 92 22:54:47 +1200
Organization: Equinox Networks

In article <1992Apr11.123452.5400@vax.oxford.ac.uk>,
                            loader@vax.oxford.ac.uk (R Loader) writes:

>  I have heard of Erdos, but know next to nothing about what fields he
>contributed to, what his major results are etc etc. Perhaps a sensible end to
>this thread of flames would be for someone to post such info.

Gidday Ralph - how are things on the other side of the world from your old
haunts?  :-)

The following info is all I could find on Paul Erdos at short notice:

Paul Erdos (pronounced `air-dersh' approximately) is a Hungarian
mathematician, and probably one of the half-dozen or so greatest
mathematicians of this century. His interests include subjects such as
number theory, analysis, combinatorics, etc. His published papers by now
probably number about 2000.  One of his early ones was a purely
arithmetical proof of the Prime Number Theorem, discovered independently
of Selberg's proof, and at about the same time.

Erdos is probably as well known for his personal quirks as for his
mathematics. When he enters a room, his first remark is about mathematics,
and his letters begin `Suppose that x is ...'  He has no job, supporting
himself by lectures in various places and staying with friends. He speaks
his own slang, in which lecturing is `preaching', husband is `boss' and
wife `slave' (or the other way around?), children are `epsilons' and God
is the SF (supreme fascist). If he praises another's work, he may describe
it as `from The Book' (`The Book' contains all the true theorems of
mathematics, together with their most elegant proofs).

Erdos occasionally offers small cash prizes (usually up to a few hundred
dollars) for solutions to problems which he has not been able to solve
himself. As another poster has remarked, attempting to solve such problems
is not a good way to get rich quickly!

--
 +-------------------  pete@bignode.equinox.gen.nz  -------------------+
 | The effort to understand the universe is one of the very few things |
 | that lifts human life above the level of farce, and gives it some   |  
 | of the grace of tragedy   -  Steven Weinberg                        |
 +---------------------------------------------------------------------+
From: ojuarez@mtecv2.mty.itesm.mx (Octavio Juarez Espinosa)
Newsgroups: sci.math
Subject: looking for a source code for graphical tool for math. teaching.
Summary: I need source code
Keywords: source code graphical tool
Date: 17 Apr 92 17:11:17 GMT
Organization: I.T.E.S.M. Campus Monterrey



Hi,

I am a mexican teacher and I am very interested for to receive  source
code for mathemetical graphics. 
I'll appreciate if you send me some references (books, articles,etc)
about this area.

Thanks in advance.

Sincerely,


Octavio Juarez
ojuarez@mtecv2.mty.itesm.mx
From: jmarlan@titan.nmt.edu (Jon Marlan)
Newsgroups: sci.math
Subject: Thanks
Date: 7 Apr 92 20:17:15 GMT
Article-I.D.: nmt.1992Apr7.201715.22712
Organization: New Mexico Institute of Mining and Technology

I just wanted to thank everyone who offered to help me out, 
especially Michael (michaelc@osceola.cs.ucf.edu) who I couldn't
seem to reach via e-mail.   

Jon

-------------------------------------------------------
"You are what goes into your mind" -- Zig Ziglar
-------------------------------------------------------
From: sibley@math.psu.edu (David Sibley)
Newsgroups: sci.math
Subject: Re: fun with primes
Date: 6 Apr 92 16:44:45 GMT
Reply-To: sibley@math.psu.edu
Organization: Dept. of Mathematics, Penn State University

>The only primes in A are the ones in S.

Up to associates, of course. Should have said that originally.  Sorry.

And of course there's always the question of whether to count 0 as a
prime.

David Sibley
sibley@math.psu.edu
Newsgroups: sci.math
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: fun with primes
Keywords: prime numbers
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Mon, 6 Apr 1992 18:24:51 GMT

In article <1992Apr2.205716.2004@informix.com> proberts@informix.com (Paul Roberts) writes:
:In article <um4JiB3w164w@obmarket.UUCP> michaelc@obmarket.UUCP (Michael Campbell) writes:
:>proberts@informix.com (Paul Roberts) writes:
:>
:>> 
:>> Er, supposing p!+1 has factors, but none of them are prime?
:>> (Just an innocent question .... :-)
:>> 
:>> Paul
:>
:>
:>[...]
:>Now, we know all composite numbers are the product of some number of
:>primes. 
:>[...]
:
:Right, but I am just being awkward by expressing scepticism of this
:claim, since it is much harder to prove than any other step in the
:proof (I think). Comes of just having re-read "Mathematics made difficult".
:
:Maybe p!+1 has factors which are not prime, and they in turn have
:factors that are not prime, etc, etc? 
 
I don't see any smileys here, so I must assume these posts are serious.

To all of you who keep asking these questions I would suggest running
to your nearest bookstore or library, getting a book on elementary
number theory, and looking up the Fundamental Theorem of Arithmetic.

EVERY integer is the product of prime factors in a unique way (up to order).

Let me try to shed a little light on the confusion around Euclid's proof that
there are an infinite number of primes.

Suppose there are only a finite number of primes. (2,3,5,7,11,.....N) for
some N. Consider the number S =  2*3*5*7*11*.... *N + 1.  This is NOT N!+1,
but only the product of the primes up to and including N.
 
Now S is not divisible by any of 2,3,5,7,11,.....N since it leaves a
remainder of 1. Therefore if S is composite, then it is divisible by
a prime not in our presumed finite set of primes. And if S is prime, then
it is not in our list. 

We have therefore shown that if we assume there is a finite list of primes,
there must be another prime that is not included in our list.

Contradiction.


Does this make it clear???????

--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
From: courtes@clipper.ens.fr (Francois Courtes)
Newsgroups: sci.math
Subject: Re: Tiling problem
Date: 9 Apr 92 16:54:40 GMT
Organization: Ecole Normale Superieure, PARIS, France

In article <1992Apr8.224056.10844@wdl.loral.com> mab@wdl39.wdl.loral.com (Mark A Biggar) writes:
> (...)
>Now the problem turns into tiling the shape made of X's above.
>
>	XXXXXXX
>         XXXXXX
>         XXXXXX
>         XXXXXX
>          XXXXX
>          XXXX
>          X
>
>This contains 35 x's so 7 may tile it.  But, if we checker board it like so:
>
>	XYXYXYX
>         XYXYXY
>         YXYXYX
>         XYXYXY
>          XYXYX
>          YXYX
>          X
>
>There are 19 X'x and 16 Y's.  combined with the fact that the shape can 
>have either 3 x's and 2 Y's or 2 X's and 3 Y's given us the following
>over specified set of simultanious equations:
>
>a + b = 7			a pieces of one parity and b of the other
>3a + 2b = 19			the a pieces will have 3 x's and the b's 2
>2a + 3b = 16			the b pieces will have 3 Y's and the a's 2
>
>There is no solution to this set of equations, so the above shape can not
>be tiled with the r pentanimo. 
>
What about a=5, b=2 ?

However, the above shape cannot be tiled because no r pentamino will reach
the leftmost X.
From: bs@gauss.mitre.org (Robert D. Silverman)
Newsgroups: sci.math
Subject: Re: Fermat's Last Theorem
Date: 9 Apr 92 13:33:16 GMT
Article-I.D.: linus.1992Apr9.133316.24615
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA

In article <sundquis.702591357@s6.math.umn.edu> sundquis@s6.math.umn.edu (Thomas Sundquist) writes:
:>   >>No, Erdos only offers money for his own problems.
:>   >Pardon my ignorance. Who is this Erdos dude?
:
:>   You're joking right???  April 1 is tomorrow, not today, right???
:>   This must be a joke. How can anyone who reads or posts to this newsgroup
:>   not know who Paul Erdos is???
:>   I can understand Joe Blow off the street not knowing, but how can anyone
:>   with an interest in math [evidenced by the fact that he reads this group]
:>   Bob Silverman
:>   These are my opinions and not MITRE's.
:>   Mitre Corporation, Bedford, MA 01730
:
:>Come on, Bob, as a reader of this group you must have noticed that its
:>contributors range from the professional to the not-so-professional.
:>Why not just answer the question? After all, the poster says "Pardon
:>my ignorance", and then he does not deserve to be run over like that.
:>Stein 
:
:My thoughts exactly.	Tom


Huh?  I was simply expressing my surprise that someone who claims an
interest in math did not know who one of the greatest mathematicians of
the 20th century is!!! How is that "running over someone"???

The relevent phrase is "interest in mathematics". One need not be a
professional to still recognize who the outstanding contibutors are!

You are probably not a professional sports player, yet I'm sure you
know who the greatest pros are. Why do you know? Because you are
interested in sports and follow them! Why should not the same thing
apply in mathematics??? 
--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
Newsgroups: sci.aeronautics,soc.veterans
From: maddog@kuhub.cc.ukans.edu
Newsgroups: sci.aeronautics
Subject: Sonic Boom stuff.        :-)
Date: 12 Apr 92 14:41:22 GMT
Article-I.D.: kuhub.1992Apr12.094123.39265
Organization: University of Kansas Academic Computing Services

When a sonic boom is heard, there are actually two shock waves hitting the
observer.  The first is formed at the nose of the aircraft (assuming, of course
it is the furthest forward point) and the second is at the trailing edge of the
wing or aircraft where the pressure gradient returns to normal.  These two
booms are so close together that they sound like one boom.

The aerodynamic center does move aft as the plane crosses the sonic mark.  It
starts at roughly 1/4 chord subsonic, and ends up at roughly 1/2 chord after 
Mach 1.

One thing to note.  Just because the plane is going over Mach 1 doesn't mean
that an observer will hear a boom.  The shock wave dissipates through the
atmosphere as the pressure differential is "eaten away" and returns to uniform
pressure.  If the shock wave is strong enough (the faster the speed, the more
pressure difference and higher Mach angle) and if the aircraft is low enough
(so that the atmosphere doesn't absorb the pressure differential) the observer
will get a nice BOOM!  . . .or two, as I mentioned before.

This explanation is very crude.  I'm sure mine won't be the last, either.  So,
feel free to add to what I've said.  (Anybody wanna tackle a "simple"
explanation of a shock wave?)  :-)

Catch me later!

					Maddog
				Programmed to serve. . .
From: hobbes@den.mmc.com
Newsgroups: sci.aeronautics
Subject: Exhaust plume induced oscillations???
Summary: Looking for information on rocket plume induced oscillations on cables
Keywords: plume, oscillations, cable
Date: 9 Apr 92 17:37:28 GMT
Organization: Denver, Colorado



Wind induced oscillations of cables (telephone, electric, guy wires, etc)
is a fairly well known phenomenon.  Even if a lot of theory does not exist 
for this phenomenon (does anyone know IF there IS much theory on this 
phenomenon?), there seems to exist much empirical information.  This emp-
irical data seems primarily concerned with cable frequency vs. Strouhal
number where Strouhal number is a funtion of Reynold's number for different
shapes;  with cable frequency vs. wind speed;  cable frequency vs. Reynold's 
number, etc.

All this empirical information which has been around for a long time for
civil engineers and civil type structure is primarily concerned with low
subsonic wind flows... 0->200 mph.

Does anyone know of reference material / studies / methods / charts etc.
for cable vibration/frequency/galloping/magnitude of dynamic forces developed/
etc. for transonic/supersonic flow past cables?  - in general, or specifically
for cables in a jet/rocket engine exhaust plume?  maybe even for a 
solid rocket motor plume, with it's stream of particulate matter?

Thanks in advance for any leads,

-Steve Camp
Martin Marietta Corp
hobbes@spacemanspiff.den.mmc.com
Newsgroups: sci.aeronautics
From: cabruen@athena.mit.edu (Charles Alan Bruen)
Subject: Anybody know where these people are?
Organization: Massachusetts Institute of Technology
Distribution: usa
Date: Sun, 12 Apr 1992 22:12:52 GMT

Hello:

I having been wondering where these people are, or what they are up to
now.


1. MacCready. Of Gossamer and HPA fame.

2. Paul Poberenzy - a driver behind the formation of EAA

3. Bob Traux - also EAA

Thanks.


Charles Bruen
cabruen@athena.mit.edu
From: mm2j@vax5.cit.cornell.edu
Newsgroups: sci.aeronautics
Subject: 747-400
Date: 6 Apr 92 17:07:03 EST
Distribution: sci
Organization: Cornell University

Can anybody tell me about 747-400 performance, (range, cieling, endurance....)
and also about the engines/avionics?
The 747 is the most beautiful plane in the world, and I just want to find 
out some real facts about it...












Newsgroups: sci.aeronautics
From: br105@cleveland.Freenet.Edu (Jeffrey A. Del Col)
Subject: Re: XB-70 Valkyrie (was: Re: Sonic Boom stuff.        :-)
Organization: Case Western Reserve University, Cleveland, Ohio, (USA)
Date: Fri, 17 Apr 92 13:32:57 GMT


I believe the stainless steel honeycomb structures were brazed,
not glued.  It was a production nightmare.  They also had
many hours of hair-pulling struggle to get the viton lined
fuel tanks to seal--never did get all the leaks stopped. At
least one fuel tank in one of the planes was unusable because
of this.

They used high speed pumps to redistribute fuel to adjust CG in
flight.  I don't know if fuel was used as a collant.  According
to Steve Pace's book VALKYRIE  NORTH AMERICAN XB-70A, the 
insulating properties of the honeycomb structure protected the
fuel tanks.  

The XB-70 co-pilot killed in the mid-air was Maj. Carl S. Cross.
Al White managed to pull his arm into the clamshell, but dislocated
it in the process.  He also suffered back injuries because the
airbag on the bottom of the escape capsul failed to work.

It was a great ship, but, ironically, obsolete before it ever
got off the ground.

All the time NA was working t  on the Valkyrie under the impression 
that it was going to be the first Mach 3 ship, Kelly Johnson and the
Skunk Works were building and flying the A-12.  Apparently NA was
never informed of what the Skunk Works was up to.  

J. Del Col
Newsgroups: sci.aeronautics
From: dlevy@viper.engin.umich.edu (David W Levy)
Subject: Re: Sonic Boom stuff.        :-)
Date: Thu, 16 Apr 92 09:16:54 EDT
Organization: University of Michigan Engineering, Ann Arbor
Originator: dlevy@viper.engin.umich.edu


In article <15APR199223181904@zeus.tamu.edu>, bdd0066@zeus.tamu.edu (Bryan, kick the tire and light the fire, Duke) writes:
> There was a plane (Valkyrie  (?)) designed a while back as a long range
> high speend bomber that rode it's own shockwave.  The outer panels of
> the wings were movable in flight to (ummmmm..) make use of the energy
> lost in the shock wave.  The only prototype (i think) was lost in a 
> *high* speed collision with an f-104.  They planes were flying in 
> formation and the lillle fighter crept up knocked the bomber out of
> the sky.  The project was cancelled.  Too bad.  Actually, I think
> it was cancelled because somebody thought that the soviets could hit it
> with their SAMs.   
> 
There were two XB-70 Valkyrie bomber prototypes.  One was lost in the incident
you describe.  The F-104 got caught in the wake vortex of the XB-70 and
caught its vertical tail on the wing as it tried to move forward out of
the way.  The F-104 pitched up and went over the top of the XB-70 taking
the two vertical tails out and killing the F104 pilot.  The XB-70 went into
a flat spin and crashed.

I'm not sure about the details, but I understand
the XB-70 was equipped with an ejection capsule, and the pilot and copilot
seats were designed to retract into the capsule before ejection.  However,
during the spin, the outward g-forces wee in the 5-6 range, so the seat
retraction system didn't work right.  Not everyone made it out.

The F-104 and XB-70 were on a photo mission for General Electric, with at
least one other airplane (an F-4?).  GE wanted a picture of all these airplanes
which were equipped with GE engines.  Anybody else have more info?

The other prototype is on display at the USAF Museum in Dayton, Ohio,
in the Modern Flight Gallery.  Go see it, it is very impressive.
From: crouse@eng.umd.edu (Gil Crouse)
Newsgroups: sci.aeronautics
Subject: Re: Aeronautical misconceptions
Summary: Be careful what you call a "myth"!
Date: 7 Apr 92 02:26:35 GMT
Organization: University of Maryland

Max Feil (mkfeil@bnr.ca) wrote:
>
>                   AERONAUTICAL MYTHS AND MISCONCEPTIONS
>                   -------------------------------------
>
>Myths propagated by "informed" people, who should know better:
>
>1. Explanation of Lift
>
>A wing produces lift because the top surface of the wing is longer. The air
>flowing over the top of the wing has to travel faster to meet up with the
>air flowing over the bottom of the wing. Lift is then created by Bernoulli's
>principle which states that faster flowing air exerts less pressure.


This was just beat into the ground, but I guess it still isn't clear
to all.  This is NOT a misconception.  It is an explanation of
what happens on a lifting surface.  It is an observable fact, that the
air on a lifting surface moves faster over the upper surface than the
lower surface and thus there is a pressure difference between the
upper and lower surface and thus lift is generated.

The counter example that Mr. Feil gave was that of a flat plate, but
I'll talk about the general case of a symmetric airfoil.  On a
symmetric airfoil at a positive angle of attack, the stagnation point
at the leading edge moves onto the lower surface as the angle of
attack increases.  This implies that the distance from the stagnation
point at the leading edge (LE) around the top surface to the
stagnation point at the trailing edge (TE) is LONGER than the distance
from the stagnation point at the LE around the lower surface to the
stagnation point at the TE.  Thus the air traveling over the upper
surface does in fact travel further than the air over the lower
surface, EVEN FOR A SYMMETRIC AIRFOIL!!!!!

As has been hotly debated recently, this may or may not be a good
explanation of the origin of lift, but is a valid observation about
what occurs when lift is generated.

Gil Crouse
Newsgroups: sci.aeronautics
From: br105@cleveland.Freenet.Edu (Jeffrey A. Del Col)
Subject: Cooling the Valkyrie
Organization: Case Western Reserve University, Cleveland, Ohio, (USA)
Date: Fri, 17 Apr 92 14:16:55 GMT


The crew cabin, wheel wells, electronics bays and braking chute
compartments were cooled by something called a "transpiration
water wall" system that used heat exchangers and powerful 
refrigeration units to maintain a 70-80F temperature.

Titanium (about 9.5% of overall vehicle weight) was used to
form the fuselage forward of the wings, the canards, the vertical
stabilizers, the leading edge of part of the wings and the
aft housing of the engines. For the rest, the heat resistance
of the stainless steel honeycomb was essential.  Pieces of the
outer skin of the wings and the area in front of the intakes
ripped loose during several flights.  In one case about
one square meter's worth got sucked into the engines--FOD
from hell!  The cause of the faile  failures was a combination
of heat and flex stress.  Considering that the overall area of
the wings was 6.300  6,300 sq ft. a few chunks here and there
wasn't too bad:-).

A friend of mine who was present at Edwards wheen the Valkyrie's
were being tested says that the noise on take-off was hellacious.

J. Del Col
Newsgroups: sci.aeronautics
From: pdb1@ra.msstate.edu (Philip D Bridges)
Subject: Re: Augmenting cooling by exaust pipe placement
Organization: Mississippi State University
Date: Thu, 16 Apr 1992 18:53:13 GMT

geoffm@purplehaze.Corp.Sun.COM (Geoff Miller) writes:


>This idea was used on the Convair 240/340/440 series of airliners back
>in the Fifties.  The exhaust pipes terminated inside the cowling, just
>in front of a pair of trumpet-shaped devices called augmentors; there
>were two per engine.  This setup obviated the need for cowl flaps.  If
>you've ever seen a Convair-Liner that hasn't been converted to turboprop
>engines (540/580/600), you might've noticed how smooth the cowlings are
>compared to those on contemporary machines like the DC-6 (which uses the
>same engine, incidentally, the P&W R-2800).

The Beech T-34 also used augmentor cooling for its IO-470. One problem
is getting adequate cooling during taxiing and holding on the ground,
since there is little exhaust flow to pump the cooling flow through.
The Navy installed an extra oil cooler on the T-34B to alleviate this.
Dr. Stan Miley, when he was with us, conducted extensive tests on 
cooling drag of aircraft. His work was published in some SAE papers
and a NASA Contract Report, somewhere around 1980. This would 
probably provide some data on this cooling arrangement.


 

--------------------------------------------------------------------------
|      Philip Bridges                 |  "Strive for design simplicity:  |
|      Dept. of Aerospace Eng.        |   you never have to fix anything |
|      Miss. State University         |   you leave out."                |
|      (601) 325-3623                 |                                  |
|      pdb1@ra.msstate.edu            |           Bill Lear (1903-1978)  |
--------------------------------------------------------------------------

Newsgroups: sci.aeronautics