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Given a plane convex closed curve
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William Elliot
science forum Guru


Joined: 24 Mar 2005
Posts: 1906

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: Easy set theory query Reply with quote

Damn, I've already given an answer in other newsgroup. Do
learn to cross post into two groups at once as I've done here.

On Thu, 24 Feb 2005, Dylan wrote:

Quote:
What does it mean for a set to be *consistent* with another?

What does it mean for that consistency to be transitive and reflexive?

Any explanations are references will be welcome

(This is not a homework question btw. I'm a 46 year old programmer
with math anxiety trying to implement an algorithm written in pseudo
code)
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Paul Murray
science forum beginner


Joined: 30 Apr 2005
Posts: 12

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: lumens question Reply with quote

Quote:
BTW, rather than describing the inner circle as "white", it might be
more correct to say it is clear.

Damn, is *everything* in the US about race? Or is this a scientology joke?
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sdr
science forum addict


Joined: 27 Jun 2005
Posts: 82

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: The Origin of The Universe / S D Rodrian Reply with quote

Lady Chatterly <not-bot@catcher.in.the.rye> wrote in message
news:<3917370.2e828904@news.1usenet.com>...
Quote:
In article <58087ec7.0502152341.1d00e31f@posting.google.com
sdrodrian@sdrodrian.com (SDR) wrote:

"Bill Hobba" <bhobba@rubbish.net.au> wrote in message news:<XbzQd.162847$K7.141657@news-server.bigpond.net.au>...
"SDR" <sdrodrian@sdrodrian.com> wrote in message
news:58087ec7.0502150144.7c65764d@posting.google.com...
Uncle Al <UncleAl0@hate.spam.net> wrote in message
news:<42116116.D7319A61@hate.spam.net>...
SDR wrote:
[snip insignificance]

God fart. The universe and everything in it is an ignited god fart.

Well, that's ... nice. But, do you happen to know
what God could have possibly been eating to cause
Him to undergo such an all-get-out (and get-out-of-
my-way) blow?

S D Rodrian
http://poems.sdrodrian.com
http://physics.sdrodrian.com
http://ar.sdrodrian.com
http://music.sdrodrian.com

Always base yourself firmly on reality not math: Math
can be made to stand for anything and thereby give any
results you like. But once you start trying to substitute
other things for reality... well, that's obviously crazy.

Such rot always gives me a laugh.

Okay... one vote for crazy.

So the particle does not work.

That's correct: The particle gets stuck right when
you're trying to do your work. The answer is to
scrub harder, or to use a harsher cleaning fluid.
Although there's no guarantee this'll work either.
Sometimes the best thing's to just consider it a
past particle and leave it to the semantics freaks.

Quote:
Physics is not math and physicists and
mathematicians know this eg Hilberts famous remark - "Every boy in the
streets of Gottingen understands more about four-dimensional geometry than
Einstein.

I rather suspect Hilbert's boys were probably up to
no good, just like all such boys should (be).

The only way you can control anybody is to lie to them.

No. For example, you could threaten to let one go (lot-of-
times this is even more effective... in the end). Or you
could ask somebody's mother--they're experts on this stuff.

Quote:
Yet, in spite of that, Einstein did the work and not the
mathematicians.' http://www.math.umn.edu/~wittman/Biography.html.
However math is the natural language of physics.

Especially that part that's all about equations, yes.

Good one.

Everybody has one good 1 in them (sooner or later).
Sometimes it's by design, sometimes it's an accident,
and sometimes it's in prison.

Quote:
You often see rot from
cranks like GR can not be true because it is just a math theory.

Ok. You can stop saying that now.

Jus ' waitin '.

Good job. You do it very well, albeit in slang.

Quote:
Anyone who
has studied math to second year uni level can grasp the math of GR.

.... but not the math of bicycle building: That takes
at least a third year level.

So the popup stopper is pointless to study it.

This is a very telling sentence: I would copy it down
carefully, and show it to your doctor: Tell him/her that
you demand a brain scan on an IMMEDIATE emergency basis
and that you're willing to pay CASH (that'll expedite it).

Quote:
Understanding the physics is a lot harder and by far the most important
part. Bill

Well, as long as you understand where the PHYSICS part
comes from (physical, as in "the stuff you can touch/feel")
all's right with the world then!

Nada.

Waitaminute: I know this word. It's either Hindu for "Shirley"
or Spanish for "swims" (either way it's very Impressionist).

Darn this vile, unraveling thread!

Quote:
S D Rodrian
http://poems.sdrodrian.com
http://physics.sdrodrian.com
http://ar.sdrodrian.com
http://music.sdrodrian.com

When the measurements become more important than what
they measure... that disconnect right there, that's pretty
much modern physics. And then... what can one not build
on such numbers!

Why, you could even build time travel and worm holes
from past to present, or even future to past... without
having to take into consideration the little matter of
the past and the future having no separate existence.
And nifty tricks like that...

They are defending ron and the rest of us become abstract.

Madam, we are on the cutting edge of idiocy here!
Do you really hunger to out-expert us all that much?

For fiction's sake, Lady, to thy lover go thou back...
you can use one of those Fridge-moving dollies upon
which you can pretend you're one of the dead locust.

S D Rodrian
http://poems.sdrodrian.com
http://physics.sdrodrian.com
http://ar.sdrodrian.com
http://music.sdrodrian.com
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Bill Dubuque
science forum Guru Wannabe


Joined: 04 May 2005
Posts: 236

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: Infinite integers Reply with quote

magidin@math.berkeley.edu (Arturo Magidin) wrote:
Quote:
slowhands <bullypug_gummer@yahoo.com> wrote:

I am wondering if integers are all considered to be finite?

All integers are indeed finite. It follows from the Induction
Principle (Peano's 5th Axiom).

It's clearer contrapositively, i.e. by descent.
For if n were the smallest infinite integer
then n-1 would be a smaller one.

I.e. w infinite => w > w-1 > w-2 > ... is an
infinite descending chain of infinite numbers > 0,
something which can't occur in any well-ordered set
such as the positive integers.

A simple model is the set of polynomials in x with
real coefs, ordered by f(x) > g(x) if it is true
eventually for x large enough (i.e. "at x = oo");
equivalently f(x) > 0 iff its leading coef is > 0.
Then x > x-1 > x-2 > ... > r, all reals r in R.
See also my prior post [1].

--Bill Dubuque

[1] http://groups-beta.google.com/group/sci.math/msg/8f40e6eed6af2e20
http://google.com/groups?selm=y8zof42c4ws.fsf@nestle.ai.mit.edu
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Gottfried Helms
science forum Guru


Joined: 24 Mar 2005
Posts: 301

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: Infinite integers Reply with quote

Hi Tim -
Am 06.02.05 12:26 schrieb Timothy Little:

Quote:
Yes, but an alternative could be, that one could find an infinite
sum of such "ultimate" periodic strings, each one -for instance-
shifted by one digit like

....3333333333
+ ....1111111110
+ ....4242424700
+...
etc. (assumed a certain, but simple (or analyzable) regularity)
may give a non-periodic string, which mapping we could assume
to the sum of the equivalent rational numbers.


Hmm. It seems to me that such a sum would diverge:

...33333333 maps to -1/3,
...11111110 maps to -10/9,
...42424700 maps to 15100/33 if I understand correctly,
etc, the magnitude increasing each step.


- Tim

Yepp - I don't know myself. When I was fiddling around
with these strings some years ago, I stopped, when I couldn't
find a plausible map for non-periodic such strings.
Now philippe 92 presents two aperiodic strings, formally
satisfying x = x .
Thought it would be nice to give it a shot... Wink
Btw: does one exist with x^3 = x (et al.)?

Gottfried
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Timothy Little
science forum Guru Wannabe


Joined: 30 May 2005
Posts: 295

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: Infinite integers Reply with quote

Gottfried Helms wrote:
Quote:
Upps, sorry; a negative rational between 0..-1 squared gives
a positive value. This value can be understand as another
negative rational of the same range plus 1.

Ahh, OK.


Quote:
Yes, but an alternative could be, that one could find an infinite
sum of such "ultimate" periodic strings, each one -for instance-
shifted by one digit like

....3333333333
+ ....1111111110
+ ....4242424700
+...
etc. (assumed a certain, but simple (or analyzable) regularity)
may give a non-periodic string, which mapping we could assume
to the sum of the equivalent rational numbers.

Hmm. It seems to me that such a sum would diverge:

....33333333 maps to -1/3,
....11111110 maps to -10/9,
....42424700 maps to 15100/33 if I understand correctly,
etc, the magnitude increasing each step.


- Tim
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Gottfried Helms
science forum Guru


Joined: 24 Mar 2005
Posts: 301

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: Infinite integers Reply with quote

Am 05.02.05 23:23 schrieb Timothy Little:
Quote:
Gottfried Helms wrote:

one subsequent question. Since *periodic* strings of this type can
be mapped to the negative rationals between 0 and -1


Err, the product of two negative rationals is a negative rational?

Upps, sorry; a negative rational between 0..-1 squared gives

a positive value. This value can be understand as another
negative rational of the same range plus 1.
So the infinite periodic string becomes only *ultimately* periodic;
say
...3333333333 * ...33333333333 -> ...88888888888888 + 1 -> ...8889
-1/3 -1/3 -8/9 + 1

Sorry, it's a bit time, that I played with that around.
Quote:

(being consistent under addition and multiplication), what do you
think, the third and fourth number could be mapped to, preserving
the addition/multiplication consistency. Can that be answered?


If anything they must map to either 0 or 1, since X^2 = X has only
those two real solutions.

Yes, but an alternative could be, that one could find an infinite

sum of such "ultimate" periodic strings, each one -for instance-
shifted by one digit like

....3333333333
+ ....1111111110
+ ....4242424700
+...
etc. (assumed a certain, but simple (or analyzable) regularity)
may give a non-periodic string, which mapping we could assume
to the sum of the equivalent rational numbers.

Somehow this X^2 = X reminded me to this phi^2 = phi + 1 and I
was wondering, whether one could find a solution this way.


Quote:

- Tim

Gottfried
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Timothy Little
science forum Guru Wannabe


Joined: 30 May 2005
Posts: 295

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: Infinite integers Reply with quote

Gottfried Helms wrote:
Quote:
one subsequent question. Since *periodic* strings of this type can
be mapped to the negative rationals between 0 and -1

Err, the product of two negative rationals is a negative rational?

Quote:
(being consistent under addition and multiplication), what do you
think, the third and fourth number could be mapped to, preserving
the addition/multiplication consistency. Can that be answered?

If anything they must map to either 0 or 1, since X^2 = X has only
those two real solutions.


- Tim
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Gottfried Helms
science forum Guru


Joined: 24 Mar 2005
Posts: 301

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: Infinite integers Reply with quote

Am 28.01.05 23:29 schrieb Philippe 92:

Quote:

For instance you could search for X^2 = X in this set.
there are exactly four solutions :
...00000
...00001
...77392256259918212890625
...22607743740081787109376

The two latter solving the puzzle :
"find a number with n digits, whose square is ended by these same
digits"

Have fun.

Hi -


one subsequent question. Since *periodic* strings of this type
can be mapped to the negative rationals between 0 and -1 (being
consistent under addition and multiplication), what do you think,
the third and fourth number could be mapped to, preserving
the addition/multiplication consistency. Can that be answered?

Gottfried Helms
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Lits O'Hate
science forum addict


Joined: 28 Apr 2005
Posts: 52

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: JSH: Big collapse on surrogate factoring Reply with quote

jstevh@msn.com wrote:
Quote:
As far as I'm concerned I've just had a massive collapse in terms of
getting surrogate factoring working, with a recent result that
indicates you kind of need to know the factors of M ahead of time to
guarantee a factorization.

Bah. You'll just flip a sign or increase an exponent and be back
tomorrow announcing yet again that you've "solved the factoring
problem!" You'll claim this article was part of your sooper seekrit
experiment on the Usenet participants.

Hopefully we'll be treated to appearances from The Hammer and, my
personal favorite, Death Incarnate.
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fiziwig
science forum beginner


Joined: 03 Apr 2005
Posts: 36

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: JSH: Big collapse on surrogate factoring Reply with quote

This is not really a "proof", but it seems like a reasonable claim just
the same.

Let M be written pq. Is there any function not involving either p or q
explicitly that will yeild a term that has either p or q separate from
the other? In fact, no algebraic operation can pry p away from q
without explicitly using p or q. In other words, no surrogate
factoring method can work without explicitly knowing p or q in advance.

kpq; multiplication does not separate p from q.
pq/k; division does not separate p from q.
pq+k; addition does not separate p from q.
pq-k; subtraction does not separate p from q.
(pq)^k = p^k * q^k; exponentiation does not separate p from q.
X mod (pq) does not separate p from q.
pq mod X where X does not already explicity separate p and q does not
separate p from q.

No combination of the above operations will separate p from q. Thus p
cannot be separated from q algebraicly. Thus surrogate factoring is
not possible.

Disclaimer: I'm just an amateur, so there may be holes in my reasoning.
If so, feel free to give a counterexample.

--gary shannon
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Bob Pease
science forum beginner


Joined: 29 Apr 2005
Posts: 47

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: Given a plane convex closed curve Reply with quote

<astanoff@yahoo.fr> wrote in message
news:1111663342.606914.272940@f14g2000cwb.googlegroups.com...
Quote:
Thank you for clearing what was confused :
"circumference/greatest diameter <= pi "
that was exactly what i meant but could not state
correctly maybe due to my poor english !

v.a.

My first approach would be to make it the class of all curves which could be
inscribed in a unit circle.
This seems to be wlog.

Then show that by calculus that L( r (theta) ) 0,2PI is minimized iff r
= a constant .

It seems to be a difficult problem to me.

RJ P
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Guest






PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: Given a plane convex closed curve Reply with quote

Thank you for clearing what was confused :
"circumference/greatest diameter <= pi "
that was exactly what i meant but could not state
correctly maybe due to my poor english !

v.a.
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Henry1
science forum addict


Joined: 15 May 2005
Posts: 58

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: Given a plane convex closed curve Reply with quote

On 24 Mar 2005 01:32:53 -0800, astanoff@yahoo.fr (Valeri Astanoff)
wrote:
Quote:
Given a plane convex closed curve,
show that its ratio diameter/length is at most pi.

You may have to tidy up the question slightly first.
I assume that by "length" you mean "circumference",
and by "diameter" you mean the greatest distance between two points on
the curve
and that you are really saying circumference/greatest diameter <= pi
(i.e. the reverse of what you did say).
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Rainer Rosenthal
science forum Guru Wannabe


Joined: 29 Apr 2005
Posts: 114

PostPosted: Thu Mar 24, 2005 7:53 pm    Post subject: Re: A day of a CAS super-hero Reply with quote

"Alec Mihailovs" wrote
Quote:

That is a good demonstration of one specific
weakness of automated bug testing. Most of the
bugs that were found that way are such bugs
that nobody meets in real calculations and
nobody cares about (except automated bug
testing system creator).

.... and here we enter the recreational part!

There is an old joke of mine, which I am quite
proud of:

Two programs meet.
Says the one:
"Do you still believe in programmers?"

Best regards,
Rainer Rosenthal
r.rosenthal@web.de
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