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Trigonometric equations
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Lee Rudolph
science forum Guru


Joined: 28 Apr 2005
Posts: 566

PostPosted: Thu May 18, 2006 12:48 pm    Post subject: Re: Graph theory Reply with quote

mareg@mimosa.csv.warwick.ac.uk () writes:

Quote:
In article <1147902034.984619.215610@u72g2000cwu.googlegroups.com>,
"Clocker" <ugoren@gmail.com> writes:
G is connected !!!!


All upper case letters are connected - but i and j are disconnected.

Now *there's* a romanocentric viewpoint for you. What about
\Theta and \Xi, eh?

Lee Rudolph
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Proginoskes
science forum Guru


Joined: 29 Apr 2005
Posts: 2593

PostPosted: Fri May 19, 2006 4:59 am    Post subject: Re: Graph theory Reply with quote

Gerry Myerson wrote:
Quote:
In article <e4hqf7$4id$1@panix2.panix.com>,
lrudolph@panix.com (Lee Rudolph) wrote:

mareg@mimosa.csv.warwick.ac.uk () writes:

In article <1147902034.984619.215610@u72g2000cwu.googlegroups.com>,
"Clocker" <ugoren@gmail.com> writes:
G is connected !!!!


All upper case letters are connected - but i and j are disconnected.

Now *there's* a romanocentric viewpoint for you. What about
\Theta and \Xi, eh?

Not to mention the 5th letter of the Hebrew alphabet (are there
TeX sequences for Hebrew letters?).

TeX offers \Aleph for the first one. Otherwise, I think you need to
download a Hebrew font.

--- Christopher Heckman
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Matlock
science forum beginner


Joined: 19 May 2006
Posts: 13

PostPosted: Fri May 26, 2006 7:24 am    Post subject: Re: What does the area under a curve actually mean? Reply with quote

Well I must say that you have asked a very good question.If I am not
mistaken then you are trying to grasp the concept and abstractness of
mathematics.I will recommend you to read as many booksyou can and
always ask why and THINK.First of all you should know that when you
find the area of a velocity graph then you get distance not the
position.Now you are aware that distance = velocity * time. A
multiplication on a graph is always represented by an area.Thus the
area on a velocity time graph gives you the distance.To understand what
does an "area under a curve" means then you should know that a curve is
made up of infinite straight lines.Now join the end points of these
straight lines to the base perpendicularly.Thus you get infinite
rectangle.Find the area of the rectangles and add you will get the area
of the curve.This is how the integral calculus was invented.There is a
famous paradox which goes like this

"If a body moves from A to B then before it reaches B it passes through
the mid-point, say B1 of AB. Now to move to B1 it must first reach the
mid-point B2 of AB1 . Continue this argument to see that A must move
through an infinite number of distances and so cannot move".

A method of exhaustion was practiced by Greek mathematician
Archimedes.They practiced the method of finding the area using the
method infinite series.

Well regarding what is the difference between differentiation and
integration is that the slope the curve selects a a single point on the
curve and draw the tangent and find the tan of the angle you get.Thus
it selects only one point. Integration adds all the area of the
rectangle so it unconsciously adds all the point.I hope this will
satisfy your answer.
You should read lots and lots of books for one topic and always THINK
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Amadeus Train-Owwell Zirc
science forum Guru


Joined: 24 Mar 2005
Posts: 507

PostPosted: Sat May 27, 2006 3:25 am    Post subject: Re: What does the area under a curve actually mean? Reply with quote

Newton didn't do that, contrary to the Royal Society Industry;
for instance, the only calculus in *Principia* is "dxdy,"
that little rectangle (book2section2paragraph2, as I recall,
as told at a 15' talk at the first joint North and South Calif. Meeting
of the MAA .-)

thus:
that's beautiful -- when I configure it out.

thus quoth:
Larson-Hostetler-Edwards, for instance, call the above the *second* F
T of C. To them, "the" F T of C is that when F(x) is an
antiderivative of f(x) then
integral[ f(x) dx, a, b ] = F(b) - F(a)

thus:
I tend to go with Bucky -- with *some* math thrown in, but,
as LaRouche says, the "quod erat demonstrandum"
of Euclid is rather antipythagorean --
which is how the stuff was dyscovered.

that said, Euclid can profitably be digested,
by starting with Book XIV by Hyspicles,
which is in accordance with one of Bucky's better dicta.

(I am not a "buckywitch;" see the last URL in my sig .-)

Quote:
think that learning geometry by looking at shapes and
memorizing formulas instead of a good Euclid course is even
adequate, and that understanding induction is not needed,
how can the children learn anything important?

--It takes at least two to polka!
http://www.lsbu.ac.uk/water/anmlies.html
http://www.21stcenturysciencetech.com/2006_articles/Keplerian.W05.pdf
http://larouchepub.com/other/2006/3315greenland_ice.html
http://members.tripod.com/~american_almanac
http://wlym.com/pdf/iclc/walterlippman.pdf
http://www.benfranklinbooks.com/
http://tarpley.net/bush12.htm
http://www.wlym.com/pdf/iclc/howthenation.pdf
http://larouchepub.com/other/2003/3048iraq_58_const.html
http://www.rand.org/publications/randreview/issues/rr.12.00/
http://www.rwgrayprojects.com/synergetics/plates/figs/plate01.html
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Brian M. Scott
science forum Guru


Joined: 10 May 2005
Posts: 332

PostPosted: Sun May 28, 2006 4:07 pm    Post subject: Re: Optimizing a rectangle Reply with quote

On 28 May 2006 09:01:48 -0700, DarkProtoman
<Protoman2050@gmail.com> wrote in
<news:1148832108.625462.199620@u72g2000cwu.googlegroups.com>
in alt.math.undergrad,alt.algebra.help:

Quote:
Is my answer to this rectangle perimeter optimization problem correct?

Work:

Area=xy
Perimeter=2x+2y=100

[...]

Quote:
Max area=49 units^2

Stop and think for a moment. Is a long, skinny rectangle
going to have more or less area than a square of the same
perimeter?

Or just experiment a little. Instead of a 49 x 1 rectangle,
try 40 x 10, which still has a perimeter of 100: its area is
400 units^2.

Your actual calculation makes almost no sense, I'm afraid.
Using the second equation to write y = 50 - x is fine, but
now you need to substitute that into A = xy to get A as a
function of x. Then the derivative dA/dx can be used to
find where A has its maximum.

[...]

Brian
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lingyai
science forum beginner


Joined: 14 Apr 2006
Posts: 21

PostPosted: Mon May 29, 2006 9:22 am    Post subject: Re: Self-serving limitations, math world needs scrutiny Reply with quote

This a somewhat narrow response to Bob Marlow's response to the original post.

Bob, twice you write "English is not your first language is it?" with reference to passeges in James' original.

English is my first language, and I fail to see what you mean. Those passages are error-free.

If you want to fault someone or something, it might be better stick to real faults.

Regards,

Ken (lingyai)
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Robert B. Israel
science forum Guru


Joined: 24 Mar 2005
Posts: 2151

PostPosted: Tue May 30, 2006 1:34 am    Post subject: Re: Derivative/Integral of x^x Reply with quote

In article <1148900816.620649.62830@j33g2000cwa.googlegroups.com>,
Protoman <Protoman2050@gmail.com> wrote:
Quote:
What is the derivative/integral of x^x? I know they exist, b/c my
graphing calculator can calculate them, but what are the formulas?
Thanks!!!!!


As mentioned, the integral is not elementary. You can express it
in terms of a series, though: write
x^x = exp(x ln(x)) = sum_{n=0}^infty (x ln(x))^n/n!
[converging] for all x], so the antiderivative that is 0 at x=0 is
F(x) = sum_{n=0}^infty int_0^x (t ln(t))^n/n! dt
= sum_{n=0}^infty (-1)^n Gamma(n+1,-(n+1) ln(x))/(n! (n+1)^(n+1))
where Gamma(a,z) = int_z^infty exp(-t) t^(a-1) is the incomplete
Gamma function.

You can also write it as a double sum:
F(x) = sum_{n=0}^infty sum_{j=0}^n
(-1)^(n-j) ln(x)^j x^(n+1)/(j! (n+1)^(n-j+1))

In particular, F(1) = sum_{n=0}^infty (-1)^n/(n+1)^(n+1)

Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
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ya mutha
science forum beginner


Joined: 30 May 2006
Posts: 1

PostPosted: Tue May 30, 2006 3:01 am    Post subject: Re: Derivative/Integral of x^x Reply with quote

wel i realli dont care... i think u should jump off a cliff and tumble to death hahahahahi am the maths wizzard and may u hav BAD sex forever
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Robert B. Israel
science forum Guru


Joined: 24 Mar 2005
Posts: 2151

PostPosted: Tue May 30, 2006 3:42 am    Post subject: Re: Derivative/Integral of x^x Reply with quote

In article <1148959011.509791.325290@y43g2000cwc.googlegroups.com>,
Proginoskes <CCHeckman@gmail.com> wrote:
Quote:

Robert Israel wrote:
In article <1148900816.620649.62830@j33g2000cwa.googlegroups.com>,
Protoman <Protoman2050@gmail.com> wrote:
What is the derivative/integral of x^x? I know they exist, b/c my
graphing calculator can calculate them, but what are the formulas?
Thanks!!!!!


As mentioned, the integral is not elementary. You can express it
in terms of a series, though: write
x^x = exp(x ln(x)) = sum_{n=0}^infty (x ln(x))^n/n!
[converging] for all x],

Even if x <= 0?

Yes.
x^x = exp(x ln(x)) is true because in general we define
x^y = exp(y ln(x)). You can use this for all nonzero complex numbers
x, using whichever branch of ln you choose. Of course, different
branches give you different values.
And for x = 0 you identify x ln(x) as 0 so x^x is 1.

Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
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bigben
science forum beginner


Joined: 30 May 2006
Posts: 1

PostPosted: Tue May 30, 2006 2:23 pm    Post subject: Re: Derivative/Integral of x^x Reply with quote

If I am being you I say use the formulae x^a=ax^(x-1) put a=x and get x*x^(x-1)=x^x
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David Moran
science forum Guru Wannabe


Joined: 13 May 2005
Posts: 252

PostPosted: Mon Jun 05, 2006 12:35 am    Post subject: Re: JSH: But what if I AM right? Reply with quote

Quote:
No I am a real mathematician who clearly now must have an ace in the
hole.

To be a mathematician, you have to know something about mathematics. A
degree in physics doesn't qualify you to be a mathematician.

Dave
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Tim Smith
science forum beginner


Joined: 16 May 2005
Posts: 15

PostPosted: Mon Jun 05, 2006 7:04 am    Post subject: Re: JSH: Same prob in cosmology, wrong academics Reply with quote

In article <BLOCKSPAMfishfry-B86AC7.17081304062006@comcast.dca.giganews.com>, fishfry wrote:
Quote:
For those of you who used to feel proud about working in "pure
mathematics" before I pointed out that you are just relying on your
judgement and that of other people, hey, don't feel too bad.

Judgment, dude, judgment. One thing I like about you is your spelling is

Judgement is a correct spelling.

--
--Tim Smith
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Ben Young
science forum beginner


Joined: 15 Jun 2006
Posts: 9

PostPosted: Fri Jun 16, 2006 2:15 am    Post subject: Re: JSH: Fighting mathematical research Reply with quote

why do you waste time posting here?
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Ben Young
science forum beginner


Joined: 15 Jun 2006
Posts: 9

PostPosted: Wed Jun 28, 2006 1:08 pm    Post subject: Re: JSH: Politics Reply with quote

Quote:
The faster thing might be if it doesn't work well,
and someone could
prove that quickly.


This was proven by a poster in another one of your threads, who computationally compared your method versus random method and fermat's method.
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Patrick Hull
science forum beginner


Joined: 20 Jul 2006
Posts: 1

PostPosted: Thu Jul 20, 2006 4:05 am    Post subject: Re: JSH: Gloves are off now Reply with quote

i just wanted to say... wow.

-ph
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