On 11 Feb 00, at 16:51, Chip Lynch wrote:
> While I think the topic is stimulating and important, the Mersenne list
> probably isn't the best medium for it, unfortunately. Anyone recommend a
> few good links on the subject? (Pi, The Language of Mathematics, any of
> that)
"The Joy of Pi" by Da
> > At 10:50 AM 2/9/00 -0500, Jeff Woods wrote:
> > >You're bumping up against the Fundamental Theorem of Calculus here. Pi
> > >DOES have a precisely defined value, but you cannot express it in decimal
>
> > >form. You can express it as an infinite expansion, however.
Q: What does this have
On Fri, 11 Feb 2000 [EMAIL PROTECTED] wrote:
> It is my understanding that this list is for the promotion of the search
> for mersenne primes. I may be a laymen when it comes to mathematics, but to
> my knowlege, this is not a requirement of the list.
...
> I would hope that your opinion is in th
> Circumference/diameter is a ratio. The decimal value 3.1415->
...
> Seems to me a ratio is needed for pi.
you already gave it, the 'ratio of pi' is
circumference / diameter
There are NO two integers which can divide to create PI. Thats
why PI is considered a 'irrational' number. It ha
Disclaimer: I am not a mathematician. It is a hobby. I am a cabinetmaker.
At 03:19 PM 2/11/00 -0600, Jeremy Blosser wrote:
>I think the mistake you are making is that the *precision* of PI is infinite
>(never ending), but PI itself is not "infinity".
>
>3.14159.->ininite number of numbers
>
At 04:51 PM 2/11/00 -0500, Chip Lynch wrote:
>Language, NOT Mathematics, is (precisely) why these discussions are
>problematic. If you've ever read original works by Archimedes, Euclid,
>and others who try to define mathematics with a common language, you
>understand the frustration.
>
>While I t
> >> Infinite to me means never ending. A precisely defined value to me is a
> >> finite value.
> >
> > Your definition of infinite is not correct.
>
> Just glanced at my Websters Dictionary. infinite: 1. lacking limits; endless.
> Endless and never ending seem synonymous to me.
> What dictionar
I think the mistake you are making is that the *precision* of PI is infinite
(never ending), but PI itself is not "infinity".
3.14159.->ininite number of numbers
Since it is 3.something we know it is > 3 and < 4.
Take 1/3 for example.
Its decimal value us 0.3-> infinte # of 3's
At 01:14 PM 2/11/00 -0600, Kyle Evans wrote:
>
>> I have a circle with a area of 5 square inches drawn on my pad. 5 inches
>is
>> precise.
>
>You do?? How did you do that? Did you set your compass so that the points
>were exactly sqrt (5/pi) inches apart?
>
>What you probably have really is a
>Date: Fri, 11 Feb 2000 14:32:48 -0600
>To: "Vincent J. Mooney Jr." <[EMAIL PROTECTED]>
>From: [EMAIL PROTECTED]
>Subject: Re: Mersenne: Pi and Greek
>In-Reply-To: <[EMAIL PROTECTED]>
>
>Disclaimer: I am not a mathematician. It is a hobby. I am a cabi
At 11:39 AM 2/11/00 -0600, you wrote:
>
>
>On Fri, 11 Feb 2000 [EMAIL PROTECTED] wrote:
>
>> Infinite to me means never ending. A precisely defined value to me is a
>> finite value.
>
> Your definition of infinite is not correct.
Just glanced at my Websters Dictionary. infinite: 1. lacking limit
> I have a circle with a area of 5 square inches drawn on my pad. 5 inches
is
> precise.
You do?? How did you do that? Did you set your compass so that the points
were exactly sqrt (5/pi) inches apart?
What you probably have really is a circle that approximates 5 sq inches
enough to suit YO
> At 10:50 AM 2/9/00 -0500, Jeff Woods wrote:
> >You're bumping up against the Fundamental Theorem of Calculus here. Pi
> >DOES have a precisely defined value, but you cannot express it in decimal
> >form. You can express it as an infinite expansion, however.
>
> Infinite to me means never
At 10:50 AM 2/9/00 -0500, Jeff Woods wrote:
>You're bumping up against the Fundamental Theorem of Calculus here. Pi
>DOES have a precisely defined value, but you cannot express it in decimal
>form. You can express it as an infinite expansion, however.
Infinite to me means never ending. A pre
I just found out that pi is the 16th letter of the Greek Alphabet. So this
is more evidence for the theory that the numbers 4 and 16 are important in
regards to pi and also to mersenne primes.
Dan
___
>Date: Wed, 09 Feb 2000 10:50:44 -0500
>From: Jeff Woods <[EMAIL PROTECTED]>
>Subject: Re: Mersenne: pi
>You're bumping up against the Fundamental Theorem of Calculus here. Pi
>DOES have a precisely defined value, but you cannot express it in decimal
>form. You
Ken Kriesel, are you sure you did not mistype just ONE digit or parens in
that humongous expression at the end?
At 01:10 AM 2/10/00 -0600, Ken wrote:
>At 08:35 PM 2/9/2000 -0500, <[EMAIL PROTECTED]> wrote:
>>It would take infinite area of an infinitesimally thin layer of paint, which
>>would have
At 08:35 PM 2/9/2000 -0500, <[EMAIL PROTECTED]> wrote:
>It would take infinite area of an infinitesimally thin layer of paint, which
>would have no volume due to its thinness. Since paint can't be infinitely
>thin,
>this also means you can't actually fill the object with paint, because there
>will
Hi folks
> >> I think my favorite counterexample to arguments like this is Gabriel's
> >>Horn. Take the function 1/x, and revolve it around the x-axis. You now
> >>have something that looks very similar to a trumpet's bell. Now, find
the
> >>volume of this from 0 to infinity. It has a finite
From: "Ethan O'Connor" <[EMAIL PROTECTED]>
To: "'Mike Bandsmer'" <[EMAIL PROTECTED]>,
"Mersenne List \(E-mail\)" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: pi
Date: Wed, 9 Feb 2000 20:35:20 -0500
Message-ID: <001301bf736
At 09:58 AM 2/10/00 +0800, Low Hwee Boon wrote:
> 6. But most irrational numbers can be obtained from solving a polynomial
>equations
Actually almost all irrational numbers are transcendental, and therefore
not the root of a polynomial with rational coefficients.
+---
You're on the right track, but the mistake you're making is that the
paint can be infinitesimally thin in order to coat the surface. So, if the
thickness of the paint decreases proportionately to the function, then
you've only used a finite amount of paint (as the volume is only finite),
but yo
I recall my study of Maths in high school:-
1. First we learn about Integers : 0, 1, 2, 3,.. positive and negative
2. Then about Decimals : 0.1, 0.23, 3.5 etc
3. Follow by Fractions in the form of a/b where a and b are integers.
4. By converting fractions to decimals, we discover infinite
>-Original Message-
>From: [EMAIL PROTECTED]
>[mailto:[EMAIL PROTECTED]]On Behalf Of Mike
>Bandsmer
>Sent: Wednesday, February 09, 2000 7:32 PM
>To: [EMAIL PROTECTED]
>Subject: Re: Mersenne: pi
>
>
>At 02:31 AM 2/9/00 -0500, gav wrote:
>> I think my
At 02:31 AM 2/9/00 -0500, gav wrote:
> I think my favorite counterexample to arguments like this is Gabriel's
>Horn. Take the function 1/x, and revolve it around the x-axis. You now
>have something that looks very similar to a trumpet's bell. Now, find the
>volume of this from 0 to infinity.
> "Aaron" == Aaron Blosser <[EMAIL PROTECTED]>
> wrote the following on Wed, 9 Feb 2000 07:40:37 -0700
Aaron> If we were to calculate the radius of this sphere down to a
Aaron> single atomic width, using some decently expanded version of
Aaron> pi would could come up with an exact n
wrong.
-Original Message-
From: Grieken, Paul van <[EMAIL PROTECTED]>
To: 'Jud McCranie' <[EMAIL PROTECTED]>
Cc: [EMAIL PROTECTED] <[EMAIL PROTECTED]>
Date: Wednesday, February 09, 2000 11:53 AM
Subject: RE: Mersenne: pi
>I am not a math man but I follow thi
Actually, you can express PI in heaxadecimal form. This was proven by Simon
Plouffe. A decimal expression is still unknown.
Bassam Abdul-Baki
[EMAIL PROTECTED] wrote:
> > Date: Wed, 09 Feb 2000 10:50:44 -0500
> > From: Jeff Woods <[EMAIL PROTECTED]>
> > S
> Date: Wed, 09 Feb 2000 10:50:44 -0500
> From: Jeff Woods <[EMAIL PROTECTED]>
> Subject: Re: Mersenne: pi
>
> You're bumping up against the Fundamental Theorem of Calculus here. Pi
> DOES have a precisely defined value, but you cannot express it in decimal
ts on that line... So even the simple function y=x
has infinite precision, yet I can precisely determine that the length of
that line is 2*sqrt(2).
-Original Message-
From: Aaron Blosser [mailto:[EMAIL PROTECTED]]
Sent: Wednesday, February 09, 2000 8:41 AM
To: Mersenne@Base. Com
Subject: R
Grieken
> -Original Message-
> From: Jud McCranie [SMTP:[EMAIL PROTECTED]]
> Sent: Wednesday, February 09, 2000 3:22 PM
> To: [EMAIL PROTECTED]
> Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED]
> Subject: Re: Mersenne: pi
>
> At 12:06 AM 2/9/00 -0600, [EMAIL PROT
You're bumping up against the Fundamental Theorem of Calculus here. Pi
DOES have a precisely defined value, but you cannot express it in decimal
form. You can express it as an infinite expansion, however.
Just as you can never get to the end of pi, though its value is known, you
can never P
At 12:06 AM 2/9/00 -0600, [EMAIL PROTECTED] wrote:
>But when I look at a circle I see a finite area within the circle with no
>means of growing or escape. Logic seems to indicate that pi would have to
>be a finite exact value since the area in the circle is finite.
No, pi is irrational, which
> The problem isn't that Pi isn't finite, it's less than 4 so it's finite.
> The problem isn't that it isn't exact.
> The problem is that it can't be represented exactly in decimals which mens
> that when we write the expansion, we'll always have to make do with an
> approximation to the exact val
On Wed, 9 Feb 2000 [EMAIL PROTECTED] wrote:
> Hi, I have been considering the possible role pi might play in the
> progression of mersennes. It is generally accepted that the value of pi is
> a never ending series.
>
> But when I look at the circle, the formula for the area of a circle with a
>
I think my favorite counterexample to arguments like this is Gabriel's
Horn. Take the function 1/x, and revolve it around the x-axis. You now
have something that looks very similar to a trumpet's bell. Now, find the
volume of this from 0 to infinity. It has a finite volume. However, it
has
Quoting from Dan: "Logic seems to indicate that pi would have to be a
finite exact value since the area in the circle is finite. So, either the
figure for pi is in error (not likely) or pi has a end."
No, this might be called one of the pathologies of mathematics. What seems
to be so isn't. I
Hi, I have been considering the possible role pi might play in the
progression of mersennes. It is generally accepted that the value of pi is
a never ending series.
But when I look at the circle, the formula for the area of a circle with a
radius of 6 inches is: A=pi*r^2 = 3.1416 * (6)^2 = 113.
For those interested in Pi, the distribution of its digits and repeating
sequences, look at ftp://www.cc.u-tokyo.ac.jp/README.our_latest_record
Regards,
Benoit Potvin
[EMAIL PROTECTED]
_
Unsubscribe & list info -- http://www.scruz.ne
At 04:27 PM 10/21/99 -0400, Jud McCranie wrote:
>At 01:36 PM 10/21/99 -0500, Herb Savage wrote:
>
>> I remember reading an interview with the Chudnovsky brothers
>> a long time ago. I think they had computed about 4 billion digits
>> at the time. Then they felt that there would be something
>> i
At 01:36 PM 10/21/99 -0500, Herb Savage wrote:
> I remember reading an interview with the Chudnovsky brothers a long time
>ago. I think they had computed about 4 billion digits at the time.
>Then they
>felt that there would be something interesting in the digits of PI if
>you computed
>them o
At 01:40 PM 10/21/99 -0400, Darxus wrote:
>On Thu, 21 Oct 1999, Philippe Trottier wrote:
>
>> Yes, I have learned math in French and its very far away. And my
english
>> start to get rusted in Finland. sorry for the confusion, I know that
PI is
>> irrational, but like the mersenne grouping , if yo
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