2.7183... What is this number?
Daniel Dutch
A friend is trying to find out what this infintely repeating number is
related to. The only clue is that it is related to physics and has
something to do with 'e to the x power'. Any ideas? This would be
greatly appreciated.
Thanks
-dj
Daniel Dutch
Daniel Dutch
Daniel Dutch
Daniel Dutch
Daniel Dutch
Daniel Dutch
Daniel Dutch
Christopher R Volpe
Infinitely repeating this message is not going to make an answer come
faster.
First of all, the number is "e" or "Euler's number", and is the base of
the natural logarithm function.
Secondly, it's a transcendental number, which is one level beyond an
irrational number. It's not an infinitely repeating number, since those
numbers are rational.
--
Chris Volpe Phone: (518) 387-7766 (Dial Comm 8*833
GE Corporate R&D Fax: (518) 387-6560
PO Box 8, Schenectady, NY 12301 Email: vol...@crd.ge.com
Web: http://www.crd.ge.com/~volpecr
Kevin J. McCann
Maybe if you post this about 25 more times you will get an answer!
Jonathan Stott
In article <319B40...@vrinet.com>, Daniel Dutch <dut...@vrinet.com> wrote:
>A friend is trying to find out what this infintely repeating number is
>related to. The only clue is that it is related to physics and has
>something to do with 'e to the x power'. Any ideas? This would be
>greatly appreciated.
>
27181 / 9999 = 2.7183.... etc, repeats forever.
-JS
PS. Any repeating number less than 1 can be written this way. If you
have a sequence 'x' that repeats forever, it's equal to 'x'/(10^n-1)
where n is the number of digits in 'x'. To get your number, I took
this and added 2 (= 2*9999/9999) to it to get the numerator.
--
Jonathan Stott O- jj...@po.cwru.edu
CWRU Dept. of Physics jst...@poly.phys.cwru.edu
School of Graduate Studies http://poly.phys.cwru.edu:8080/~jstott/
Michael Leone
Daniel Dutch <dut...@vrinet.com> wrote:
>A friend is trying to find out what this infintely repeating number is
>related to. The only clue is that it is related to physics and has
>something to do with 'e to the x power'. Any ideas? This would be
>greatly appreciated.
>Thanks
>-dj
2.71828 is simply e to the first power or exp(1)...another way to say
it is that The natural log (not the common log) of 2.71828 is equal to
1 i.e. ln(2.7183) = . Hope this helps.
Alan "Uncle Al" Schwartz
Daniel Dutch <dut...@vrinet.com> wrote:
>A friend is trying to find out what this infintely repeating number is
>related to. The only clue is that it is related to physics and has
>something to do with 'e to the x power'. Any ideas? This would be
>greatly appreciated.
>
>Thanks
2.71828182845904523536028747135266249775724709369996... is e, the base of
natural logaritms, and the number which unites mathematics and geometry
through Euler's Equation e^[(i)(pi)]=-1. Get hold of a book on
elementary calculus.
--
Alan "Uncle Al" Schwartz
Uncl...@ix.netcom.com ("zero" before "@")
http://www.netprophet.co.nz/uncleal/ (naughty beyond measure;
"Quis custudiet ipsos custodes?" The Net! funny beyond endurance)
Jim Carr
Daniel Dutch <dut...@vrinet.com> writes:
>
>A friend is trying to find out what this infintely repeating number is
>related to.
Looks like e = 2.71828182845904523536... which is transcendental rather
than repeating (a repeating decimal implies that a number is rational).
> The only clue is that it is related to physics and has
>something to do with 'e to the x power'. Any ideas? This would be
>greatly appreciated.
It is used in physics, but its origin is in mathematics. e is the
base of the natural logarithm, so it can be defined as the number
such that the integral from 1 to e of dx/x is 1 (i.e. ln e = 1).
It then follows that e^x is the inverse function to ln x, and has
all sorts of amusing properties, such as e^{i pi} = -1.
--
James A. Carr <j...@scri.fsu.edu> | F. Lee Bailey says that
http://www.scri.fsu.edu/~jac/ | Tallahassee has a very well run
Supercomputer Computations Res. Inst. | Federal detention facility, but
Florida State, Tallahassee FL 32306 | that the food is too fatty.
ale2
> Daniel Dutch <dut...@vrinet.com> wrote:
>
> >A friend is trying to find out what this infintely repeating number is
> >related to. The only clue is that it is related to physics and has
> >something to do with 'e to the x power'. Any ideas? This would be
> >greatly appreciated.
>
> >Thanks
This number is almost mystical... it can be found by taking the
following limit...
limit as N goes to infinity of (1+1/N)^N
for example, with N = 10, 100, 1000, 10000 the above quantity is (just
plug in these numbers into the above)
2.59374... , 2.70481... , 2.71692... , 2.71814... you can see this
tends towards exp(1).
hope this helps
Robert Molan
On Friday, 17 May 1996, Michael Leone wrote...
> Daniel Dutch <dut...@vrinet.com> wrote:
>
> >A friend is trying to find out what this infintely repeating number is
> >related to. The only clue is that it is related to physics and has
> >something to do with 'e to the x power'. Any ideas? This would be
> >greatly appreciated.
>
> >Thanks
>
> >-dj
>
>
> 2.71828 is simply e to the first power or exp(1)...another way to say
> it is that The natural log (not the common log) of 2.71828 is equal to
> 1 i.e. ln(2.7183) = . Hope this helps.
>
>
>
No e to the power of 1 is NOT a repeating number, i.e. it is not rational.
Robert
Erik Max Francis
Daniel Dutch wrote:
> A friend is trying to find out what this infintely repeating number is
> related to. The only clue is that it is related to physics and has
> something to do with 'e to the x power'. Any ideas? This would be
> greatly appreciated.
Presumably you're talking about e, the base of the natural logarithms. e is
approximately 2.718 281 828 46. Note that it does _not_ repeat; it is
irrational (it never repeats, but it never ends, either).
--
Erik Max Francis &tSftDotIotE && http://www.alcyone.com/max && m...@alcyone.com
San Jose, California, U.S.A. && 37 20 07 N 121 53 38 W && the 4th R is respect
H.3`S,3,P,3$S,#$Q,C`Q,3,P,3$S,#$Q,3`Q,3,P,C$Q,#(Q.#`-"C`- && 1love && folasade
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"Out from his breast/his soul went to seek/the doom of the just." -- _Beowulf_
MARSHALL DUDLEY
al...@psu.edu (ale2) writes:
-> This number is almost mystical... it can be found by taking the
-> following limit...
->
-> limit as N goes to infinity of (1+1/N)^N
That is interesting. I always thought that e had to be computed through an
infinite series.
Marshall
Paasschens
Several ways exist to find the value of e=2.71828..., or even define the
number. Combining the two statements above:
exp(x) = e^x = lim(N->infinity) (1+x/N)^N
= 1 + x + x^2/2 + x^3/3
This series can be found frm the definition using (1+x/N)^N
It can also be found by demanding d(e^x)/dx = e^x.
Both methods are however probably not the fasted way to determine e^x,
or even the number e itself.
In a similar way, the number pi can be calculated by a number of ways.
Actually by a ery great number of ways. The more simple ways are in
most cases not the fastest ones.
--
greetings, Jeroen Paasschens | Disclaimer - These are my opinions, and
Philips Research Laboratories| not those of the company I work for.
Eindhoven, The Netherlands |"Physics is simple, but subtle" (Ehrenfest)
David P Norwood
MARSHALL DUDLEY (mdu...@brbbs.brbbs.com) wrote:
: al...@psu.edu (ale2) writes:
:
: -> This number is almost mystical... it can be found by taking the
: -> following limit...
: ->
: -> limit as N goes to infinity of (1+1/N)^N
:
: That is interesting. I always thought that e had to be computed through an
: infinite series.
I have a half-memory of treating an absorbing medium as a large number of
weakly absorbing planes. I get something like the power law above, and
when I took the limit of infinitely many planes, I got the normal
exponential absorption profile.
dave
dave's sig
Dan Evens
> : -> This number is almost mystical... it can be found by taking the
> : -> following limit...
> : ->
> : -> limit as N goes to infinity of (1+1/N)^N
> :
> : That is interesting. I always thought that e had to be computed through an
> : infinite series.
This can be found in any good first year calculus textbook.
Dan Evens
Erik Max Francis
MARSHALL DUDLEY wrote:
> That is interesting. I always thought that e had to be computed through an
> infinite series.
That works, too.