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Topic: Can a fraction have none noneending and nonerepeating decimal representation?
Replies: 108   Last Post: Aug 16, 2013 5:22 PM

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David Bernier

Posts: 3,317
Registered: 12/13/04
Re: Can a fraction have none noneending and nonerepeating decimal
representation?

Posted: Aug 2, 2013 1:38 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 08/02/2013 06:49 AM, Richard Tobin wrote:
> In article <85ffb478-968f-4de6-9284-b1e53fc19f0d@googlegroups.com>,
> <jonas.thornvall@gmail.com> wrote:
>

>> But one 1/phi is not a rational ratio, but the 1/6 hexagon (center to
>> vertex/sum of sides) is and so is all polygons derived from multiplying
>> the vertices.

>
> You were claiming that pi is rational. It is not.
>
> -- Richard
>


This jogged my memory about Lagrange and irrational numbers.
Lambert was the first to prove the irrationality of pi:
in 1761,

< http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational > .

Lagrange showed that if x > 0 is rational, then sin(x)
is irrational.

Ref.: (from sci.math in 2011)
======================================================================
In Jean-Guillaume Garnier's
"Analyse algebrique, faisant suite a la premiere section de l'algebre",
1814,

pages 538 and 539, he mentions Lagrange and C. Haros.
He writes that Lagrange showed that, if x > 0 is a rational
number, say x = p/q with gcd(p, q) = 1, then
sin(x) is irrational.

This uses the Taylor series:
<snip>
=======================================================================
d.b. in sci.math, http://mathforum.org/kb/message.jspa?messageID=7364740


sin(pi) = 0 is rational. pi>0.

If we assume Lagrange's result:
x>0, x rational ==> sin(x) is irrational,
then we can conclude that pi must be irrational.

david


--
On Hypnos,
http://messagenetcommresearch.com/myths/bios/hypnos.html


Date Subject Author
7/30/13
Read Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/30/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/30/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Tucsondrew@me.com
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Tucsondrew@me.com
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Tucsondrew@me.com
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
7/31/13
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Virgil
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Tucsondrew@me.com
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Tucsondrew@me.com
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
LudovicoVan
7/31/13
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JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
LudovicoVan
7/31/13
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JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/3/13
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grei
7/31/13
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JT
8/4/13
Read the surfer's value (Nicholas de Cusa proved that pi was
transcendental in the 15th cue (http://21stcenturysciencetech.com
Brian Q. Hutchings
8/4/13
Read Re: the surfer's value (Nicholas de Cusa proved that pi was
transcendental in the 15th cue (http://21stcenturysciencetech.com
Brian Q. Hutchings
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Tucsondrew@me.com
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation? NO!
Virgil
8/1/13
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magidin@math.berkeley.edu
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
Peter Percival
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
Peter Percival
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
Peter Percival
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
magidin@math.berkeley.edu
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
Peter Percival
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
magidin@math.berkeley.edu
8/1/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Richard Tobin
8/2/13
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representation?
David Bernier
8/2/13
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JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Richard Tobin
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
Peter Percival
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Richard Tobin
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
Peter Percival
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Richard Tobin
8/16/13
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Earle Jones
8/2/13
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Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
RGVickson@shaw.ca
8/2/13
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JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal
representation?
David Bernier
8/2/13
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JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/3/13
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representation?
David Bernier
8/3/13
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representation?
David Bernier
8/4/13
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representation?
David Bernier
8/2/13
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quasi
8/2/13
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JT
8/2/13
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JT
8/2/13
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Virgil
8/2/13
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Shmuel (Seymour J.) Metz
8/2/13
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JT
8/2/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Virgil
8/2/13
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FredJeffries@gmail.com
8/16/13
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Earle Jones
7/31/13
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JT
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Phil H
7/31/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
JT
7/30/13
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
Earle Jones

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