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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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quasi

Posts: 10,470
Registered: 7/15/05
Re: Can a fraction have none noneending and nonerepeating decimal representation?
Posted: Aug 2, 2013 2:56 PM
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jonas.thornvall 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.


Let n be an integer with n >= 3, and let p be the perimeter
of a regular n-gon inscribed in a circle of radius r. Then
p/r is rational if and only if n = 6.

In other words, the regular hexagon is the _only_ regular
n-gon for which p/r is rational.

Thus, your claim that the ratio p/r remains rational for regular
polygons derived from "multiplying the vertices" (which
presumably just means "increasing the number of vertices") is a
false claim.

With the exception of the case n = 6, all of those ratios are
irrational.

But as has been pointed out by others, even if those ratios were
all rational, that would _not_ automatically imply that the limit
is rational.

For example, let x be an irrational number between 0 and 1.

Define x_1,x_2,x_3,... by

x_1 = (x rounded to the nearest 1/10)
x_2 = (x rounded to the nearest 1/10^2)
x_3 = (x rounded to the nearest 1/10^3)
...
x_k = (x rounded to the nearest 1/10^k)
...

The numbers x_1,x_2,x_3,... are clearly rational.

It's also clear that the limit of the sequence x_1,x_2,x_3,...
exists and equals x.

Thus it's possible for a sequence of rational numbers to have
a limit which is irrational.

quasi


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
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?
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
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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
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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
Read Re: Can a fraction have none noneending and nonerepeating decimal representation?
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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