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Topic: Science > Physics
User: ""
Date: 09 Mar 2007 05:34:15 PM
Object: an ingenius problem ...
you must to find a graph where 25 points are set in such a way it
forms
(only) 12 stright lines each one with 5 points ...
a hint : for example a 5 x 5 square doesnt work, because altough there
are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 diagonals
lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 points, 3,
etc ... so t doesn=B4t work ...
wich is the solution graph ??
best regard
juan
.

User: "Autymn D. C."

Title: Re: an ingenius problem ... 16 Mar 2007 09:56:09 PM
On Mar 9, 4:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:

you must to find a graph where 25 points are set in such a way it
forms
(only) 12 stright lines each one with 5 points ...

a hint : for example a 5 x 5 square doesnt work, because altough there

: is not a word.

are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 diagonals
lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 points, 3,
etc ... so t doesn=B4t work ...

wich is the solution graph ??

which
?? is not a word.
What's wrong with yours? A line of five points already has four
points, and so on.
.
User: ""

Title: Re: an ingenius problem ... 17 Mar 2007 09:41:53 AM
On Mar 16, 11:56 pm, "Autymn D. C." <lysde...@sbcglobal.net> wrote:

On Mar 9, 4:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:> you must to find a graph where 25 points are set in such a way it

forms
(only) 12 stright lines each one with 5 points ...


a hint : for example a 5 x 5 square doesnt work, because altough there

: is not a word.

are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 diagonals
lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 points, 3,
etc ... so t doesn=B4t work ...


wich is the solution graph ??


which
?? is not a word.

What's wrong with yours? A line of five points already has four
points, and so on.

yes but there are lines that has four points that not has five ...
.
User: "Autymn D. C."

Title: Re: an ingenius problem ... 17 Mar 2007 10:44:35 PM
On Mar 17, 7:41 am, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:

What's wrong with yours? A line of five points already has four
points, and so on.


yes but there are lines that has four points that not has five ...

So? Whereoff did you get this problem?
.
User: ""

Title: Re: an ingenius problem ... 19 Mar 2007 06:15:22 AM
On Mar 18, 12:44 am, "Autymn D. C." <lysde...@sbcglobal.net> wrote:

On Mar 17, 7:41 am, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:

What's wrong with yours? A line of five points already has four
points, and so on.


yes but there are lines that has four points that not has five ...


So? Whereoff did you get this problem?

in some forum ... who post it lately shows to me an answer where all
the conditions here required (and originaly required) where not
covered ... in other words ... in the
solution presented by who post the problem, there where lines of less
than fives points ... as it must to be from the proof given by Jim
Black
best regards
juan
.




User: "Jim Black"

Title: Re: an ingenius problem ... 09 Mar 2007 11:18:35 PM
On Mar 9, 5:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:

you must to find a graph where 25 points are set in such a way it
forms
(only) 12 stright lines each one with 5 points ...

a hint : for example a 5 x 5 square doesnt work, because altough there
are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 diagonals
lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 points, 3,
etc ... so t doesn=B4t work ...

wich is the solution graph ??

If I read you correctly, your conditions are:
1=2E The graph consists of 25 points and 12 straight lines.
2=2E Each line in the graph passes through exactly 5 of the points in
the graph.
3=2E For every pair of points in the graph, there is a line in the graph
that passes through both of them.
Let N be the number of pairs (P,l) of points and lines in the graph
such that the point P is on the line l.
To illustrate what I mean, I will calculate N for the 2 x 2 square
depicted below:
Q a R
o-------o
|\ /|
| \e f/ |
| \ / |
b | X | c
| / \ |
| / \ |
|/ \|
o-------o
S d T
[You may need to copy the diagram above to a text editor and change
the font to a fixed-width font such as Courier to read it.]
Above, Q, R, S, and T are points. The lines are a, b, c, d, e, and f.
I make a chart showing which lines intersect which points:
a b c d e f
Q X X X
R X X X
S X X X
T X X X
If we count up the number of X's in the table, we find N =3D 12.
Now, back to the original problem.
The problem specifies that there are 12 lines, each line of which goes
through 5 points. That implies N =3D 60.
Select one of the points. Call it A. Each line passing through A
contains 4 points other than A. Note that every point other than A
must be connected to A by some line. Also, it is impossible for two
lines through A to share a point other than A, because that would make
them the same line. Since there are 24 points other than A, there
must be 6 lines through A.
Since the above is valid for any point chosen, each point has 6 lines
passing through it. This implies N =3D 150.
This contradiction shows that your problem has no solution, unless I
made a mistake or misunderstood you.
I have set the Followup-To header to request that replies be sent to
sci.math.
--
Jim E. Black
.
User: ""

Title: Re: an ingenius problem ... 12 Mar 2007 07:35:53 AM
On Mar 10, 2:18 am, "Jim Black" <trams...@yahoo.com> wrote:

On Mar 9, 5:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:

you must to find a graph where 25 points are set in such a way it
forms
(only) 12 stright lines each one with 5 points ...


a hint : for example a 5 x 5 square doesnt work, because altough there
are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 diagonals
lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 points, 3,
etc ... so t doesn=B4t work ...


wich is the solution graph ??


If I read you correctly, your conditions are:

1. The graph consists of 25 points and 12 straight lines.
2. Each line in the graph passes through exactly 5 of the points in
the graph.
3. For every pair of points in the graph, there is a line in the graph
that passes through both of them.

Let N be the number of pairs (P,l) of points and lines in the graph
such that the point P is on the line l.

To illustrate what I mean, I will calculate N for the 2 x 2 square
depicted below:

Q a R
o-------o
|\ /|
| \e f/ |
| \ / |
b | X | c
| / \ |
| / \ |
|/ \|
o-------o
S d T

[You may need to copy the diagram above to a text editor and change
the font to a fixed-width font such as Courier to read it.]

Above, Q, R, S, and T are points. The lines are a, b, c, d, e, and f.

I make a chart showing which lines intersect which points:

a b c d e f
Q X X X
R X X X
S X X X
T X X X

If we count up the number of X's in the table, we find N =3D 12.

Now, back to the original problem.

The problem specifies that there are 12 lines, each line of which goes
through 5 points. That implies N =3D 60.

Select one of the points. Call it A. Each line passing through A
contains 4 points other than A. Note that every point other than A
must be connected to A by some line. Also, it is impossible for two
lines through A to share a point other than A, because that would make
them the same line. Since there are 24 points other than A, there
must be 6 lines through A.

Since the above is valid for any point chosen, each point has 6 lines
passing through it. This implies N =3D 150.

This contradiction shows that your problem has no solution, unless I
made a mistake or misunderstood you.

I have set the Followup-To header to request that replies be sent to
sci.math.

--
Jim E. Black

Jim ... your answer seems to be right ... thanks very much for your
help ...
best regards
juan
.
User: "Douglas Eagleson"

Title: Re: an ingenius problem ... 12 Mar 2007 08:42:37 AM
On Mar 12, 8:35 am, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:

On Mar 10, 2:18 am, "Jim Black" <trams...@yahoo.com> wrote:





On Mar 9, 5:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:


you must to find a graph where 25 points are set in such a way it
forms
(only) 12 stright lines each one with 5 points ...


a hint : for example a 5 x 5 square doesnt work, because altough there
are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 diagonals
lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 points, 3,
etc ... so t doesn=B4t work ...


wich is the solution graph ??


If I read you correctly, your conditions are:


1. The graph consists of 25 points and 12 straight lines.
2. Each line in the graph passes through exactly 5 of the points in
the graph.
3. For every pair of points in the graph, there is a line in the graph
that passes through both of them.


Let N be the number of pairs (P,l) of points and lines in the graph
such that the point P is on the line l.


To illustrate what I mean, I will calculate N for the 2 x 2 square
depicted below:


Q a R
o-------o
|\ /|
| \e f/ |
| \ / |
b | X | c
| / \ |
| / \ |
|/ \|
o-------o
S d T


[You may need to copy the diagram above to a text editor and change
the font to a fixed-width font such as Courier to read it.]


Above, Q, R, S, and T are points. The lines are a, b, c, d, e, and f.


I make a chart showing which lines intersect which points:


a b c d e f
Q X X X
R X X X
S X X X
T X X X


If we count up the number of X's in the table, we find N =3D 12.


Now, back to the original problem.


The problem specifies that there are 12 lines, each line of which goes
through 5 points. That implies N =3D 60.


Select one of the points. Call it A. Each line passing through A
contains 4 points other than A. Note that every point other than A
must be connected to A by some line. Also, it is impossible for two
lines through A to share a point other than A, because that would make
them the same line. Since there are 24 points other than A, there
must be 6 lines through A.


Since the above is valid for any point chosen, each point has 6 lines
passing through it. This implies N =3D 150.


This contradiction shows that your problem has no solution, unless I
made a mistake or misunderstood you.


I have set the Followup-To header to request that replies be sent to
sci.math.


--
Jim E. Black


Jim ... your answer seems to be right ... thanks very much for your
help ...

best regards

juan- Hide quoted text -

- Show quoted text -

Hey, MY answer is rignt. A graph is a topology.
And the six Long lines defined in topology are dividable into 12 rays
each defining a geometric line. A ray is the half long line defined by
the ray starting at the center of the circle set.
An intersection as the number was used, but it fails to account for
size!
A size of geometric infinity relative to topologic infinity.
.
User: ""

Title: Re: an ingenius problem ... 12 Mar 2007 06:00:54 PM
On Mar 12, 10:42 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:

On Mar 12, 8:35 am, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:



On Mar 10, 2:18 am, "Jim Black" <trams...@yahoo.com> wrote:


On Mar 9, 5:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:


you must to find a graph where 25 points are set in such a way it
forms
(only) 12 stright lines each one with 5 points ...


a hint : for example a 5 x 5 square doesnt work, because altough th=

ere

are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 diagonals
lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 points, =

3,

etc ... so t doesn=B4t work ...


wich is the solution graph ??


If I read you correctly, your conditions are:


1. The graph consists of 25 points and 12 straight lines.
2. Each line in the graph passes through exactly 5 of the points in
the graph.
3. For every pair of points in the graph, there is a line in the graph
that passes through both of them.


Let N be the number of pairs (P,l) of points and lines in the graph
such that the point P is on the line l.


To illustrate what I mean, I will calculate N for the 2 x 2 square
depicted below:


Q a R
o-------o
|\ /|
| \e f/ |
| \ / |
b | X | c
| / \ |
| / \ |
|/ \|
o-------o
S d T


[You may need to copy the diagram above to a text editor and change
the font to a fixed-width font such as Courier to read it.]


Above, Q, R, S, and T are points. The lines are a, b, c, d, e, and f.


I make a chart showing which lines intersect which points:


a b c d e f
Q X X X
R X X X
S X X X
T X X X


If we count up the number of X's in the table, we find N =3D 12.


Now, back to the original problem.


The problem specifies that there are 12 lines, each line of which goes
through 5 points. That implies N =3D 60.


Select one of the points. Call it A. Each line passing through A
contains 4 points other than A. Note that every point other than A
must be connected to A by some line. Also, it is impossible for two
lines through A to share a point other than A, because that would make
them the same line. Since there are 24 points other than A, there
must be 6 lines through A.


Since the above is valid for any point chosen, each point has 6 lines
passing through it. This implies N =3D 150.


This contradiction shows that your problem has no solution, unless I
made a mistake or misunderstood you.


I have set the Followup-To header to request that replies be sent to
sci.math.


--
Jim E. Black


Jim ... your answer seems to be right ... thanks very much for your
help ...


best regards


juan- Hide quoted text -


- Show quoted text -


Hey, MY answer is rignt. A graph is a topology.

And the six Long lines defined in topology are dividable into 12 rays
each defining a geometric line. A ray is the half long line defined by
the ray starting at the center of the circle set.

An intersection as the number was used, but it fails to account for
size!
A size of geometric infinity relative to topologic infinity.

sorry ... may be you are right ... but I don't understand you ...
you are talking about a curved space ?? maybe you may post a link to a
picture
using some filesharing service ...
best regards
juan
.
User: "Richard Herring"

Title: Re: an ingenius problem ... 14 Mar 2007 07:04:50 AM
In message <1173740454.743859.276240@v33g2000cwv.googlegroups.com>,
"rayohauno@yahoo.com.ar" <juanpool@gmail.com> writes

On Mar 12, 10:42 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:

[...]


Hey, MY answer is rignt. A graph is a topology.

And the six Long lines defined in topology are dividable into 12 rays
each defining a geometric line. A ray is the half long line defined by
the ray starting at the center of the circle set.

An intersection as the number was used, but it fails to account for
size!
A size of geometric infinity relative to topologic infinity.


sorry ... may be you are right ... but I don't understand you ...

Don't worry. *Nobody* understands Eagleson.
http://groups.google.com/groups?as_uauthors=douglas+eagleson


you are talking about a curved space ?? maybe you may post a link to a
picture
using some filesharing service ...

http://llef.tripod.com/FirstLinear.jpg
--
Richard Herring
.
User: "Douglas Eagleson"

Title: Re: an ingenius problem ... 14 Mar 2007 07:42:47 AM
On Mar 14, 8:04 am, Richard Herring <junk@[127.0.0.1]> wrote:

In message <1173740454.743859.276...@v33g2000cwv.googlegroups.com>,
"rayoha...@yahoo.com.ar" <juanp...@gmail.com> writes

On Mar 12, 10:42 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:

[...]

Hey, MY answer is rignt. A graph is a topology.


And the six Long lines defined in topology are dividable into 12 rays
each defining a geometric line. A ray is the half long line defined by
the ray starting at the center of the circle set.


An intersection as the number was used, but it fails to account for
size!
A size of geometric infinity relative to topologic infinity.


sorry ... may be you are right ... but I don't understand you ...


Don't worry. *Nobody* understands Eagleson.

http://groups.google.com/groups?as_uauthors=douglas+eagleson



you are talking about a curved space ?? maybe you may post a link to a
picture
using some filesharing service ...


http://llef.tripod.com/FirstLinear.jpg

--
Richard Herring

It is another topic, but th epicture of the generalized first order
differential equations device is a fairly importent topic.
What I wrote is a requirment for the reader to infer the definiton of
a certain symbol based on the meaning of index. What does the index do
in the General Equation?
And to clarify, the the odd symbol matrix allows usage in a profouund
fashion.
N- means number
A- means rate
C- means total number
So it can solve for these three items!!! It is a very versitile
equattion where used like the matrix says.
The top row indicate the transform to cause the symbol to apply. And
the symbol inference is the relation of triangle line symbol on th
eleft to the symbol on the top row.
It should only take a minute to infer. It is another IQ test.
.
User: "Richard Herring"

Title: Re: an ingenius problem ... 14 Mar 2007 08:35:09 AM
In message <1173876167.167758.320930@b75g2000hsg.googlegroups.com>,
Douglas Eagleson <eaglesondouglas@yahoo.com> writes

On Mar 14, 8:04 am, Richard Herring <junk@[127.0.0.1]> wrote:

In message <1173740454.743859.276...@v33g2000cwv.googlegroups.com>,
"rayoha...@yahoo.com.ar" <juanp...@gmail.com> writes

On Mar 12, 10:42 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:

[...]

Hey, MY answer is rignt. A graph is a topology.


And the six Long lines defined in topology are dividable into 12 rays
each defining a geometric line. A ray is the half long line defined by
the ray starting at the center of the circle set.


An intersection as the number was used, but it fails to account for
size!
A size of geometric infinity relative to topologic infinity.


sorry ... may be you are right ... but I don't understand you ...


Don't worry. *Nobody* understands Eagleson.

http://groups.google.com/groups?as_uauthors=douglas+eagleson



you are talking about a curved space ?? maybe you may post a link to a
picture
using some filesharing service ...


http://llef.tripod.com/FirstLinear.jpg

--
Richard Herring


It is another topic, but th epicture of the generalized first order
differential equations device is a fairly importent topic.

What I wrote is a requirment for the reader to infer the definiton of
a certain symbol based on the meaning of index. What does the index do
in the General Equation?

And to clarify, the the odd symbol matrix allows usage in a profouund
fashion.

N- means number
A- means rate
C- means total number

So it can solve for these three items!!! It is a very versitile
equattion where used like the matrix says.

The top row indicate the transform to cause the symbol to apply. And
the symbol inference is the relation of triangle line symbol on th
eleft to the symbol on the top row.

It should only take a minute to infer. It is another IQ test.

I rest my case.
--
Richard Herring
.



User: "Douglas Eagleson"

Title: Re: an ingenius problem ... 14 Mar 2007 08:28:02 AM
On Mar 12, 7:00 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:

On Mar 12, 10:42 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:





On Mar 12, 8:35 am, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:


On Mar 10, 2:18 am, "Jim Black" <trams...@yahoo.com> wrote:


On Mar 9, 5:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:


you must to find a graph where 25 points are set in such a way it
forms
(only) 12 stright lines each one with 5 points ...


a hint : for example a 5 x 5 square doesnt work, because altough =

there

are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 diagonals
lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 points=

, 3,

etc ... so t doesn=B4t work ...


wich is the solution graph ??


If I read you correctly, your conditions are:


1. The graph consists of 25 points and 12 straight lines.
2. Each line in the graph passes through exactly 5 of the points in
the graph.
3. For every pair of points in the graph, there is a line in the gr=

aph

that passes through both of them.


Let N be the number of pairs (P,l) of points and lines in the graph
such that the point P is on the line l.


To illustrate what I mean, I will calculate N for the 2 x 2 square
depicted below:


Q a R
o-------o
|\ /|
| \e f/ |
| \ / |
b | X | c
| / \ |
| / \ |
|/ \|
o-------o
S d T


[You may need to copy the diagram above to a text editor and change
the font to a fixed-width font such as Courier to read it.]


Above, Q, R, S, and T are points. The lines are a, b, c, d, e, and=

f.


I make a chart showing which lines intersect which points:


a b c d e f
Q X X X
R X X X
S X X X
T X X X


If we count up the number of X's in the table, we find N =3D 12.


Now, back to the original problem.


The problem specifies that there are 12 lines, each line of which g=

oes

through 5 points. That implies N =3D 60.


Select one of the points. Call it A. Each line passing through A
contains 4 points other than A. Note that every point other than A
must be connected to A by some line. Also, it is impossible for two
lines through A to share a point other than A, because that would m=

ake

them the same line. Since there are 24 points other than A, there
must be 6 lines through A.


Since the above is valid for any point chosen, each point has 6 lin=

es

passing through it. This implies N =3D 150.


This contradiction shows that your problem has no solution, unless I
made a mistake or misunderstood you.


I have set the Followup-To header to request that replies be sent to
sci.math.


--
Jim E. Black


Jim ... your answer seems to be right ... thanks very much for your
help ...


best regards


juan- Hide quoted text -


- Show quoted text -


Hey, MY answer is rignt. A graph is a topology.


And the six Long lines defined in topology are dividable into 12 rays
each defining a geometric line. A ray is the half long line defined by
the ray starting at the center of the circle set.


An intersection as the number was used, but it fails to account for
size!
A size of geometric infinity relative to topologic infinity.


sorry ... may be you are right ... but I don't understand you ...

you are talking about a curved space ?? maybe you may post a link to a
picture
using some filesharing service ...

best regards

juan- Hide quoted text -

- Show quoted text -

Try going to teh first set of art images at my art website
the first image, in set 1, is a graph.
http://www.angelfire.com/md3/dougeagleson
It has one point, five circles, 12 rays. A set of points in any
arraingment make a graph. A basic idea is to make the set the most
dimensionless, i.e. the fewest triangles? I is hard like that, I
think.
Graphs stink, and a basic topology is the correct interpretation.
.
User: "Douglas Eagleson"

Title: Re: an ingenius problem ... 14 Mar 2007 08:58:43 AM
On Mar 14, 9:28 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:

On Mar 12, 7:00 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:





On Mar 12, 10:42 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:


On Mar 12, 8:35 am, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:


On Mar 10, 2:18 am, "Jim Black" <trams...@yahoo.com> wrote:


On Mar 9, 5:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:


you must to find a graph where 25 points are set in such a way =

it

forms
(only) 12 stright lines each one with 5 points ...


a hint : for example a 5 x 5 square doesnt work, because altoug=

h there

are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 diagona=

ls

lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 poin=

ts, 3,

etc ... so t doesn=B4t work ...


wich is the solution graph ??


If I read you correctly, your conditions are:


1. The graph consists of 25 points and 12 straight lines.
2. Each line in the graph passes through exactly 5 of the points =

in

the graph.
3. For every pair of points in the graph, there is a line in the =

graph

that passes through both of them.


Let N be the number of pairs (P,l) of points and lines in the gra=

ph

such that the point P is on the line l.


To illustrate what I mean, I will calculate N for the 2 x 2 square
depicted below:


Q a R
o-------o
|\ /|
| \e f/ |
| \ / |
b | X | c
| / \ |
| / \ |
|/ \|
o-------o
S d T


[You may need to copy the diagram above to a text editor and chan=

ge

the font to a fixed-width font such as Courier to read it.]


Above, Q, R, S, and T are points. The lines are a, b, c, d, e, a=

nd f.


I make a chart showing which lines intersect which points:


a b c d e f
Q X X X
R X X X
S X X X
T X X X


If we count up the number of X's in the table, we find N =3D 12.


Now, back to the original problem.


The problem specifies that there are 12 lines, each line of which=

goes

through 5 points. That implies N =3D 60.


Select one of the points. Call it A. Each line passing through A
contains 4 points other than A. Note that every point other than=

A

must be connected to A by some line. Also, it is impossible for =

two

lines through A to share a point other than A, because that would=

make

them the same line. Since there are 24 points other than A, there
must be 6 lines through A.


Since the above is valid for any point chosen, each point has 6 l=

ines

passing through it. This implies N =3D 150.


This contradiction shows that your problem has no solution, unles=

s I

made a mistake or misunderstood you.


I have set the Followup-To header to request that replies be sent=

to

sci.math.


--
Jim E. Black


Jim ... your answer seems to be right ... thanks very much for your
help ...


best regards


juan- Hide quoted text -


- Show quoted text -


Hey, MY answer is rignt. A graph is a topology.


And the six Long lines defined in topology are dividable into 12 rays
each defining a geometric line. A ray is the half long line defined by
the ray starting at the center of the circle set.


An intersection as the number was used, but it fails to account for
size!
A size of geometric infinity relative to topologic infinity.


sorry ... may be you are right ... but I don't understand you ...


you are talking about a curved space ?? maybe you may post a link to a
picture
using some filesharing service ...


best regards


juan- Hide quoted text -


- Show quoted text -


Try going to teh first set of art images at my art website

the first image, in set 1, is a graph.

http://www.angelfire.com/md3/dougeagleson

It has one point, five circles, 12 rays. A set of points in any
arraingment make a graph. A basic idea is to make the set the most
dimensionless, i.e. the fewest triangles? I is hard like that, I
think.

Graphs stink, and a basic topology is the correct interpretation.- Hide q=

uoted text -


- Show quoted text -

I was trying to remember why I heard that a ray in tolopoogy causes a
full line in geometric space.
A space as the cause is the toplogic space. And the cause to a line
must be all one dimensional effect. A point is locatable, but a
second point has no reference in relation. A cause to the origin as
location itself is undedfinable in topology. Ergo, two origins are
made for the two attmepts.
So it is some implication of the cause to distance. That is as far as
i can defend.
It is weird topology.
A homeomorphism appears to make the function equate geometric shapes.
A pair of points has a homeomorphisim. What is it? That is a real
interesting question. BUt points you to the topic that makes topology
very difficult because geometric analogy fails. Intuition fails.
.
User: ""

Title: Re: an ingenius problem ... 14 Mar 2007 03:54:45 PM
On Mar 14, 10:58 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:

On Mar 14, 9:28 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:





On Mar 12, 7:00 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:


On Mar 12, 10:42 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:


On Mar 12, 8:35 am, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:


On Mar 10, 2:18 am, "Jim Black" <trams...@yahoo.com> wrote:


On Mar 9, 5:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:


you must to find a graph where 25 points are set in such a wa=

y it

forms
(only) 12 stright lines each one with 5 points ...


a hint : for example a 5 x 5 square doesnt work, because alto=

ugh there

are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 diago=

nals

lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 po=

ints, 3,

etc ... so t doesn=B4t work ...


wich is the solution graph ??


If I read you correctly, your conditions are:


1. The graph consists of 25 points and 12 straight lines.
2. Each line in the graph passes through exactly 5 of the point=

s in

the graph.
3. For every pair of points in the graph, there is a line in th=

e graph

that passes through both of them.


Let N be the number of pairs (P,l) of points and lines in the g=

raph

such that the point P is on the line l.


To illustrate what I mean, I will calculate N for the 2 x 2 squ=

are

depicted below:


Q a R
o-------o
|\ /|
| \e f/ |
| \ / |
b | X | c
| / \ |
| / \ |
|/ \|
o-------o
S d T


[You may need to copy the diagram above to a text editor and ch=

ange

the font to a fixed-width font such as Courier to read it.]


Above, Q, R, S, and T are points. The lines are a, b, c, d, e,=

and f.


I make a chart showing which lines intersect which points:


a b c d e f
Q X X X
R X X X
S X X X
T X X X


If we count up the number of X's in the table, we find N =3D 12.


Now, back to the original problem.


The problem specifies that there are 12 lines, each line of whi=

ch goes

through 5 points. That implies N =3D 60.


Select one of the points. Call it A. Each line passing throug=

h A

contains 4 points other than A. Note that every point other th=

an A

must be connected to A by some line. Also, it is impossible fo=

r two

lines through A to share a point other than A, because that wou=

ld make

them the same line. Since there are 24 points other than A, th=

ere

must be 6 lines through A.


Since the above is valid for any point chosen, each point has 6=

lines

passing through it. This implies N =3D 150.


This contradiction shows that your problem has no solution, unl=

ess I

made a mistake or misunderstood you.


I have set the Followup-To header to request that replies be se=

nt to

sci.math.


--
Jim E. Black


Jim ... your answer seems to be right ... thanks very much for yo=

ur

help ...


best regards


juan- Hide quoted text -


- Show quoted text -


Hey, MY answer is rignt. A graph is a topology.


And the six Long lines defined in topology are dividable into 12 ra=

ys

each defining a geometric line. A ray is the half long line defined=

by

the ray starting at the center of the circle set.


An intersection as the number was used, but it fails to account for
size!
A size of geometric infinity relative to topologic infinity.


sorry ... may be you are right ... but I don't understand you ...


you are talking about a curved space ?? maybe you may post a link to a
picture
using some filesharing service ...


best regards


juan- Hide quoted text -


- Show quoted text -


Try going to teh first set of art images at my art website


the first image, in set 1, is a graph.


http://www.angelfire.com/md3/dougeagleson


It has one point, five circles, 12 rays. A set of points in any
arraingment make a graph. A basic idea is to make the set the most
dimensionless, i.e. the fewest triangles? I is hard like that, I
think.


Graphs stink, and a basic topology is the correct interpretation.- Hide=

quoted text -


- Show quoted text -


I was trying to remember why I heard that a ray in tolopoogy causes a
full line in geometric space.

A space as the cause is the toplogic space. And the cause to a line
must be all one dimensional effect. A point is locatable, but a
second point has no reference in relation. A cause to the origin as
location itself is undedfinable in topology. Ergo, two origins are
made for the two attmepts.

So it is some implication of the cause to distance. That is as far as
i can defend.
It is weird topology.

A homeomorphism appears to make the function equate geometric shapes.
A pair of points has a homeomorphisim. What is it? That is a real
interesting question. BUt points you to the topic that makes topology
very difficult because geometric analogy fails. Intuition fails.- Hide qu=

oted text -


- Show quoted text -

douglas ... sorry but the solution on the picture fail to cover all
the requirements
pick two points at the outside ... then you have a line with only two
points and not five
best regards
juan
.
User: "Androcles"

Title: Re: an ingenius problem ... 14 Mar 2007 04:16:53 PM
"rayohauno@yahoo.com.ar" <juanpool@gmail.com> wrote in message =
news:1173905685.072064.46850@y80g2000hsf.googlegroups.com...

I was trying to remember why I heard that a ray in tolopoogy causes a
full line in geometric space.

What the ***** is tolopoogy when it has a ray in it?
.

User: "Douglas Eagleson"

Title: Re: an ingenius problem ... 14 Mar 2007 05:10:29 PM
On Mar 14, 4:54 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:

On Mar 14, 10:58 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:





On Mar 14, 9:28 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:


On Mar 12, 7:00 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:


On Mar 12, 10:42 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:


On Mar 12, 8:35 am, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:


On Mar 10, 2:18 am, "Jim Black" <trams...@yahoo.com> wrote:


On Mar 9, 5:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.c=

om>

wrote:


you must to find a graph where 25 points are set in such a =

way it

forms
(only) 12 stright lines each one with 5 points ...


a hint : for example a 5 x 5 square doesnt work, because al=

tough there

are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 dia=

gonals

lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 =

points, 3,

etc ... so t doesn=B4t work ...


wich is the solution graph ??


If I read you correctly, your conditions are:


1. The graph consists of 25 points and 12 straight lines.
2. Each line in the graph passes through exactly 5 of the poi=

nts in

the graph.
3. For every pair of points in the graph, there is a line in =

the graph

that passes through both of them.


Let N be the number of pairs (P,l) of points and lines in the=

graph

such that the point P is on the line l.


To illustrate what I mean, I will calculate N for the 2 x 2 s=

quare

depicted below:


Q a R
o-------o
|\ /|
| \e f/ |
| \ / |
b | X | c
| / \ |
| / \ |
|/ \|
o-------o
S d T


[You may need to copy the diagram above to a text editor and =

change

the font to a fixed-width font such as Courier to read it.]


Above, Q, R, S, and T are points. The lines are a, b, c, d, =

e, and f.


I make a chart showing which lines intersect which points:


a b c d e f
Q X X X
R X X X
S X X X
T X X X


If we count up the number of X's in the table, we find N =3D =

12.


Now, back to the original problem.


The problem specifies that there are 12 lines, each line of w=

hich goes

through 5 points. That implies N =3D 60.


Select one of the points. Call it A. Each line passing thro=

ugh A

contains 4 points other than A. Note that every point other =

than A

must be connected to A by some line. Also, it is impossible =

for two

lines through A to share a point other than A, because that w=

ould make

them the same line. Since there are 24 points other than A, =

there

must be 6 lines through A.


Since the above is valid for any point chosen, each point has=

6 lines

passing through it. This implies N =3D 150.


This contradiction shows that your problem has no solution, u=

nless I

made a mistake or misunderstood you.


I have set the Followup-To header to request that replies be =

sent to

sci.math.


--
Jim E. Black


Jim ... your answer seems to be right ... thanks very much for =

your

help ...


best regards


juan- Hide quoted text -


- Show quoted text -


Hey, MY answer is rignt. A graph is a topology.


And the six Long lines defined in topology are dividable into 12 =

rays

each defining a geometric line. A ray is the half long line defin=

ed by

the ray starting at the center of the circle set.


An intersection as the number was used, but it fails to account f=

or

size!
A size of geometric infinity relative to topologic infinity.


sorry ... may be you are right ... but I don't understand you ...


you are talking about a curved space ?? maybe you may post a link t=

o a

picture
using some filesharing service ...


best regards


juan- Hide quoted text -


- Show quoted text -


Try going to teh first set of art images at my art website


the first image, in set 1, is a graph.


http://www.angelfire.com/md3/dougeagleson


It has one point, five circles, 12 rays. A set of points in any
arraingment make a graph. A basic idea is to make the set the most
dimensionless, i.e. the fewest triangles? I is hard like that, I
think.


Graphs stink, and a basic topology is the correct interpretation.- Hi=

de quoted text -


- Show quoted text -


I was trying to remember why I heard that a ray in tolopoogy causes a
full line in geometric space.


A space as the cause is the toplogic space. And the cause to a line
must be all one dimensional effect. A point is locatable, but a
second point has no reference in relation. A cause to the origin as
location itself is undedfinable in topology. Ergo, two origins are
made for the two attmepts.


So it is some implication of the cause to distance. That is as far as
i can defend.
It is weird topology.


A homeomorphism appears to make the function equate geometric shapes.
A pair of points has a homeomorphisim. What is it? That is a real
interesting question. BUt points you to the topic that makes topology
very difficult because geometric analogy fails. Intuition fails.- Hide =

quoted text -


- Show quoted text -


douglas ... sorry but the solution on the picture fail to cover all
the requirements
pick two points at the outside ... then you have a line with only two
points and not five

best regards

juan- Hide quoted text -

- Show quoted text -

I tried to explain. A graph is not an x/y plot. A venn Diagram as
the topolopy abstracted all set. A graph as topology abstracted a
class and I believe it was a triangle.
I explained the reasoning behind the two points. A ray in the diagram
corresponds or causes a geometric shape called a full line!
Now if two lines are superimposed on the same spot, believe it or not
they can be shifted so one is toward the left and one is toward the
right direction of the one dimension they exist on.
So when somebody say please do not read it as a geometric plot. Youo
read as one and say sorry.
I am correct and I defended as best I could without a teacher to
explain. Teachers get to say I have the answer, I do not.
.
User: ""

Title: Re: an ingenius problem ... 14 Mar 2007 10:09:14 PM
On Mar 14, 7:10 pm, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:

On Mar 14, 4:54 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:





On Mar 14, 10:58 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:


On Mar 14, 9:28 am, "Douglas Eagleson" <eaglesondoug...@yahoo.com>
wrote:


On Mar 12, 7:00 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:


On Mar 12, 10:42 am, "Douglas Eagleson" <eaglesondoug...@yahoo.co=

m>

wrote:


On Mar 12, 8:35 am, "rayoha...@yahoo.com.ar" <juanp...@gmail.co=

m>

wrote:


On Mar 10, 2:18 am, "Jim Black" <trams...@yahoo.com> wrote:


On Mar 9, 5:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail=

..com>

wrote:


you must to find a graph where 25 points are set in such =

a way it

forms
(only) 12 stright lines each one with 5 points ...


a hint : for example a 5 x 5 square doesnt work, because =

altough there

are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 d=

iagonals

lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of =

4 points, 3,

etc ... so t doesn=B4t work ...


wich is the solution graph ??


If I read you correctly, your conditions are:


1. The graph consists of 25 points and 12 straight lines.
2. Each line in the graph passes through exactly 5 of the p=

oints in

the graph.
3. For every pair of points in the graph, there is a line i=

n the graph

that passes through both of them.


Let N be the number of pairs (P,l) of points and lines in t=

he graph

such that the point P is on the line l.


To illustrate what I mean, I will calculate N for the 2 x 2=

square

depicted below:


Q a R
o-------o
|\ /|
| \e f/ |
| \ / |
b | X | c
| / \ |
| / \ |
|/ \|
o-------o
S d T


[You may need to copy the diagram above to a text editor an=

d change

the font to a fixed-width font such as Courier to read it.]


Above, Q, R, S, and T are points. The lines are a, b, c, d=

, e, and f.


I make a chart showing which lines intersect which points:


a b c d e f
Q X X X
R X X X
S X X X
T X X X


If we count up the number of X's in the table, we find N =

=3D 12.


Now, back to the original problem.


The problem specifies that there are 12 lines, each line of=

which goes

through 5 points. That implies N =3D 60.


Select one of the points. Call it A. Each line passing th=

rough A

contains 4 points other than A. Note that every point othe=

r than A

must be connected to A by some line. Also, it is impossibl=

e for two

lines through A to share a point other than A, because that=

would make

them the same line. Since there are 24 points other than A=

, there

must be 6 lines through A.


Since the above is valid for any point chosen, each point h=

as 6 lines

passing through it. This implies N =3D 150.


This contradiction shows that your problem has no solution,=

unless I

made a mistake or misunderstood you.


I have set the Followup-To header to request that replies b=

e sent to

sci.math.


--
Jim E. Black


Jim ... your answer seems to be right ... thanks very much fo=

r your

help ...


best regards


juan- Hide quoted text -


- Show quoted text -


Hey, MY answer is rignt. A graph is a topology.


And the six Long lines defined in topology are dividable into 1=

2 rays

each defining a geometric line. A ray is the half long line def=

ined by

the ray starting at the center of the circle set.


An intersection as the number was used, but it fails to account=

for

size!
A size of geometric infinity relative to topologic infinity.


sorry ... may be you are right ... but I don't understand you ...


you are talking about a curved space ?? maybe you may post a link=

to a

picture
using some filesharing service ...


best regards


juan- Hide quoted text -


- Show quoted text -


Try going to teh first set of art images at my art website


the first image, in set 1, is a graph.


http://www.angelfire.com/md3/dougeagleson


It has one point, five circles, 12 rays. A set of points in any
arraingment make a graph. A basic idea is to make the set the most
dimensionless, i.e. the fewest triangles? I is hard like that, I
think.


Graphs stink, and a basic topology is the correct interpretation.- =

Hide quoted text -


- Show quoted text -


I was trying to remember why I heard that a ray in tolopoogy causes a
full line in geometric space.


A space as the cause is the toplogic space. And the cause to a line
must be all one dimensional effect. A point is locatable, but a
second point has no reference in relation. A cause to the origin as
location itself is undedfinable in topology. Ergo, two origins are
made for the two attmepts.


So it is some implication of the cause to distance. That is as far as
i can defend.
It is weird topology.


A homeomorphism appears to make the function equate geometric shapes.
A pair of points has a homeomorphisim. What is it? That is a real
interesting question. BUt points you to the topic that makes topology
very difficult because geometric analogy fails. Intuition fails.- Hid=

e quoted text -


- Show quoted text -


douglas ... sorry but the solution on the picture fail to cover all
the requirements
pick two points at the outside ... then you have a line with only two
points and not five


best regards


juan- Hide quoted text -


- Show quoted text -


I tried to explain. A graph is not an x/y plot. A venn Diagram as
the topolopy abstracted all set. A graph as topology abstracted a
class and I believe it was a triangle.

I explained the reasoning behind the two points. A ray in the diagram
corresponds or causes a geometric shape called a full line!

Now if two lines are superimposed on the same spot, believe it or not
they can be shifted so one is toward the left and one is toward the
right direction of the one dimension they exist on.

So when somebody say please do not read it as a geometric plot. Youo
read as one and say sorry.

I am correct and I defended as best I could without a teacher to
explain. Teachers get to say I have the answer, I do not.- Hide quoted te=

xt -


- Show quoted text -

ok ... you are right that a graph may not live in some euclidean
space ... but this is not de case ...
what do you think when I say stright lines ??
.









User: "Douglas Eagleson"

Title: Re: an ingenius problem ... 09 Mar 2007 05:38:37 PM
On Mar 9, 6:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:

you must to find a graph where 25 points are set in such a way it
forms
(only) 12 stright lines each one with 5 points ...

a hint : for example a 5 x 5 square doesnt work, because altough there
are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 diagonals
lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 points, 3,
etc ... so t doesn=B4t work ...

wich is the solution graph ??

best regard

juan

A basic circle set is designed to allow a five.
And the center is a point.
.
User: ""

Title: Re: an ingenius problem ... 09 Mar 2007 06:43:41 PM
On 9 mar, 20:38, "Douglas Eagleson" <eaglesondoug...@yahoo.com> wrote:

On Mar 9, 6:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:





you must to find a graph where 25 points are set in such a way it
forms
(only) 12 stright lines each one with 5 points ...


a hint : for example a 5 x 5 square doesnt work, because altough there
are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 diagonals
lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 points, 3,
etc ... so t doesn=B4t work ...


wich is the solution graph ??


best regard


juan


A basic circle set is designed to allow a five.

And the center is a point.- Ocultar texto de la cita -

- Mostrar texto de la cita -

where are the stright lines there ?? where are the 12 stright lines ??
.
User: "Douglas Eagleson"

Title: Re: an ingenius problem ... 09 Mar 2007 08:13:17 PM
On Mar 9, 7:43 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:

On 9 mar, 20:38, "Douglas Eagleson" <eaglesondoug...@yahoo.com> wrote:





On Mar 9, 6:34 pm, "rayoha...@yahoo.com.ar" <juanp...@gmail.com>
wrote:


you must to find a graph where 25 points are set in such a way it
forms
(only) 12 stright lines each one with 5 points ...


a hint : for example a 5 x 5 square doesnt work, because altough there
are 5 horizontal lines of 5
points, plus 5 vertical lines with 5 points, and plus 2 diagonals
lines with 5 points, that is
a total of 12 lines of 5 points, there are also lines of 4 points, 3,
etc ... so t doesn=B4t work ...


wich is the solution graph ??


best regard


juan


A basic circle set is designed to allow a five.


And the center is a point.- Ocultar texto de la cita -


- Mostrar texto de la cita -


where are the stright lines there ?? where are the 12 stright lines ??- H=

ide quoted text -


- Show quoted text -

Make four circles, each placed inside the other, out of six points
defining each circle.
Make two points on one side of the center point, and two on the other
side.
Making six*2. lines. NOT SIX lines.
A graph defined the line. A segment to cause the set of geometric
infinite sets of points! In topology set theory the set of half
segments defines the segments of all infinite line sets!
So a play on the word line allows the answer.
.




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