|
|
| Author |
Message |
Guest
|
 Posted: Wed Aug 10, 2005 4:21 pm Post subject:
The Numerica Format
|
|
|
====================================================
"The Numerica Format: a numerical sequencing method"
By: Paul Allen Panks (dunric@yahoo.com)
Date: August 09, 2005
(Version 1.3 - Revised and Expanded)
====================================================
=======
Summary
=======
This is a simple encoding sequence using numbers assigned
as letters and punctuation. The sequence is comprised of an
encoding arrangement of 49 total letters, punctuation and
numerical mathematical assignments.
The resulting sequence uses the multiplication table of zero [0]
through
nine [9]. Some numbers -- 11,13,17,19,22,23,26, etc. -- are not
reachable
via the regular 0 through 9 multiplication tables. Such numbers must
then
be added together to simulate actual values not reachable via the
normal
multiplication standard.
This sequencing method is best described as the "Numerica Format".
Encoded sequences are called "Numericas". Individual sequence lines are
termed "Numeri".
=================
Binary Assignment
=================
To make full use of the sequence, letters, basic punctuation and
numbers
are approximated through simple mathematical equations. Forty-nine
total
letters, numbers and punctuation are assigned to the following numeric
values:
A = 1
B = 2
C = 3
D = 4
E = 5
F = 6
G = 7
H = 8
I = 9
J = 10
K = 11
L = 12
M = 13
N = 14
O = 15
P = 16
Q = 17
R = 18
S = 19
T = 20
U = 21
V = 22
W = 23
X = 24
Y = 25
Z = 26
Punctuation is also required, and thus is assigned to the following
numbers:
27 = .
28 = !
29 = ?
30 = ,
31 = &
32 = (space)
33 = *
34 = @
35 = %
36 = $
37 = +
38 = -
39 = #
40 = 0
41 = 1
42 = 2
43 = 3
44 = 4
45 = 5
46 = 6
47 = 7
48 = 8
49 = 9
50 = (undefined)
The sequence is straightforward and easily used. A brief explanation
(with an example of the sequence as it is normally used) will follow
later on during the course of this article.
===================
The Multiples Table
===================
Listed below is a standard multiplication table (used in the
Numerica Format). Note that numbers never go above 81, or below 0:
1 2 3 4 5 6 7 8 9
------------------------------------
0|1 2 3 4 5 6 7 8 9
1|1 2 3 4 5 6 7 8 9
2|2 4 6 8 10 12 14 16 18
3|3 6 9 12 15 18 21 24 27
4|4 8 12 16 20 24 28 32 36
5|5 10 15 20 25 30 35 40 45
6|6 12 18 24 30 36 42 48 54
7|7 14 21 28 35 42 49 56 63
8|8 16 24 32 40 48 56 64 72
9|9 18 27 36 45 54 63 72 81
------------------------------------
=====================================
How numbers are added (or multiplied)
=====================================
Some values (e.g. 11,13,17,19,22,23,26, etc.) have no possibility
of being multiplied successfully by numbers ranging from 0 through 9.
Therefore, they must be added together. In special cases, the added
numbers represent the larger numbers themselves (i.e. 2+9 will be
equal to the number "29",etc.)
In order to differentiate between multiplication of two numbers
(and addition), the sequence in which they are added together
is reversed in logical order.
The forty-nine numeric assignments are reached via the following
Simple mathematical equations (Note: Some equations arenequations;
rather,
they are quite literal representations of the
numbers themselves):
0+1=1 [A]
0+2=2 [B]
0+3=3 [C]
0+4=4 [D]
0+5=5 [E]
0+6=6 [F]
0+7=7 [G]
0+8=8 [H]
0+9=9 [I]
5*2=10 [J]
5+6=11 [K]
6*2=12 [L]
6+7=13 [M]
7*2=14 [N]
5*3=15 [O]
8*2=16 [P]
8+9=17 [Q]
9*2=18 [R]
1+9=19 [S]
5*4=20 [T]
7*3=21 [U]
2+2=22 [V]
2+3=23 [W]
6*4=24 [X]
5*5=25 [Y]
2+6=26 [Z]
9*3=27 [.]
7*4=28 [!]
2+9=29 [?]
6*5=30 [,]
3+1=31 [&]
8*4=32 [ ]
3+3=33 [*]
3+4=34 [@]
7*5=35 [%]
9*4=36 [$]
3+7=37 [+]
3+8=38 [-]
3+9=39 [#]
4+0=40 [0]
4+1=41 [1]
4+2=42 [2]
4+3=43 [3]
4+4=44 [4]
4+5=45 [5]
4+6=46 [6]
4+7=47 [7]
4+8=48 [8]
4+9=49 [9]
5+0=50 [blank]
A few notes:
The 50th sequence is left undefined, thus, the Numerica Format really
only
has 49. "Space", an invisible punctuation mark used to separate words
from
one another in normal language, is assigned as the 32nd sequence.
Addition always has the lowest value added first, followed by the
larger
value. In only a few instances, such as 2+2, are the values the same
when
adding together two numbers. When multiplying, the first number is
always
larger than the second, with one exception: 5*5 (the sum has no known
value reachable via numbers 0 through 9 outside of 5*5).
==========================
Example of a simple Numeri
==========================
A brief summary of a simple Numeri and the resulting sequence
follows. This is a simple Numeri consisting of 6 total words and
1 punctuation mark (a period, or .).
Example:
THE COW JUMPED OVER THE MOON.
Translated:
54 08 05 84 03 53 23 84 52 73 67 82 05 04 84 53 22 05 92 84 54 08
05 84 67 53 53 72 93
T H E C O W J U M P E D O V E R T H E
M
O O N .
Or:
THE COW JUMPED OVER THE MOON.
5408058403532384527367820504845322059284540805846753537293
To the casual observer, this is just random gibberish, meaning
nothing. But to the readers of the Numerica Format, it may
mean something useful -- perhaps even informative.
===========
Limitations
===========
There are a few limitations present within the sequence described
within this article. They are briefly outlined below:
1) Unfortunately, numbers are denoted beginning with the number 4, as
they
cannot be reliably sequenced by multiplication. This is a limitation
within the coding sequence itself. Therefore, it is defined as a flaw.
2) Additionally, only the most basic punctuation is included, bringing
the total coding sequence to forty-nine mathematical assignments (26
letters, 13 punctuation marks and 10 numbers). The 50th sequence is
left
undefined, and may be redefined as necessary.
3) Simple Numeri (such as "THE COW JUMPED OVER THE MOON.")
require long Numericas. This may be broken down into 40 or 80-column
singular Numeri in order to increase readability. In general, Numeri
should be indented slightly to allow for footnotes. For example:
|540805840353238452736782050484532205928454080584|
|6753537293 |
(The cow jumped over the | moon.)
4) Numeri are broken down into lines which may overlap (as above). To
designate where they might overlap, select either 40 or 80-columns set
into descending rows. Then word wrap the sentence as
suggested in the example above.
5) When translating simple documents to the Numerica Format, it is not
unusual to designate the 50th sequence (which is undefined) as a line
break. Example:
|540805840353238452736782050484532205928454080584|
|6753537293505408058405720493 |
(The cow jumped over the | moon. [line break] The End.)
==========
Conclusion
==========
The simplicity of the Numerica Format, combined with the difficulty
in determining source data, allows it to be invaluable for encoding
brief messages to those requiring security of information. The
majority of individuals who come across messages encoded as
Numerica will confuse the data with useless or trivial
information. If data needs to be secure, but decodable, this
is an easy and fairly straightforward method of accomplishing
such a task.
I have written a short program to take a sentence the user inputs and
translate it into the Numerica Format. See below:
http://members.tripod.com/~panks/numerica.html
Sincerely,
Paul Allen Panks
dunric@yahoo.com
Phoenix, Arizona |
|
| Back to top |
|
 |
mensanator@aol.compost
science forum Guru
Joined: 24 Mar 2005
Posts: 826
|
| Posted: Wed Aug 10, 2005 5:28 pm Post subject:
Re: The Numerica Format
|
|
|
dunric@yahoo.com wrote:
| Quote: | ====================================================
"The Numerica Format: a numerical sequencing method"
By: Paul Allen Panks (dunric@yahoo.com)
Date: August 09, 2005
(Version 1.3 - Revised and Expanded)
====================================================
=======
Summary
=======
This is a simple encoding sequence using numbers assigned
as letters and punctuation. The sequence is comprised of an
encoding arrangement of 49 total letters, punctuation and
numerical mathematical assignments.
The resulting sequence uses the multiplication table of zero [0]
through
nine [9]. Some numbers -- 11,13,17,19,22,23,26, etc. -- are not
reachable
via the regular 0 through 9 multiplication tables. Such numbers must
then
be added together to simulate actual values not reachable via the
normal
multiplication standard.
This sequencing method is best described as the "Numerica Format".
Encoded sequences are called "Numericas". Individual sequence lines are
termed "Numeri".
=================
Binary Assignment
=================
To make full use of the sequence, letters, basic punctuation and
numbers
are approximated through simple mathematical equations. Forty-nine
total
letters, numbers and punctuation are assigned to the following numeric
values:
A = 1
B = 2
C = 3
D = 4
E = 5
F = 6
G = 7
H = 8
I = 9
J = 10
K = 11
L = 12
M = 13
N = 14
O = 15
P = 16
Q = 17
R = 18
S = 19
T = 20
U = 21
V = 22
W = 23
X = 24
Y = 25
Z = 26
Punctuation is also required, and thus is assigned to the following
numbers:
27 = .
28 = !
29 = ?
30 = ,
31 = &
32 = (space)
33 = *
34 = @
35 = %
36 = $
37 = +
38 = -
39 = #
40 = 0
41 = 1
42 = 2
43 = 3
44 = 4
45 = 5
46 = 6
47 = 7
48 = 8
49 = 9
50 = (undefined)
The sequence is straightforward and easily used. A brief explanation
(with an example of the sequence as it is normally used) will follow
later on during the course of this article.
===================
The Multiples Table
===================
Listed below is a standard multiplication table (used in the
Numerica Format). Note that numbers never go above 81, or below 0:
1 2 3 4 5 6 7 8 9
------------------------------------
0|1 2 3 4 5 6 7 8 9
1|1 2 3 4 5 6 7 8 9
2|2 4 6 8 10 12 14 16 18
3|3 6 9 12 15 18 21 24 27
4|4 8 12 16 20 24 28 32 36
5|5 10 15 20 25 30 35 40 45
6|6 12 18 24 30 36 42 48 54
7|7 14 21 28 35 42 49 56 63
8|8 16 24 32 40 48 56 64 72
9|9 18 27 36 45 54 63 72 81
------------------------------------
=====================================
How numbers are added (or multiplied)
=====================================
Some values (e.g. 11,13,17,19,22,23,26, etc.) have no possibility
of being multiplied successfully by numbers ranging from 0 through 9.
Therefore, they must be added together. In special cases, the added
numbers represent the larger numbers themselves (i.e. 2+9 will be
equal to the number "29",etc.)
In order to differentiate between multiplication of two numbers
(and addition), the sequence in which they are added together
is reversed in logical order.
The forty-nine numeric assignments are reached via the following
Simple mathematical equations (Note: Some equations arenequations;
rather,
they are quite literal representations of the
numbers themselves):
0+1=1 [A]
0+2=2 [B]
0+3=3 [C]
0+4=4 [D]
0+5=5 [E]
0+6=6 [F]
0+7=7 [G]
0+8=8 [H]
0+9=9 [I]
5*2=10 [J]
5+6=11 [K]
6*2=12 [L]
6+7=13 [M]
7*2=14 [N]
5*3=15 [O]
8*2=16 [P]
8+9=17 [Q]
9*2=18 [R]
1+9=19 [S]
5*4=20 [T]
7*3=21 [U]
2+2=22 [V]
2+3=23 [W]
6*4=24 [X]
5*5=25 [Y]
2+6=26 [Z]
9*3=27 [.]
7*4=28 [!]
2+9=29 [?]
6*5=30 [,]
3+1=31 [&]
8*4=32 [ ]
3+3=33 [*]
3+4=34 [@]
7*5=35 [%]
9*4=36 [$]
3+7=37 [+]
3+8=38 [-]
3+9=39 [#]
4+0=40 [0]
4+1=41 [1]
4+2=42 [2]
4+3=43 [3]
4+4=44 [4]
4+5=45 [5]
4+6=46 [6]
4+7=47 [7]
4+8=48 [8]
4+9=49 [9]
5+0=50 [blank]
A few notes:
The 50th sequence is left undefined, thus, the Numerica Format really
only
has 49. "Space", an invisible punctuation mark used to separate words
from
one another in normal language, is assigned as the 32nd sequence.
Addition always has the lowest value added first, followed by the
larger
value. In only a few instances, such as 2+2, are the values the same
when
adding together two numbers. When multiplying, the first number is
always
larger than the second, with one exception: 5*5 (the sum has no known
value reachable via numbers 0 through 9 outside of 5*5).
==========================
Example of a simple Numeri
==========================
A brief summary of a simple Numeri and the resulting sequence
follows. This is a simple Numeri consisting of 6 total words and
1 punctuation mark (a period, or .).
Example:
THE COW JUMPED OVER THE MOON.
Translated:
54 08 05 84 03 53 23 84 52 73 67 82 05 04 84 53 22 05 92 84 54 08
05 84 67 53 53 72 93
T H E C O W J U M P E D O V E R T H E
M
O O N .
Or:
THE COW JUMPED OVER THE MOON.
5408058403532384527367820504845322059284540805846753537293
To the casual observer, this is just random gibberish, meaning
nothing. But to the readers of the Numerica Format, it may
mean something useful -- perhaps even informative.
===========
Limitations
===========
There are a few limitations present within the sequence described
within this article. They are briefly outlined below:
1) Unfortunately, numbers are denoted beginning with the number 4, as
they
cannot be reliably sequenced by multiplication. This is a limitation
within the coding sequence itself. Therefore, it is defined as a flaw.
2) Additionally, only the most basic punctuation is included, bringing
the total coding sequence to forty-nine mathematical assignments (26
letters, 13 punctuation marks and 10 numbers). The 50th sequence is
left
undefined, and may be redefined as necessary.
3) Simple Numeri (such as "THE COW JUMPED OVER THE MOON.")
require long Numericas. This may be broken down into 40 or 80-column
singular Numeri in order to increase readability. In general, Numeri
should be indented slightly to allow for footnotes. For example:
|540805840353238452736782050484532205928454080584|
|6753537293 |
(The cow jumped over the | moon.)
4) Numeri are broken down into lines which may overlap (as above). To
designate where they might overlap, select either 40 or 80-columns set
into descending rows. Then word wrap the sentence as
suggested in the example above.
5) When translating simple documents to the Numerica Format, it is not
unusual to designate the 50th sequence (which is undefined) as a line
break. Example:
|540805840353238452736782050484532205928454080584|
|6753537293505408058405720493 |
(The cow jumped over the | moon. [line break] The End.)
==========
Conclusion
==========
The simplicity of the Numerica Format, combined with the difficulty
in determining source data, allows it to be invaluable for encoding
brief messages to those requiring security of information. The
majority of individuals who come across messages encoded as
Numerica will confuse the data with useless or trivial
information. If data needs to be secure, but decodable, this
is an easy and fairly straightforward method of accomplishing
such a task.
I have written a short program to take a sentence the user inputs and
translate it into the Numerica Format. See below:
http://members.tripod.com/~panks/numerica.html
Sincerely,
Paul Allen Panks
dunric@yahoo.com
Phoenix, Arizona
|
540805845492010962840919841954096262840401925693
197304040572625584555373840572035373725405928401
840653736238196705626209720784549253626293
080584029201720409190805198401846701720906051954
538401720484677367026205198419536705540809720784
010253735484727367059209030162841905897305720309
720793
035367670172048409077253920584549253626293
549253626284015454010356198467057219017254539293
840184080954938402625323840253737203051984530606
840192675392938467057219017201545392840919841954
096262840972840753530484190801820593
035367670172048419015584230853840119560504840653
92845408091929
540805840972030172540154095372840301731905198454
080584549253626284545384035322059284080919840501
921984017204840601626284545384540805840792537372
048419039205016709720793
5492536262840919840873925409720793
549253626284066205051984537354840172840564095493
5553738419050584260982840609620593
03536767017204840705548401626293
260982840609620584540156057293
0353676701720484737226098293
0353676701720484920501048419537392030593
540805841953739203058409198409728493
67057219017201545392840919840972848201097293
035367670172048492737284727367059209030193
54080584829253079201728403017272535484820192190584
09728273549384540564548406536262532309720784018403
53676701840919840907725392050493
67057219017201545392840919840873925409720793
01725354080592845572298455
82925307920167840453051984045354841973828253925484
54080584620192070584035367670172048482925367825484
19039205057284027306060592938492051973625419841903
92536262845306068419039205057284017204840192058462
53195493
67057219017201545392840919840154840405015408501984
04535392
03536767017204848973095493
67057219017201545392840919840405010493 |
|
| Back to top |
|
|
Guest
|
| Posted: Wed Aug 10, 2005 5:34 pm Post subject:
Re: The Numerica Format
|
|
|
Not quite sure what that means. I need a program to decode numerica
now.
Paul
mensanator@aol.compost wrote:
| Quote: | dunric@yahoo.com wrote:
====================================================
"The Numerica Format: a numerical sequencing method"
By: Paul Allen Panks (dunric@yahoo.com)
Date: August 09, 2005
(Version 1.3 - Revised and Expanded)
====================================================
=======
Summary
=======
This is a simple encoding sequence using numbers assigned
as letters and punctuation. The sequence is comprised of an
encoding arrangement of 49 total letters, punctuation and
numerical mathematical assignments.
The resulting sequence uses the multiplication table of zero [0]
through
nine [9]. Some numbers -- 11,13,17,19,22,23,26, etc. -- are not
reachable
via the regular 0 through 9 multiplication tables. Such numbers must
then
be added together to simulate actual values not reachable via the
normal
multiplication standard.
This sequencing method is best described as the "Numerica Format".
Encoded sequences are called "Numericas". Individual sequence lines are
termed "Numeri".
=================
Binary Assignment
=================
To make full use of the sequence, letters, basic punctuation and
numbers
are approximated through simple mathematical equations. Forty-nine
total
letters, numbers and punctuation are assigned to the following numeric
values:
A = 1
B = 2
C = 3
D = 4
E = 5
F = 6
G = 7
H = 8
I = 9
J = 10
K = 11
L = 12
M = 13
N = 14
O = 15
P = 16
Q = 17
R = 18
S = 19
T = 20
U = 21
V = 22
W = 23
X = 24
Y = 25
Z = 26
Punctuation is also required, and thus is assigned to the following
numbers:
27 = .
28 = !
29 = ?
30 = ,
31 = &
32 = (space)
33 = *
34 = @
35 = %
36 = $
37 = +
38 = -
39 = #
40 = 0
41 = 1
42 = 2
43 = 3
44 = 4
45 = 5
46 = 6
47 = 7
48 = 8
49 = 9
50 = (undefined)
The sequence is straightforward and easily used. A brief explanation
(with an example of the sequence as it is normally used) will follow
later on during the course of this article.
===================
The Multiples Table
===================
Listed below is a standard multiplication table (used in the
Numerica Format). Note that numbers never go above 81, or below 0:
1 2 3 4 5 6 7 8 9
------------------------------------
0|1 2 3 4 5 6 7 8 9
1|1 2 3 4 5 6 7 8 9
2|2 4 6 8 10 12 14 16 18
3|3 6 9 12 15 18 21 24 27
4|4 8 12 16 20 24 28 32 36
5|5 10 15 20 25 30 35 40 45
6|6 12 18 24 30 36 42 48 54
7|7 14 21 28 35 42 49 56 63
8|8 16 24 32 40 48 56 64 72
9|9 18 27 36 45 54 63 72 81
------------------------------------
=====================================
How numbers are added (or multiplied)
=====================================
Some values (e.g. 11,13,17,19,22,23,26, etc.) have no possibility
of being multiplied successfully by numbers ranging from 0 through 9.
Therefore, they must be added together. In special cases, the added
numbers represent the larger numbers themselves (i.e. 2+9 will be
equal to the number "29",etc.)
In order to differentiate between multiplication of two numbers
(and addition), the sequence in which they are added together
is reversed in logical order.
The forty-nine numeric assignments are reached via the following
Simple mathematical equations (Note: Some equations arenequations;
rather,
they are quite literal representations of the
numbers themselves):
0+1=1 [A]
0+2=2 [B]
0+3=3 [C]
0+4=4 [D]
0+5=5 [E]
0+6=6 [F]
0+7=7 [G]
0+8=8 [H]
0+9=9 [I]
5*2=10 [J]
5+6=11 [K]
6*2=12 [L]
6+7=13 [M]
7*2=14 [N]
5*3=15 [O]
8*2=16 [P]
8+9=17 [Q]
9*2=18 [R]
1+9=19 [S]
5*4=20 [T]
7*3=21 [U]
2+2=22 [V]
2+3=23 [W]
6*4=24 [X]
5*5=25 [Y]
2+6=26 [Z]
9*3=27 [.]
7*4=28 [!]
2+9=29 [?]
6*5=30 [,]
3+1=31 [&]
8*4=32 [ ]
3+3=33 [*]
3+4=34 [@]
7*5=35 [%]
9*4=36 [$]
3+7=37 [+]
3+8=38 [-]
3+9=39 [#]
4+0=40 [0]
4+1=41 [1]
4+2=42 [2]
4+3=43 [3]
4+4=44 [4]
4+5=45 [5]
4+6=46 [6]
4+7=47 [7]
4+8=48 [8]
4+9=49 [9]
5+0=50 [blank]
A few notes:
The 50th sequence is left undefined, thus, the Numerica Format really
only
has 49. "Space", an invisible punctuation mark used to separate words
from
one another in normal language, is assigned as the 32nd sequence.
Addition always has the lowest value added first, followed by the
larger
value. In only a few instances, such as 2+2, are the values the same
when
adding together two numbers. When multiplying, the first number is
always
larger than the second, with one exception: 5*5 (the sum has no known
value reachable via numbers 0 through 9 outside of 5*5).
==========================
Example of a simple Numeri
==========================
A brief summary of a simple Numeri and the resulting sequence
follows. This is a simple Numeri consisting of 6 total words and
1 punctuation mark (a period, or .).
Example:
THE COW JUMPED OVER THE MOON.
Translated:
54 08 05 84 03 53 23 84 52 73 67 82 05 04 84 53 22 05 92 84 54 08
05 84 67 53 53 72 93
T H E C O W J U M P E D O V E R T H E
M
O O N .
Or:
THE COW JUMPED OVER THE MOON.
5408058403532384527367820504845322059284540805846753537293
To the casual observer, this is just random gibberish, meaning
nothing. But to the readers of the Numerica Format, it may
mean something useful -- perhaps even informative.
===========
Limitations
===========
There are a few limitations present within the sequence described
within this article. They are briefly outlined below:
1) Unfortunately, numbers are denoted beginning with the number 4, as
they
cannot be reliably sequenced by multiplication. This is a limitation
within the coding sequence itself. Therefore, it is defined as a flaw.
2) Additionally, only the most basic punctuation is included, bringing
the total coding sequence to forty-nine mathematical assignments (26
letters, 13 punctuation marks and 10 numbers). The 50th sequence is
left
undefined, and may be redefined as necessary.
3) Simple Numeri (such as "THE COW JUMPED OVER THE MOON.")
require long Numericas. This may be broken down into 40 or 80-column
singular Numeri in order to increase readability. In general, Numeri
should be indented slightly to allow for footnotes. For example:
|540805840353238452736782050484532205928454080584|
|6753537293 |
(The cow jumped over the | moon.)
4) Numeri are broken down into lines which may overlap (as above). To
designate where they might overlap, select either 40 or 80-columns set
into descending rows. Then word wrap the sentence as
suggested in the example above.
5) When translating simple documents to the Numerica Format, it is not
unusual to designate the 50th sequence (which is undefined) as a line
break. Example:
|540805840353238452736782050484532205928454080584|
|6753537293505408058405720493 |
(The cow jumped over the | moon. [line break] The End.)
==========
Conclusion
==========
The simplicity of the Numerica Format, combined with the difficulty
in determining source data, allows it to be invaluable for encoding
brief messages to those requiring security of information. The
majority of individuals who come across messages encoded as
Numerica will confuse the data with useless or trivial
information. If data needs to be secure, but decodable, this
is an easy and fairly straightforward method of accomplishing
such a task.
I have written a short program to take a sentence the user inputs and
translate it into the Numerica Format. See below:
http://members.tripod.com/~panks/numerica.html
Sincerely,
Paul Allen Panks
dunric@yahoo.com
Phoenix, Arizona
540805845492010962840919841954096262840401925693
197304040572625584555373840572035373725405928401
840653736238196705626209720784549253626293
080584029201720409190805198401846701720906051954
538401720484677367026205198419536705540809720784
010253735484727367059209030162841905897305720309
720793
035367670172048409077253920584549253626293
549253626284015454010356198467057219017254539293
840184080954938402625323840253737203051984530606
840192675392938467057219017201545392840919841954
096262840972840753530484190801820593
035367670172048419015584230853840119560504840653
92845408091929
540805840972030172540154095372840301731905198454
080584549253626284545384035322059284080919840501
921984017204840601626284545384540805840792537372
048419039205016709720793
5492536262840919840873925409720793
549253626284066205051984537354840172840564095493
5553738419050584260982840609620593
03536767017204840705548401626293
260982840609620584540156057293
0353676701720484737226098293
0353676701720484920501048419537392030593
540805841953739203058409198409728493
67057219017201545392840919840972848201097293
035367670172048492737284727367059209030193
54080584829253079201728403017272535484820192190584
09728273549384540564548406536262532309720784018403
53676701840919840907725392050493
67057219017201545392840919840873925409720793
01725354080592845572298455
82925307920167840453051984045354841973828253925484
54080584620192070584035367670172048482925367825484
19039205057284027306060592938492051973625419841903
92536262845306068419039205057284017204840192058462
53195493
67057219017201545392840919840154840405015408501984
04535392
03536767017204848973095493
67057219017201545392840919840405010493 |
|
|
| Back to top |
|
|
mensanator@aol.compost
science forum Guru
Joined: 24 Mar 2005
Posts: 826
|
| Posted: Wed Aug 10, 2005 5:41 pm Post subject:
Re: The Numerica Format
|
|
|
mensanator@aol.compost wrote:
| Quote: | dunric@yahoo.com wrote:
====================================================
"The Numerica Format: a numerical sequencing method"
By: Paul Allen Panks (dunric@yahoo.com)
Date: August 09, 2005
(Version 1.3 - Revised and Expanded)
====================================================
=======
Summary
=======
This is a simple encoding sequence using numbers assigned
as letters and punctuation. The sequence is comprised of an
encoding arrangement of 49 total letters, punctuation and
numerical mathematical assignments.
The resulting sequence uses the multiplication table of zero [0]
through
nine [9]. Some numbers -- 11,13,17,19,22,23,26, etc. -- are not
reachable
via the regular 0 through 9 multiplication tables. Such numbers must
then
be added together to simulate actual values not reachable via the
normal
multiplication standard.
This sequencing method is best described as the "Numerica Format".
Encoded sequences are called "Numericas". Individual sequence lines are
termed "Numeri".
=================
Binary Assignment
=================
To make full use of the sequence, letters, basic punctuation and
numbers
are approximated through simple mathematical equations. Forty-nine
total
letters, numbers and punctuation are assigned to the following numeric
values:
A = 1
B = 2
C = 3
D = 4
E = 5
F = 6
G = 7
H = 8
I = 9
J = 10
K = 11
L = 12
M = 13
N = 14
O = 15
P = 16
Q = 17
R = 18
S = 19
T = 20
U = 21
V = 22
W = 23
X = 24
Y = 25
Z = 26
Punctuation is also required, and thus is assigned to the following
numbers:
27 = .
28 = !
29 = ?
30 = ,
31 = &
32 = (space)
33 = *
34 = @
35 = %
36 = $
37 = +
38 = -
39 = #
40 = 0
41 = 1
42 = 2
43 = 3
44 = 4
45 = 5
46 = 6
47 = 7
48 = 8
49 = 9
50 = (undefined)
The sequence is straightforward and easily used. A brief explanation
(with an example of the sequence as it is normally used) will follow
later on during the course of this article.
===================
The Multiples Table
===================
Listed below is a standard multiplication table (used in the
Numerica Format). Note that numbers never go above 81, or below 0:
1 2 3 4 5 6 7 8 9
------------------------------------
0|1 2 3 4 5 6 7 8 9
1|1 2 3 4 5 6 7 8 9
2|2 4 6 8 10 12 14 16 18
3|3 6 9 12 15 18 21 24 27
4|4 8 12 16 20 24 28 32 36
5|5 10 15 20 25 30 35 40 45
6|6 12 18 24 30 36 42 48 54
7|7 14 21 28 35 42 49 56 63
8|8 16 24 32 40 48 56 64 72
9|9 18 27 36 45 54 63 72 81
------------------------------------
=====================================
How numbers are added (or multiplied)
=====================================
Some values (e.g. 11,13,17,19,22,23,26, etc.) have no possibility
of being multiplied successfully by numbers ranging from 0 through 9.
Therefore, they must be added together. In special cases, the added
numbers represent the larger numbers themselves (i.e. 2+9 will be
equal to the number "29",etc.)
In order to differentiate between multiplication of two numbers
(and addition), the sequence in which they are added together
is reversed in logical order.
The forty-nine numeric assignments are reached via the following
Simple mathematical equations (Note: Some equations arenequations;
rather,
they are quite literal representations of the
numbers themselves):
0+1=1 [A]
0+2=2 [B]
0+3=3 [C]
0+4=4 [D]
0+5=5 [E]
0+6=6 [F]
0+7=7 [G]
0+8=8 [H]
0+9=9 [I]
5*2=10 [J]
5+6=11 [K]
6*2=12 [L]
6+7=13 [M]
7*2=14 [N]
5*3=15 [O]
8*2=16 [P]
8+9=17 [Q]
9*2=18 [R]
1+9=19 [S]
5*4=20 [T]
7*3=21 [U]
2+2=22 [V]
2+3=23 [W]
6*4=24 [X]
5*5=25 [Y]
2+6=26 [Z]
9*3=27 [.]
7*4=28 [!]
2+9=29 [?]
6*5=30 [,]
3+1=31 [&]
8*4=32 [ ]
3+3=33 [*]
3+4=34 [@]
7*5=35 [%]
9*4=36 [$]
3+7=37 [+]
3+8=38 [-]
3+9=39 [#]
4+0=40 [0]
4+1=41 [1]
4+2=42 [2]
4+3=43 [3]
4+4=44 [4]
4+5=45 [5]
4+6=46 [6]
4+7=47 [7]
4+8=48 [8]
4+9=49 [9]
5+0=50 [blank]
A few notes:
The 50th sequence is left undefined, thus, the Numerica Format really
only
has 49. "Space", an invisible punctuation mark used to separate words
from
one another in normal language, is assigned as the 32nd sequence.
Addition always has the lowest value added first, followed by the
larger
value. In only a few instances, such as 2+2, are the values the same
when
adding together two numbers. When multiplying, the first number is
always
larger than the second, with one exception: 5*5 (the sum has no known
value reachable via numbers 0 through 9 outside of 5*5).
==========================
Example of a simple Numeri
==========================
A brief summary of a simple Numeri and the resulting sequence
follows. This is a simple Numeri consisting of 6 total words and
1 punctuation mark (a period, or .).
Example:
THE COW JUMPED OVER THE MOON.
Translated:
54 08 05 84 03 53 23 84 52 73 67 82 05 04 84 53 22 05 92 84 54 08
05 84 67 53 53 72 93
T H E C O W J U M P E D O V E R T H E
M
O O N .
Or:
THE COW JUMPED OVER THE MOON.
5408058403532384527367820504845322059284540805846753537293
To the casual observer, this is just random gibberish, meaning
nothing. But to the readers of the Numerica Format, it may
mean something useful -- perhaps even informative.
===========
Limitations
===========
There are a few limitations present within the sequence described
within this article. They are briefly outlined below:
1) Unfortunately, numbers are denoted beginning with the number 4, as
they
cannot be reliably sequenced by multiplication. This is a limitation
within the coding sequence itself. Therefore, it is defined as a flaw.
2) Additionally, only the most basic punctuation is included, bringing
the total coding sequence to forty-nine mathematical assignments (26
letters, 13 punctuation marks and 10 numbers). The 50th sequence is
left
undefined, and may be redefined as necessary.
3) Simple Numeri (such as "THE COW JUMPED OVER THE MOON.")
require long Numericas. This may be broken down into 40 or 80-column
singular Numeri in order to increase readability. In general, Numeri
should be indented slightly to allow for footnotes. For example:
|540805840353238452736782050484532205928454080584|
|6753537293 |
(The cow jumped over the | moon.)
4) Numeri are broken down into lines which may overlap (as above). To
designate where they might overlap, select either 40 or 80-columns set
into descending rows. Then word wrap the sentence as
suggested in the example above.
5) When translating simple documents to the Numerica Format, it is not
unusual to designate the 50th sequence (which is undefined) as a line
break. Example:
|540805840353238452736782050484532205928454080584|
|6753537293505408058405720493 |
(The cow jumped over the | moon. [line break] The End.)
==========
Conclusion
==========
The simplicity of the Numerica Format, combined with the difficulty
in determining source data, allows it to be invaluable for encoding
brief messages to those requiring security of information. The
majority of individuals who come across messages encoded as
Numerica will confuse the data with useless or trivial
information. If data needs to be secure, but decodable, this
is an easy and fairly straightforward method of accomplishing
such a task.
I have written a short program to take a sentence the user inputs and
translate it into the Numerica Format. See below:
http://members.tripod.com/~panks/numerica.html
Sincerely,
Paul Allen Panks
dunric@yahoo.com
Phoenix, Arizona
540805845492010962840919841954096262840401925693
197304040572625584555373840572035373725405928401
840653736238196705626209720784549253626293
080584029201720409190805198401846701720906051954
538401720484677367026205198419536705540809720784
010253735484727367059209030162841905897305720309
720793
035367670172048409077253920584549253626293
549253626284015454010356198467057219017254539293
840184080954938402625323840253737203051984530606
840192675392938467057219017201545392840919841954
096262840972840753530484190801820593
035367670172048419015584230853840119560504840653
92845408091929
540805840972030172540154095372840301731905198454
080584549253626284545384035322059284080919840501
921984017204840601626284545384540805840792537372
048419039205016709720793
5492536262840919840873925409720793
549253626284066205051984537354840172840564095493
5553738419050584260982840609620593
03536767017204840705548401626293
260982840609620584540156057293
0353676701720484737226098293
0353676701720484920501048419537392030593
540805841953739203058409198409728493
67057219017201545392840919840972848201097293
035367670172048492737284727367059209030193
54080584829253079201728403017272535484820192190584
09728273549384540564548406536262532309720784018403
53676701840919840907725392050493
67057219017201545392840919840873925409720793
01725354080592845572298455
82925307920167840453051984045354841973828253925484
54080584620192070584035367670172048482925367825484
19039205057284027306060592938492051973625419841903
92536262845306068419039205057284017204840192058462
53195493
|
Oops! Typo. That should be
82925307920167840453051984725354841973828253925484
54080584620192070584035367670172048482925367825484
19039205057284027306060592938492051973625419841903
92536262845306068419039205057284017204840192058462
53195493
| Quote: |
67057219017201545392840919840154840405015408501984
04535392
03536767017204848973095493
67057219017201545392840919840405010493 |
|
|
| Back to top |
|
|
mensanator@aol.compost
science forum Guru
Joined: 24 Mar 2005
Posts: 826
|
| Posted: Wed Aug 10, 2005 5:52 pm Post subject:
Re: The Numerica Format
|
|
|
dunric@yahoo.com wrote:
| Quote: | Not quite sure what that means. I need a program to decode numerica
now.
|
You don't have a decoder?! Will that be in version 2.0?
How do you know your program's working?
I didn't want to spoil the fun by posting the source in case
anyone wanted to build a decoder (or use crypto since it is
trivially encoded).
But here it is:
S
P
O
I
L
E
R
the trail is still dark.
suddenly you encounter a foul-smelling troll.
he brandishes a manifesto and mumbles something about
numerical sequencing.
command> ignore troll.
troll attacks mensantor. a hit. blow bounces off armor.
mensanator is still in good shape.
command> say "who asked for this?"
the incantation causes the troll to cover his ears and
fall to the ground screaming.
troll is hurting.
troll flees out an exit.
you see zip file.
command> get all.
zip file taken.
command> unzip.
command> read source.
the source is in BASIC.
mensanator is in pain.
command> run numerica.
the progran cannot parse input. text following a comma
is ignored.
mensanator is hurting.
another (y/n)? y
program does not support the large command prompt screen
buffer. results scroll off screen and are lost.
mensanator is at death's door, knocking loudly.
command> quit.
mensanator is dead. |
|
| Back to top |
|
|
Guest
|
| Posted: Wed Aug 10, 2005 6:15 pm Post subject:
Re: The Numerica Format
|
|
|
BASIC was just a very quick job to see if I could write a program to
translate to numerica. It's rough, but it seems to work.
Now I just need to work on a decoder.
Paul
mensanator@aol.compost wrote:
| Quote: | dunric@yahoo.com wrote:
Not quite sure what that means. I need a program to decode numerica
now.
You don't have a decoder?! Will that be in version 2.0?
How do you know your program's working?
I didn't want to spoil the fun by posting the source in case
anyone wanted to build a decoder (or use crypto since it is
trivially encoded).
But here it is:
S
P
O
I
L
E
R
the trail is still dark.
suddenly you encounter a foul-smelling troll.
he brandishes a manifesto and mumbles something about
numerical sequencing.
command> ignore troll.
troll attacks mensantor. a hit. blow bounces off armor.
mensanator is still in good shape.
command> say "who asked for this?"
the incantation causes the troll to cover his ears and
fall to the ground screaming.
troll is hurting.
troll flees out an exit.
you see zip file.
command> get all.
zip file taken.
command> unzip.
command> read source.
the source is in BASIC.
mensanator is in pain.
command> run numerica.
the progran cannot parse input. text following a comma
is ignored.
mensanator is hurting.
another (y/n)? y
program does not support the large command prompt screen
buffer. results scroll off screen and are lost.
mensanator is at death's door, knocking loudly.
command> quit.
mensanator is dead. |
|
|
| Back to top |
|
|
Guest
|
| Posted: Wed Aug 10, 2005 8:03 pm Post subject:
Re: The Numerica Format
|
|
|
Here's an updated version of the program that should work correctly:
5 dim a$(55):dim b$(55)
100 for x=1 to 50:read a$(x):read b$(x):next x
105 print"numerica format":print
106 print"enter a sentence to convert to numerica format:":print
110 line input ry$:ry$=lcase$(ry$)
115 print:print"working..."
120 print
125 c$="":for x=1 to len(ry$):for y=1 to 50:if mid$(ry$,x,1)=a$(y) then
c$=c$+b$(y)
130 next:next
135 print:print"in numerica format:":print
140 print c$
145 print
146 rem input"convert back (y/n)";ry$
147 rem if ry$="y" or ry$="Y" then goto 160
149 rem print
150 input"another (y/n)";ry$
151 if ry$="y" or ry$="Y" then run
152 end
160 rem print
161 rem print "converting back...":print
162 rem d$="":for x=1 to len(c$):for y=1 to 50:if mid$(c$,x,1)=b$(y)
then d$=d$+a$(y)
163 rem next:next
164 rem print d$
165 rem print:goto 150
1000 rem numerica format
1001 data"a","01","b","02","c","03","d","04","e","05"
1002 data"f","06","g","07","h","08","i","09","j","52"
1003 data"k","56","l","62","m","67","n","72","o","53"
1004 data"p","82","q","89","r","92","s","19","t","54"
1005 data"u","73","v","22","w","23","x","64","y","55"
1006 data"z","26",".","93","!","74","?","29",",","65"
1007 data"&","31"," ","84","*","33","@","34","%","75"
1008 data"$","94","+","37","-","38","#","39","0","40"
1009 data"1","41","2","42","3","43","4","44","5","45"
1010 data"6","46","7","47","8","48","9","49","'","50"
Paul
mensanator@aol.compost wrote:
| Quote: | dunric@yahoo.com wrote:
Not quite sure what that means. I need a program to decode numerica
now.
You don't have a decoder?! Will that be in version 2.0?
How do you know your program's working?
I didn't want to spoil the fun by posting the source in case
anyone wanted to build a decoder (or use crypto since it is
trivially encoded).
But here it is:
S
P
O
I
L
E
R
the trail is still dark.
suddenly you encounter a foul-smelling troll.
he brandishes a manifesto and mumbles something about
numerical sequencing.
command> ignore troll.
troll attacks mensantor. a hit. blow bounces off armor.
mensanator is still in good shape.
command> say "who asked for this?"
the incantation causes the troll to cover his ears and
fall to the ground screaming.
troll is hurting.
troll flees out an exit.
you see zip file.
command> get all.
zip file taken.
command> unzip.
command> read source.
the source is in BASIC.
mensanator is in pain.
command> run numerica.
the progran cannot parse input. text following a comma
is ignored.
mensanator is hurting.
another (y/n)? y
program does not support the large command prompt screen
buffer. results scroll off screen and are lost.
mensanator is at death's door, knocking loudly.
command> quit.
mensanator is dead. |
|
|
| Back to top |
|
|
Guest
|
| Posted: Wed Aug 10, 2005 11:34 pm Post subject:
Re: The Numerica Format
|
|
|
Here's a version of the program which converts to and from the Numerica
Format:
5 dim a$(55):dim b$(55)
100 for x=1 to 50:read a$(x):read b$(x):next x
105 print"numerica format":print
106 print"enter a sentence to convert to numerica format:":print
110 line input ry$:ry$=lcase$(ry$)
115 print:print"working..."
120 print
125 c$="":for x=1 to len(ry$):for y=1 to 50:if mid$(ry$,x,1)=a$(y) then
c$=c$+b$(y)
130 next:next
135 print:print"in numerica format:":print
140 print c$
145 print
146 input"convert back (y/n)";ry$
147 if ry$="y" or ry$="Y" then goto 160
149 print
150 input"another (y/n)";ry$
151 if ry$="y" or ry$="Y" then run
152 end
160 print
161 print "converting back...":print
162 d$="":for x=1 to len(c$) step 2:for y=1 to 50:if mid$(c$,x,2)=b$(y)
then d$=d$+a$(y)
163 next:next
164 print d$
165 print:goto 150
1000 rem numerica format
1001 data"a","01","b","02","c","03","d","04","e","05"
1002 data"f","06","g","07","h","08","i","09","j","52"
1003 data"k","56","l","62","m","67","n","72","o","53"
1004 data"p","82","q","89","r","92","s","19","t","54"
1005 data"u","73","v","22","w","23","x","64","y","55"
1006 data"z","26",".","93","!","74","?","29",",","65"
1007 data"&","31"," ","84","*","33","@","34","%","75"
1008 data"$","94","+","37","-","38","#","39","0","40"
1009 data"1","41","2","42","3","43","4","44","5","45"
1010 data"6","46","7","47","8","48","9","49","'","50"
Paul |
|
| Back to top |
|
|
mensanator@aol.compost
science forum Guru
Joined: 24 Mar 2005
Posts: 826
|
| Posted: Wed Aug 10, 2005 11:53 pm Post subject:
Re: The Numerica Format
|
|
|
dunric@yahoo.com wrote:
| Quote: | Here's an updated version of the program that should work correctly:
|
But I don't have BASIC.
And by the way, there is a BIG difference between "working
correctly" and being CORRECT!
Your encodings in the BASIC program do NOT match your document.
Note that your codes are not 1-50. Did you forget to adjust for
lower case? And why do you have "'" assigned to "50"? I thought
"50" was undefined?
I put together a quick Python encoder/decoder but didn't notice
the code discrepency in time to fix it. So here's my bullshit
encoder/decoder:
import string
def encode(s):
t = ""
for i in s:
t = t + bsnumerica[i]
return t
def decode(s):
t = ""
if (len(s) % 2)==1:
# invalid string length, valid strings have even char count
# delete extra character and append the undefined code
s = s[:-1] + "50"
for i in xrange(len(s)/2):
t = t + inv_bsnumerica[s[i*2:i*2+2]]
return t
# this dictionary is labeled 'bs' because the bullshit BASIC program
# from which it was copied is inconsistent with the table given in
# "The Numerica Format: a numerical sequencing method"
bsnumerica =
dict([["a","01"],["b","02"],["c","03"],["d","04"],["e","05"], \
["f","06"],["g","07"],["h","08"],["i","09"],["j","52"], \
["k","56"],["l","62"],["m","67"],["n","72"],["o","53"], \
["p","82"],["q","89"],["r","92"],["s","19"],["t","54"], \
["u","73"],["v","22"],["w","23"],["x","64"],["y","55"], \
["z","26"],[".","93"],["!","74"],["?","29"],[",","65"], \
["&","31"],[" ","84"],["*","33"],["@","34"],["%","75"], \
["$","94"],["+","37"],["-","38"],["#","39"],["0","40"], \
["1","41"],["2","42"],["3","43"],["4","44"],["5","45"], \
["6","46"],["7","47"],["8","48"],["9","49"],["'","50"], \
])
temp = bsnumerica.items()
inv_bsnumerica = {}
# build an inverse of the dictionary to decode the encoded strings
for i in temp:
inv_bsnumerica[i[1]] = i[0]
# test file
f = open('GA.txt','r')
test = f.readlines()
# test the encoding
for t in test:
t = string.lower(t[:-1]) # drop the newline char
t = encode(t)
print t
# decode(encode(t)) should return original text
for t in test:
t = string.lower(t[:-1])
t = decode(encode(t))
print t
f.close
"""
test file (GA.txt):
Four score and seven years ago
our fathers brought forth on
this continent a new nation
conceived in liberty and
dedicated to the proposition
that all men are created equal.
test results:
065373928419035392058401720484190522057284550501921984010753
53739284060154080592198402925373070854840653925408845372
540809198403537254097205725484018472052384720154095372
035372030509220504840972846209020592545584017204
04050409030154050484545384540805848292538253190954095372
54080154840162628467057284019205840392050154050484058973016293
four score and seven years ago
our fathers brought forth on
this continent a new nation
conceived in liberty and
dedicated to the proposition
that all men are created equal.
""" |
|
| Back to top |
|
|
C Rode
science forum beginner
Joined: 25 May 2005
Posts: 18
|
| Posted: Thu Aug 11, 2005 12:48 am Post subject:
Re: The Numerica Format
|
|
|
| Quote: | Example:
THE COW JUMPED OVER THE MOON.
Translated:
54 08 05 84 03 53 23 84 52 73 67 82 05 04 84 53 22 05 92 84 54 08
05 84 67 53 53 72 93
|
Okay, 54 08 05 84 appears twice. Also, the second 54 08 05 84 has an 84
preceding it as well...
Now take 54, 84, or any other number. It may not matter how the number was
arrived at but only matter what the number represents...
And if the eight letter is tried for 08 and the fifth letter is tried for 05
then the word THE is guessed and 84 is guessed as a space. |
|
| Back to top |
|
|
Jim Brain
science forum beginner
Joined: 11 Aug 2005
Posts: 2
|
| Posted: Thu Aug 11, 2005 5:40 am Post subject:
Re: The Numerica Format
|
|
|
dunric@yahoo.com wrote:
| Quote: | ====================================================
"The Numerica Format: a numerical sequencing method"
|
More thread of discussion on this is in comp.sys.cbm.
Paul, I still say there are many beter encoders available to meet your
needs. These folks here might have some good ones to share, but
Numerica is just too trivial to decipher.
Jim
--
Jim Brain, Brain Innovations
brain@jbrain.com http://www.jbrain.com
Dabbling in WWW, Embedded Systems, Old CBM computers, and Good Times! |
|
| Back to top |
|
|
Guest
|
| Posted: Thu Aug 11, 2005 8:25 am Post subject:
Re: The Numerica Format
|
|
|
Yes, that is very true. I wanted to develop something purely for fun. I
think Numerica is just simple for a reason: it uses addition and
multiplication to arrive at numbers in a lookup table.
Paul
Jim Brain wrote:
| Quote: | dunric@yahoo.com wrote:
====================================================
"The Numerica Format: a numerical sequencing method"
More thread of discussion on this is in comp.sys.cbm.
Paul, I still say there are many beter encoders available to meet your
needs. These folks here might have some good ones to share, but
Numerica is just too trivial to decipher.
Jim
--
Jim Brain, Brain Innovations
brain@jbrain.com http://www.jbrain.com
Dabbling in WWW, Embedded Systems, Old CBM computers, and Good Times! |
|
|
| Back to top |
|
|
Jim Brain
science forum beginner
Joined: 11 Aug 2005
Posts: 2
|
| Posted: Thu Aug 11, 2005 11:55 am Post subject:
Re: The Numerica Format
|
|
|
dunric@yahoo.com wrote:
| Quote: | Yes, that is very true. I wanted to develop something purely for fun. I
think Numerica is just simple for a reason: it uses addition and
multiplication to arrive at numbers in a lookup table.
|
Not as simple as XORing a seed byte over the text, or successively
douing so. Those kind of encodings don;t even need a lookup table.
Just the seed and the encoded text and you're done. This is not my area
of epertise, but I think there are other such encodings.
JIm
--
Jim Brain, Brain Innovations
brain@jbrain.com http://www.jbrain.com
Dabbling in WWW, Embedded Systems, Old CBM computers, and Good Times! |
|
| Back to top |
|
|
Google
|
|
| Back to top |
|
|
|
|
The time now is Fri Jul 30, 2010 5:42 am | All times are GMT
|
|
Copyright © 2004-2005 DeniX Solutions SRL
|
|
Other DeniX Solutions sites:
Electronics forum |
Medicine forum |
Unix/Linux blog |
Unix/Linux documentation |
Unix/Linux forums
|
Powered by phpBB © 2001, 2005 phpBB Group
|
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
Forum index
»
Science and Technology
»
Math
»
num-analysis
