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#26 2012-10-17 13:24:52

bobbym
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Re: Pascal's square

Hi;

Perhaps, the other was too personal of a question. I have no problem with what you are.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#27 2012-10-18 01:44:11

ShivamS
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Re: Pascal's square

Meh.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann
 

#28 2012-10-18 02:00:55

bobbym
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Re: Pascal's square

Hmmmm. There is that word again.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#29 2012-10-18 02:13:05

ShivamS
Super Member

Online

Re: Pascal's square

Meh. By the way, sorry for hijacking this thread.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann
 

#30 2012-10-31 01:23:44

Mpmath
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Re: Pascal's square

Hi everyone;

I notice that in Pascal's square I can begin with every number instead 1 And the numbers of the square are exponents of 2 multiplied by that numbers. Here an example with 3:


3       3       6      12      24      48       96

3        3       6      12      24      48       96

6        6      12     24      48      96      192

12     12     24     48      96     192     384

24     24     48     96     192    384     768

48     48     96    192    384    768    1536

96     96    192   384    768   1536   3072


Which is the result of

3x1  3x1  3x2  3x4

3x1  3x1  3x2  3x4

3x2  3x2  3x4  3x8

3x4  3x4  3x4  3x16

Last edited by Mpmath (2012-10-31 01:24:39)


Winter is coming.
 

#31 2012-10-31 02:55:00

bobbym
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Re: Pascal's square

Hi Mpmath;

Sorry I could not get to you before but I had much work. Okay, also your columns are what is called a full history recurrence.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#32 2012-10-31 03:13:01

Mpmath
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Re: Pascal's square

Thanks bobbym.


Winter is coming.
 

#33 2012-10-31 03:18:16

bobbym
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Re: Pascal's square

Hi;

Have you tried primes in the top row?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#34 2012-10-31 03:53:06

Mpmath
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Re: Pascal's square

I tried. This is the result:

2    3    5    7    11
2    3    5    7    11
4    6   10   14   22
8   12  20   28   44
16 24  40   56   88


Winter is coming.
 

#35 2012-10-31 04:01:11

bobbym
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Re: Pascal's square

Hi;

And what did you notice?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#36 2012-10-31 04:24:03

Mpmath
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Re: Pascal's square

The sum of the numbers of each row doesn't give a right result, but all numbers are the product of the prime and all exponents of 2.


Winter is coming.
 

#37 2012-10-31 04:39:38

bobbym
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Re: Pascal's square

Okay, just wanted to see what happens.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#38 2012-10-31 04:54:32

Mpmath
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Re: Pascal's square

I think that the square with prime numbers is not a Pascal's square, but it's still an intersting disposition of numbers.


Winter is coming.
 

#39 2012-10-31 06:36:43

anonimnystefy
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Re: Pascal's square

By what principle do you exactly get each number of the square?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#40 2012-10-31 06:42:29

Mpmath
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Re: Pascal's square

Hi;
Here is the proceedings:


  1

   1 = 1
   =    =
   1 = 1

   1 + 1 = 2
   +    +    +
   1 + 1 = 2
   =    =    =
   2 + 2 = 4


Winter is coming.
 

#41 2012-10-31 07:42:38

MathsIsFun
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Re: Pascal's square

It might be interesting to have different rules. For example: add the numbers above, left and diagonal-above-left.

1 1  1  1
1 3  5  7
1 5 13 25


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#42 2012-10-31 08:53:50

Mpmath
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Re: Pascal's square

Of course. There are so many rules that we can use. For example we can only add the numbers in each row, or in each column, using different kinds of successions. These mustn't be just Pascal's square with one rule.


Winter is coming.
 

#43 2012-10-31 09:04:47

anonimnystefy
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Re: Pascal's square

MathsIsFun wrote:

It might be interesting to have different rules. For example: add the numbers above, left and diagonal-above-left.

1 1  1  1
1 3  5  7
1 5 13 25

This seems more in the spirit of Pascal's triangle.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#44 2012-10-31 09:27:23

Mpmath
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Re: Pascal's square

Well, this

1  1  1  1
1  3  5  7
1 5 13 25

Is a Pascal's square, similar to the triangle. The rule is the same, but numbers are very different.

Last edited by Mpmath (2012-10-31 09:28:03)


Winter is coming.
 

#45 2012-10-31 15:11:26

bobbym
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Re: Pascal's square

That one has the rule the one to the left plus the two on top.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#46 2012-10-31 18:24:12

Mpmath
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Re: Pascal's square

A Pascal's square has more rules And possibilities than a Pascal's triangle.


Winter is coming.
 

#47 2012-10-31 21:27:38

Mpmath
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Re: Pascal's square

I also find another square, similiar to that of MathIsFun. The only different is that numbers on the first column and on the first row are exponents of 2. This is the square:

1  1  2   4
1  3  6  12
2  6 15 33
4 12 33 81


Winter is coming.
 

#48 2012-10-31 21:35:29

bobbym
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Re: Pascal's square

Hi;

What is the rule that is generating each row?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#49 2012-10-31 22:09:18

Mpmath
Full Member

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Re: Pascal's square

Hi;

Add the numbers above, left and diagonal-above-left, just like the square of MathIsFun. But in mine also the numbers in the first row and in the first column are exponents of 2, obtained by the sum of the numbers.


Winter is coming.
 

#50 2012-10-31 22:29:49

bobbym
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Re: Pascal's square

Hi;

Yes, I see that now, thanks.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

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