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#26 2012-10-16 14:24:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,688

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#27 2012-10-17 02:44:11

ShivamS
Member
Registered: 2011-02-07
Posts: 3,532

Re: Pascal's square

Meh.

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#28 2012-10-17 03:00:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,688

Re: Pascal's square

Hmmmm. There is that word again.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#29 2012-10-17 03:13:05

ShivamS
Member
Registered: 2011-02-07
Posts: 3,532

Re: Pascal's square

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

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#30 2012-10-30 02:23:44

Mpmath
Member
Registered: 2012-10-11
Posts: 216

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 (2012-10-30 02:24:39)


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#31 2012-10-30 03:55:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,688

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#32 2012-10-30 04:13:01

Mpmath
Member
Registered: 2012-10-11
Posts: 216

Re: Pascal's square

Thanks bobbym.


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#33 2012-10-30 04:18:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,688

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#34 2012-10-30 04:53:06

Mpmath
Member
Registered: 2012-10-11
Posts: 216

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


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#35 2012-10-30 05:01:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,688

Re: Pascal's square

Hi;

And what did you notice?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#36 2012-10-30 05:24:03

Mpmath
Member
Registered: 2012-10-11
Posts: 216

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.


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#37 2012-10-30 05:39:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,688

Re: Pascal's square

Okay, just wanted to see what happens.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#38 2012-10-30 05:54:32

Mpmath
Member
Registered: 2012-10-11
Posts: 216

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.


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#39 2012-10-30 07:36:43

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

Re: Pascal's square

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


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#40 2012-10-30 07:42:29

Mpmath
Member
Registered: 2012-10-11
Posts: 216

Re: Pascal's square

Hi;
Here is the proceedings:


  1

   1 = 1
   =    =
   1 = 1

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


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#41 2012-10-30 08:42:38

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

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

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#42 2012-10-30 09:53:50

Mpmath
Member
Registered: 2012-10-11
Posts: 216

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.


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#43 2012-10-30 10:04:47

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

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.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#44 2012-10-30 10:27:23

Mpmath
Member
Registered: 2012-10-11
Posts: 216

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 (2012-10-30 10:28:03)


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#45 2012-10-30 16:11:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,688

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#46 2012-10-30 19:24:12

Mpmath
Member
Registered: 2012-10-11
Posts: 216

Re: Pascal's square

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


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#47 2012-10-30 22:27:38

Mpmath
Member
Registered: 2012-10-11
Posts: 216

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


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#48 2012-10-30 22:35:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,688

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#49 2012-10-30 23:09:18

Mpmath
Member
Registered: 2012-10-11
Posts: 216

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.


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#50 2012-10-30 23:29:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,688

Re: Pascal's square

Hi;

Yes, I see that now, thanks.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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