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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

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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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,528

Meh.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

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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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,528

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

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

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

Thanks bobbym.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

Hi;

Have you tried primes in the top row?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

Hi;

And what did you notice?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

Okay, just wanted to see what happens.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

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

Hi;

Here is the proceedings:

1

1 = 1

= =

1 = 1

1 + 1 = 2

+ + +

1 + 1 = 2

= = =

2 + 2 = 4

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

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

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

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

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

Hi;

What is the rule that is generating each row?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

Hi;

Yes, I see that now, thanks.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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