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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

Meh.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

Hmmmm. There is that word again.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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: 106,389

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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: 106,389

Hi;

Have you tried primes in the top row?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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: 106,389

Hi;

And what did you notice?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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: 106,389

Okay, just wanted to see what happens.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

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

The knowledge of some things as a function of age is a delta function.

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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: 7,630

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: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

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

The knowledge of some things as a function of age is a delta function.

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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: 106,389

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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: 106,389

Hi;

What is the rule that is generating each row?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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: 106,389

Hi;

Yes, I see that now, thanks.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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