Pascal's square

bobbym · 2012-10-16 14:24:52

Hi;

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

ShivamS · 2012-10-17 02:44:11

Meh.

bobbym · 2012-10-17 03:00:55

Hmmmm. There is that word again.

ShivamS · 2012-10-17 03:13:05

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

Mpmath · 2012-10-30 02:23:44

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

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

3x2 3x2 3x4 3x8

3x4 3x4 3x4 3x16

Last edited by Mpmath (2012-10-30 02:24:39)

bobbym · 2012-10-30 03:55:00

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.

Mpmath · 2012-10-30 04:13:01

Thanks bobbym.

bobbym · 2012-10-30 04:18:16

Hi;

Have you tried primes in the top row?

Mpmath · 2012-10-30 04:53:06

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

bobbym · 2012-10-30 05:01:11

Hi;

And what did you notice?

Mpmath · 2012-10-30 05:24:03

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.

bobbym · 2012-10-30 05:39:38

Okay, just wanted to see what happens.

Mpmath · 2012-10-30 05:54:32

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

anonimnystefy · 2012-10-30 07:36:43

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

Mpmath · 2012-10-30 07:42:29

Hi;
Here is the proceedings:

1

1 = 1
= =
1 = 1

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

MathsIsFun · 2012-10-30 08:42:38

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

Mpmath · 2012-10-30 09:53:50

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.

anonimnystefy · 2012-10-30 10:04:47

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.

Mpmath · 2012-10-30 10:27:23

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)

bobbym · 2012-10-30 16:11:26

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

Mpmath · 2012-10-30 19:24:12

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

Mpmath · 2012-10-30 22:27:38

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

bobbym · 2012-10-30 22:35:29

Hi;

What is the rule that is generating each row?

Mpmath · 2012-10-30 23:09:18

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.

bobbym · 2012-10-30 23:29:49

Hi;

Yes, I see that now, thanks.

Math Is Fun Forum

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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

Re: Pascal's square

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