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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#27 2012-10-18 01:44:11
- Shivamcoder3013
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Re: Pascal's square
Meh.
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.
-Archimedes
My maturity level depends on the people I am around.
#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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#29 2012-10-18 02:13:05
- Shivamcoder3013
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Re: Pascal's square
Meh. By the way, sorry for hijacking this thread.
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.
-Archimedes
My maturity level depends on the people I am around.
#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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#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.
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#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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#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.
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#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
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#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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#49 2012-10-31 22:09:18
- Mpmath
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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.