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You're welcome.
Hi;
Yes, I try. Numbers coincide. I notice right now that MathIsFun square is square array of Delannoy numbers (A008288 of OEIS).
Hi everyone;
I have carefully studied all Pascal's squares and in some of them I found some interesting successions. In this square, that MathIsFun proposed:
1 1 1 1
1 3 5 7
1 5 13 25
1 7 25 63
The sum of the numbers of every diagonal give Pell numbers (A000129 of OEIS).
1=1
1+1=2
1+3+1=5
1+5+5+1=12
1+7+13+7+1=29
Regarding my Pascal's square:
1 1 2 4 8
1 1 2 4 8
2 2 4 8 16
4 4 8 16 32
8 8 16 32 64
16 16 32 64 128
The sum of the numbers of every diagonal give numbers of 1's in all compositons of n+1 (A045623 of OEIS).
Hi MIF;
This is a very good job. Congratulations!
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.
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
A Pascal's square has more rules And possibilities than a Pascal's triangle.
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.
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.
Hi;
Here is the proceedings:
1
1 = 1
= =
1 = 1
1 + 1 = 2
+ + +
1 + 1 = 2
= = =
2 + 2 = 4
I think that the square with prime numbers is not a Pascal's square, but it's still an intersting disposition of numbers.
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.
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
Thanks bobbym.
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
And also infinity divided by infinity = undefined.
I agree with anonimnystefy, infinity-infinity is undefined.
I agree with you. I see infinity like a way to define our universe. As I said before if we find the biggest number in the world we can add one and we will have a new number, bigger than the previous number. So we can go on we will never find a final result, but we can't prove that infinity exists because we will never reach infinity, in each field of science. We can only theorize his existence, But I think that infinity is a fundamental concept for understand mathematics.
If we will find the largest number we can currently store in a computer, we can plus 1 and we will have Another largest number.
But if infinity will be eliminate, numbers will be infinite or not?
Well, no one can decide what is better Regarding infinity, we can only have a theory.
I think that eliminate infinity is absurd. Infinity is a way to define where numbers and universe can arrive.
Hi;
This small movement wants to eliminate infinity or operations with infinity?
Ok. This is most Plausible hypothesis.
Yes, that's what I was thinking.