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Ihave discovered a simple theorem in the field of mathematics.
http://www.scribd.co...s-new-discovery
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A New Discovery In Mathematics
A new theorem in mathematics(number -theory)
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#2
phillip1882 
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Posted 27 January 2012 - 09:56 PM
while interesting, not really sure its a new discovery.
to summarize for people who don't want to look at the whole thing,
if you take a constant addition series, such as 2,4,6,8,10 etc.
then the squares, cubes, ^4, ^5, etc. will also have an second, third, fourth, fifth etc. level common difference; n!*s^n.
what i find cool however is i believe you discovered this property on your own.
to summarize for people who don't want to look at the whole thing,
if you take a constant addition series, such as 2,4,6,8,10 etc.
then the squares, cubes, ^4, ^5, etc. will also have an second, third, fourth, fifth etc. level common difference; n!*s^n.
what i find cool however is i believe you discovered this property on your own.
#3
CraigD
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Posted 27 January 2012 - 11:07 PM
This isn't a new discovery, though I agree with Phillip that finding this on your own shows good thinking. 
Any collection of n pairs of real numbers defines a polynomial of no greater than degree n-1.
Isaac Newton published a complete description of a method for finding the coefficients of this polynomial given its collection of number pairs in 1687 in his famous Principia Mathematica. It's known by a variety of names, such as "Newton's divided difference interpolation method." There are many good descriptions of it (Newton's actual writing is difficult for modern readers, so not recommended), such as this wikipedia article.
By confining your work to sequences or single numbers, rather than an ordered sequence of number pairs, you're actually considering the special case of Newton's method where the first of number in each pair differs from the preceding pair's by 1, or more generally, by any constant.
Any collection of n pairs of real numbers defines a polynomial of no greater than degree n-1.
Isaac Newton published a complete description of a method for finding the coefficients of this polynomial given its collection of number pairs in 1687 in his famous Principia Mathematica. It's known by a variety of names, such as "Newton's divided difference interpolation method." There are many good descriptions of it (Newton's actual writing is difficult for modern readers, so not recommended), such as this wikipedia article.
By confining your work to sequences or single numbers, rather than an ordered sequence of number pairs, you're actually considering the special case of Newton's method where the first of number in each pair differs from the preceding pair's by 1, or more generally, by any constant.
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#4
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Posted 30 January 2012 - 06:28 AM
Dhanesh, on 27 January 2012 - 11:15 AM, said:
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#5
Dhanesh
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Posted 30 January 2012 - 11:59 PM
Thanks for your comments.
I have quoted it as a discovery, because I haven't found anywhere that such a relation exist for arithmetic progression; particularly confined to two below given aspects.
1. The powers of consecutive terms of any arithmetic progression forms a series(quadratic when n=2 , cubic when n=3 and so on)
2. There is a numerical relation between the common difference of arithmetic progression and n'th difference of the powers of the consecutive terms of the a.p.
Also there are many practical applications for this discovery. I'm writing a book on the same.
Another vital point is that this could be easily comprehended by anyone with a little knowledge in mathematics.
I have quoted it as a discovery, because I haven't found anywhere that such a relation exist for arithmetic progression; particularly confined to two below given aspects.
1. The powers of consecutive terms of any arithmetic progression forms a series(quadratic when n=2 , cubic when n=3 and so on)
2. There is a numerical relation between the common difference of arithmetic progression and n'th difference of the powers of the consecutive terms of the a.p.
Also there are many practical applications for this discovery. I'm writing a book on the same.
Another vital point is that this could be easily comprehended by anyone with a little knowledge in mathematics.
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