[Dhanesh]

Ihave discovered a simple theorem in the field of mathematics.
http://www.scribd.co...s-new-discovery

Please post your valuable feedbacks.

[phillip1882]

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.

[CraigD]

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.

[Qfwfq]

Dhanesh, on 27 January 2012 - 11:15 AM, said:

Please post your valuable feedbacks.

You might be interested to look up what purpose Charles Babbage attempted to build his Differential Engine for.

[Dhanesh]

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.

[suresh kumawat]

Ya its very interesting but i am not sure its a new discovery or not and if its a new discovery then its gonna be very helpful in the field of mathematics and as you are saying that it also has many practical applications as well so it will be very beneficial in the field of mathematics.
__________________________
spammish link removed

This post has been edited by Qfwfq: 05 March 2012 - 07:54 AM
Reason for edit: spammish link

[suresh kumawat]

Oh really it's new Do you think this ? But i don't think so .There are also many questions in which many peoples are always confused as Is a whole number a Rational Number. How many of you know answer of this questions . If yes then reply with cause.

[Robert Clark]

phillip1882, on 27 January 2012 - 09:56 PM, said:

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.

Wow, a science forum where the members are actually nice in responding to people's new ideas. That's a rarity.


- Bob Clark, new member

[7DSUSYstrings]

Dhanesh, on 27 January 2012 - 11:15 AM, said:

Ihave discovered a simple theorem in the field of mathematics.
http://www.scribd.co...s-new-discovery

Please post your valuable feedbacks.

It looks interesting. I don't have time at the moment to examine it in depth, but will stop back and do just that. To give you good feedback it's best to digest it. So far so good.

[CraigD]

Welcome to hypography, Robert! Please feel free to start a topic in the introductions forum to tell us something about yourself.

Robert Clark, on 31 March 2012 - 06:56 AM, said:

Wow, a science forum where the members are actually nice in responding to people's new ideas. That's a rarity.

Thanks for the complement.

I joined hypography because of its friendly ways. After being invited to help moderate and administer it, I learned that respectful, pleasant atmosphere isn’t a lucky coincidence, but due to a combination of a short, sensible, easily accessible list of rules (which isn’t unusual – I’d say more than half of internet discussion sites have something similar), and dedication, both by our moderators and members, to, as gently and respectfully as possible, requiring everybody to follow them. This last is unusual in my experience, and more and more stressful work than I’d imagined when I happily agreed to help with it as a moderator all those years ago.

Anyhow, glad you like the result, and hope to hear more from you – what I’ve seen so far from you on the subject of rockets is just the stuff a lot of us like to read and discuss.