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 October 19th, 2010, 01:00 PM #1 Newbie   Joined: Oct 2010 Posts: 3 Thanks: 0 Relationship between numbers Is there a simple way to design a formula to identify the relationship between two sets of numbers? For example if the numbers in column A are: A1 -20 A2 32 A3 -11 A4 60 A5 100 A6 160 A7 25 And the numbers in column B are: B1 25 B2 -32 B3 60 B4 40 B5 -19 B6 88 B7 64 If number A1 is related to B1 and A2 to B2 and so on what will be the value of B8 if the number A8 is say 10? These are random numbers but there may be some mathematical relationship between all of them? That’s what I’m trying to find out. Can a formula be designed to link all the numbers so that the next number can be predicted?
October 19th, 2010, 04:21 PM   #2
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Re: Relationship between numbers

Quote:
 Originally Posted by Hero Can a formula be designed to link all the numbers so that the next number can be predicted?
In general, no. There are too many ways to continue the sequence. In fact, not only are there infinitely many way to do so, there are uncountably many ways.

If you know something about what kinds of patterns we're looking for, though, it may be possible.

October 19th, 2010, 07:45 PM   #3
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Re: Relationship between numbers

Hello, Hero!

Quote:
 Is there a simple way to design a formula to relate two sets of numbers?

Given a finite set of points (coordinates), it is possible to construct a polynomial
[color=beige]. . [/color]which passes through all the points.

You gave us seven points:

[color=beige]. . [/color]$\begin{array}{|c|c|} x & y \\ \hline\\ \\ -20\; & 25 \\ \\ \\ -11\; & 60 \\ \\ \\ 25 & 64 \\ \\ \\ 32 & -32\; \\ \\ \\ 60 & 40 \\ \\ \\ 100 & -14\; \\ \\ \\ 160 & 88 \end{array}$

It ia possible to construct a 6th-degree polynomial which contains the seven points.

It general form is:[color=beige] .[/color]$f(x) \:=\:Ax^6\,+\,Bx^5\,+\,Cx^4\,+\,Dx^3\,+\,Ex^2\,+\, Fx\,+\,G$

We would use the seven given points to determine the above coefficients.

But the algebra is prohibitively long and tedious.

 October 20th, 2010, 02:03 PM #4 Newbie   Joined: Oct 2010 Posts: 3 Thanks: 0 Re: Relationship between numbers Thanks for the replies. I didn't ask the question properly ... sort of messed it up so I've re-written my question in more detail and posted it in the thread here: viewtopic.php?f=24&t=16504&p=63099#p63099 Thanks

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