The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Help with formula (revised question)
Replies: 7   Last Post: Nov 20, 2013 8:15 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Rock Brentwood

Posts: 129
Registered: 6/18/10
Re: Help with formula (revised question)
Posted: Nov 20, 2013 8:15 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Wednesday, November 20, 2013 1:50:59 AM UTC-6, Robert Crandal wrote:
> However, I'd now
> like to revise the data and requirements.
> Here is the new data set:


> Can this data be represented with a formula
> that only uses either addition, subtraction,
> multiplication, division, modulus, or the power (^)
> function, or any combination of these?

All finite data sets can be represented by polynomials. So that means: only constants, addition, subtraction and multiplication.

If the points are A, B, C, ..., Z, then the unique polynomial of minimal degree that is equal to 1 at A and 0 everywhere else is
p_A(x) = ((x-B)/(A-B)) ((x-C)/(A-C)) ... ((x-Z)/(A-Z)).
Similar considerations apply to the other points, yielding definitions for p_B(x), p_C(x), ..., p_Z(x).

The unique polynomial of minimal degree that matches the value a at A, b at B, c at C, ..., z at Z is then p(x) = a p_A(x) + b p_B(x) + c p_C(x) + ... + z p_Z(x).

All other polynomials matching these points have p(x) as a factor.

Any other function that matches the points must necessarily involve one of the other operations: division, modulus, exponentiation, or something else besides those.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.