2008-Feb– 23 Rambling notes to self

If one assumes that the equation describing a set of x-y points to be an nth-degree polynomial then the following method will derive the complete polynomial.

BNS provides foresight into polynomials whenever the coefficients of the polynomials are all positive and less than the base number system.  For example: (2,7), (3, 13), (4, 21), (5, 31) all have a y value of 111 in base x, thus y=1x^2+1x+1.

Taking differences and factorials enables the full discovery of any polynomial.