Therefore, if it isn't known how many points will be needed for the desired accuracy, the middle of the x-values might be far from where the interpolation is done. Gauss, Stirling, and Bessel all developed formulae to remedy that problem. Gauss's formula alternately adds new points at the left and right ends, thereby keeping the set of points centered near the same place (near the evaluated point). When so doing, it uses terms from Newton's formula, with data points and "x" values renamed in keeping with one's choice of what data point is designated as the "x"0 data point. Stirling's formula remains centered about a particular data point, for use when the evaluated point is nearer to a data point than to a middle of two data points. Bessel's formula remains centered about a particular middle between two data points, for use when the evaluated point is nearer to a middle than to a data point. Bessel and Stirling achieve that by sometimes using the average of two differences, and sometimes using the average of two products of binomials in "x", where Newton's or Gauss's would use just one difference or product. Stirling's uses an average difference in odd-degree terms (whose difference uses an even number of data points); Bessel's uses an average difference in even-degree terms (whose difference uses an odd number of data points). For any given finite set of data points, there is only one polynomial of least possible degree that passes through all of them. Thus, it is appropriate to speak of the "Newton form", or Lagrange form, etc., of the interpolation polynomial. However, the way the polynomial is obtained matters. There are several similar methods, such as those of Gauss, Bessel and Stirling. They can be derived from Newton's by renaming the "x"-values of the data points, but in practice they are important. The choice between Bessel and Stirling depends on whether the interpolated point is closer to a data point, or closer to a middle between two data points. A polynomial interpolation's error approaches zero, as the interpolation point approaches a data-point. Therefore, Stirling's formula brings its accuracy improvement where it is least needed and Bessel brings its accuracy improvement where it is most needed. So, Bessel's formula could be said to be the most consistently accurate difference formula, and, in general, the most consistently accurate of the familiar polynomial interpolation formulas.