Operational method of data treatment

Abstract

A new instrument of exploration can be used to develop unrecognized connections among points in a variety of geometric designs. Operational methods are used to derive the relationships, and a new approach to extremum location is demonstrated. The technique is suitable for interpolation problems which arise in experimental design and the treatment of data.

Equations for the four-point rectangle

“…(7) in [1] and the discussion following that equation. This observation implies the preceding methods are potentially more fertile than methods that are based on applied operational calculus [2,3]. However, one example is not a satisfactory basis for generalizations.…”

Symbolic form of a cubic equation for the four-point rectangle

“…Operational methods [2] permit the developments of many unexpected results. The representations of four-and five-point rectangles, and eight-and nine-point rectangular prisms by quadratic, cubic, exponential, and trigonometric equations are among the developments [1][2][3][4][5]. Eq.…”

“…A quadratic equation for this design was illus-trated several years ago [1]. It was first derived by operational methods [2]. That method can be used to derive a cubic equation for the eight-point cube [3,4].…”

Interpolation of the five-point rectangle by powers of polynomial expressions

“…There are many operational methods for interpolating four-and five-point rectangles [1][2][3][4][5]. They assume polynomial, exponential, or trigonometric forms.…”