Equations for the four-point rectangle

Abstract

Four numbers in a rectangular array can be interpolated by the bilinear equation. If the numbers are positive, they can be interpolated by a new bi-cubic equation. The array can be interpolated by eight new fourth-degree equations. The positive squareroots of the fourth-degree equations are new bi-quadratic equations that are applicable to the analysis of the same four-point arrays. The new equations are suitable for the analysis of two-parameter laboratory experiments. Mathematics Subject Classification: 65D05, 65D07, 65D17