Numerical integration over the triangle

describes a method for the evaluation of integrals over a triangle, based on a formula developed in [1]. The mid-points of the sides of the triangle are used as the points of evaluation in this method. Other possibilities may be used; for example, the trisection points of the medians that are not the centroid could be used as the points of evaluation. These points are symmetrically spaced and the weights, wi, again are equal. The centroid could also be used as a single point of evaluation with wi equal to the area of the triangle. As another modification to this method, one could calculate the appropriate mid-points of the reference triangle for a reasonable number of subdivisions, then retain them as constants rather than calculate each point as it is used. Recently, (1958) Mr. Walter Leffin carried out computations by the use of these methods.