More on Newton’s diameter theorem

This article continues a previous discussion on Newton's diameter theorem, which states that for a polynomial curve of degree n, the centroids of intersections with parallel lines lie on a line. It demonstrates the theorem using a fifth-degree polynomial f(x, y) = y³ + y − x(x+1)(x+2)(x−3)(x−2) and three parallel lines, not necessarily evenly spaced. The centroids are calculated and shown to align vertically. It also illustrates the necessity of each line crossing the curve exactly n times by showing a case where a line crosses only three times, shifting the centroid. This is a mathematical exploration related to algebraic curves and geometry, relevant to computer science and technical fields.