We introduce the notion of \(P_{\lambda }\) points, which canonically parametrize points on the Euler line. This allows us to show that the Euler line of any d-dimensional inscribed polygon in Euclidean space arises from the Euler lines of its sub-polygons, beginning from the Euler line of a point in the plane. Furthermore, we situate \(P_{\lambda }\) points in the literature of modern triangle centers.
