Agnes Scott College

B. M. Turner

A Configuration of Thirteen Pencils of Cubics and Cubics with Three Real Inflexions
American Journal of Mathematics, Vol. 47, No. 3 (July 1925), 149-162


In an earlier paper the writer discussed the system of plane cubics with a given quadrangle of inflexions. The nine points of inflexion of any one cubic offer a number of ways of choosing four points which form a quadrangle, but among these quadrangles some have vertices in common. It follows that all the cubics with a given quadrangle of inflexions in common with one inflexional set form a configuration with notable geometric properties. The first part of this paper gives the results of a study of the real cubics contained in this configuration. The second part is devoted to a discussion of cubics with three real inflexions given.