Agnes Scott College

B. M. Turner

An Application of the Laguerre Method for the Representation of Imaginary Points
American Journal of Mathematics, Vol 52, No. 1 (Jan. 1930), 75-84


In an earlier paper the writer directed attention to the fact that while three collinear real points of inflexion impose but five conditions on a real non-singular plane cubic curve, and hence leave the curve with four degrees of freedom; still not one of the six imaginary points of inflexion may be chosen arbitrarily. The statement of the fact was followed by a discussion of the positions of the imaginary points of inflexion and critic centers for the four-fold infinite system of cubics. This paper shows that the variable imaginary inflexions and critic centers, represented by real point-pairs in accordance with the Laguerre method for the representation of imaginary points, describe unique systems of curves; and brings out more clearly the relations of the sets of points.