Unicursal Curves by Method of Inversion.
BY
HENRY BYRON NEWSON.
This paper contains a summary of the work done during the last school year by my class in Modern Geometry. Since many of the results were suggested or entirely wrought out by class-room discussion, it becomes practically impossible to assign to each member of the class his separate portion. Many of the results were contributed by Messrs. M. E. Rice, A. L. Candy, H. C. Riggs, and Miss Annie L. MacKinnon.
The reader who is not familiar with the method of Geometric Inversion should read Townsend’s Modern Geometry, chapters IX and XXIV; or a recent monograph entitled, “Das Princep der Reziproken Radien,” by C. Wolff, of Erlangen.
When a conic is inverted from a point on the curve, the inverse curve is a nodal, circular cubic.
This is shown analytically as follows: let the equation of the conic be written
ax² + 2hxy + by² + 2gx + 2fy = 0 ;