Points of Ninth Order on Cubic Curves

Authors

Leah Balay-Wilson, Smith College
Taylor Brysiewicz, Northern Illinois UniversityFollow

Abstract

In this paper we geometrically provide a necessary and sufficient condition for points on a cubic to be associated with an infinite family of other cubics who have nine-pointic contact at that point. We then provide a parameterization of the family of cubics with nine-pointic contact at that point, based on the osculating quadratic.

Author Bio

Leah Balay-Wilson is a math major at Smith College. Her primary areas of interest are algebraic geometry, algebraic topology, and mathematical modeling.

Leah Balay-Wilson is a math major at Smith College. Her primary areas of interest are algebraic geometry, algebraic topology, and mathematical modeling.

Faculty Sponsor

Seth Dutter

Recommended Citation

Balay-Wilson, Leah and Brysiewicz, Taylor (2014) "Points of Ninth Order on Cubic Curves," Rose-Hulman Undergraduate Mathematics Journal: Vol. 15: Iss. 1, Article 1.
Available at: https://scholar.rose-hulman.edu/rhumj/vol15/iss1/1