Lela's Project Page

Who:  I am from Colorado and I came to the U for ACCESS and to explore everything Utah and its National Parks have to offer. Along with math, I enjoy rock climbing, crocheting, and reading.

My scientific/engineering interests:  I am majoring in applied mathematics, and love systems; everything from their optimization to studying their flow with differential equations and linear algebra. Math is the language of the universe and I am here to converse with it.

Academic goals:  I am majoring in applied math, and I hope to continue working in my lab. After completing my B.S. I hope to go onto graduate school.

Career goals:  For me, these are more abstract. I just want to problem solve, and I believe math will help me become the best problem solver I can be. As long as I get to continue using math I think I will be happy.

A generic cubic surface in three-dimensional space contains at most 27 straight lines, while a generic quartic curve in two-dimensional space has at most 28 bitangent lines (lines which are tangent to the curve at two distinct points). These two geometric constructions are related: if an ant sits at a point on a cubic surface floating above the ground, then looks out at the shadow, the outline will be a quartic curve, and the lines on the surface will match up with the bitangents of the curve. Working up to this, multiple pieces of code in both python and sage were created to address smaller related problems: finding a line tangent to a quadratic curve through a random point, finding the Taylor series approximation (up to the second derivative), and using numerical methods to compute a line tangent to a random cubic curve starting from a random seed line in a bounded parameter space.

Finding Tangent Lines Download Finding Tangent Lines