Preprint 24/2019

3264 Conics in a Second

Paul Breiding, Bernd Sturmfels, and Sascha Timme

Contact the author: Please use for correspondence this email.
Submission date: 15. Feb. 2019
Pages: 14
published in: Notices of the American Mathematical Society, 67 (2020) 1, p. 30-37 
Download full preprint: PDF (1560 kB)
Link to arXiv: See the arXiv entry of this preprint.

Enumerative algebraic geometry counts the solutions to certain geometric constraints. Numerical algebraic geometry determines these solutions for any given instance. This article illustrates how these two fields complement each other. Our focus lies on the 3264 conics that are tangent to five given conics in the plane. We present a web interface for computing them. It uses the software HomotopyContinuation.jl, which makes this process fast and reliable. We discuss an instance where all 3264 solutions are real.

16.03.2021, 02:18