论文标题
真正的圆圈与3个圆锥
Real circles tangent to 3 conics
论文作者
论文摘要
在本文中，我们研究了与圆锥形相切的圆圈。我们表明，通常在平面上有三个圆锥形的$ 184 $复合圆，我们表征了相应的多项式系统的真实判别。我们给出了一个明确的例子，$ 3 $圆锥，$ 136 $真实的圆圈与他们切线。我们猜想136是真实圆的最大数量。此外，我们实施了一种爬山算法，以找到具有许多真实圈子的锥体实例，并且我们引入了一种机器学习模型，鉴于三个真实的锥体，该模型可预测与这三个圆锥形相切的圆数。
In this paper we study circles tangent to conics. We show there are generically $184$ complex circles tangent to three conics in the plane and we characterize the real discriminant of the corresponding polynomial system. We give an explicit example of $3$ conics with $136$ real circles tangent to them. We conjecture that 136 is the maximal number of real circles. Furthermore, we implement a hill-climbing algorithm to find instances of conics with many real circles, and we introduce a machine learning model that, given three real conics, predicts the number of circles tangent to these three conics.
