论文标题
Fermat立方曲线和圆锥的排列
Sextactic points on the Fermat cubic curve and arrangements of conics
论文作者
论文摘要
本说明的目的是以叙事而不是严格的样式报告，内容涉及Fermat立方$ F $上的$ 6 $划分点以及自然而然地附带的各种锥体。此处介绍的大多数事实是由符号代数计划得出的，该注释的想法是提出一个研究方向，以搜索此处所述的事实及其概括的概念证明。在几个方向上的延伸似乎是可能的（采取更高程度的曲线并接触到$ f $，研究了$ f $上高订单分区点的高度曲线，研究曲线穿过已经构造的曲线的相交点，采用二元组等），我们希望一些年轻的互动可能会在以下提出的道路上找到自己的乐趣。
The purpose of this note is to report, in narrative rather than rigorous style, about the nice geometry of $6$-division points on the Fermat cubic $F$ and various conics naturally attached to them. Most facts presented here were derived by symbolic algebra programs and the idea of the note is to propose a research direction for searching for conceptual proofs of facts stated here and their generalisations. Extensions in several directions seem possible (taking curves of higher degree and contact to $F$, studying higher degree curves passing through higher order division points on $F$, studying curves passing through intersection points of already constructed curves, taking the duals etc.) and we hope some younger colleagues might find pleasure in following proposed paths as well as finding their own.
