出租车几何中的阿波罗集
Apollonian sets in taxicab geometry
摘要：
在平面上固定两个点$p$和$q$，并固定一个正数$k \neq 1$。Perga的Apollonius的一个结果指出，满足$d(x, p)/d(x, q) = k$的点集$x$形成一个圆。本文研究出租车几何中的相似集。我们发现，虽然阿波罗集是不是taxicab圈，更复杂的阿波罗集可以用简单的。
英文摘要：
Fix two points $p$ and $q$ in the plane and a positive number $k \neq 1$. A result credited to Apollonius of Perga states that the set of points $x$ that satisfy $d(x, p)/d(x, q) = k$ forms a circle. In this paper we study the analogous set in taxicab geometry. We find that while Apollonian sets are not taxicab circles, more complicated Apollonian sets can be characterized in terms of simpler ones.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
