论文标题
在接吻圈子的结构上
On a Fabric of Kissing Circles
论文作者
论文摘要
在充满圆圈的正方形网格上应用圆反转，我们获得了一种称为接吻圆的面料的配置。配置及其组件是两个正交框架和两个正交家族的链条，以某种方式连接到经典的几何配置，例如Arbelos或Pappus链，或20世纪的Apollonian包装。 在本文中，我们构建了面料并列出了该结构所产生的一些明显特性。接下来，我们专注于各个组件内部的曲率：我们表明，框架圆的曲率形成了双线无限算术序列（BI-sequerence），而每个链的圆圈的曲率则以二次二次序列排列。由于解决几何sangaku问题是通往织物发现的门户，因此我们使用曲率上的结果以两个sangaku问题及其解决方案结束了本文。
Applying circle inversion on a square grid filled with circles, we obtain a configuration that we call a fabric of kissing circles. The configuration and its components, which are two orthogonal frames and two orthogonal families of chains, are in some way connected to classical geometric configurations such as the arbelos or the Pappus chain, or the Apollonian packing from the 20th century. In this paper, we build the fabric and list some of the obvious properties that result from this construction. Next, we focus on the curvature inside the individual components: we show that the curvatures of the frame circles form a doubly infinite arithmetic sequence (bi-sequence), whereas the curvatures of the circles of each chain are arranged in a quadratic bi-sequence. Because solving geometric sangaku problems was a gateway to our discovery of the fabric, we conclude this paper with two sangaku problems and their solutions using our results on curvatures.
