Applying circle inversion on a square grid filled with circles, we obtain a configuration that we call a fabric of kissing circles. We focus on the curvature inside the individual components of the fabric, which are two orthogonal frames and two orthogonal families of chains. We show that the curvatures of the frame circles form a doubly infinite arithmetic sequence (bi-sequence), whereas the curvatures in each chain are arranged in a quadratic bi-sequence. We also prove a sufficient condition for the fabric to be integral.

中文翻译：

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在接吻圈的织物上

在一个充满圆圈的方形网格上应用圆圈反转，我们得到了一个我们称之为接吻圆圈结构的配置。我们专注于织物单个组件内部的曲率，它们是两个正交框架和两个正交链族。我们证明框架圆的曲率形成一个双重无限算术序列（双序列），而每个链中的曲率排列成二次双序列。我们还证明了织物是整体的充分条件。