On the Relevancy of the Descartes Circle Theorem and Links of Six Spheres Theorem

Abstract

In our previous paper we have an invariable among the bends of the touching circles, and to show that the extension⁽¹⁰¹⁾. Later, we applied Wilkey's Theorem⁽¹⁶⁾ 一 which is an extension of the Decartes Circle Theorem⁽¹⁾一 to this result, we have an interesting theorem⁽¹⁰¹⁾. And we show that a part of this result corresponds to Sir Frederick Soddy's "The Hexlet⁽¹⁴⁾". The main object of this paper are as follows: (1) Wasan experts are haven't the notion of bends and (2) Considerations for the concerning literatures.