Details:
Title  Extending the descartes circle theorem for Steiner $n$cycles.  Author(s)  Shuichi Moritsugu  Type  Book, Chapter in Book, Conference Proceeding  Abstract  This paper describes the extension of the Descartes circle theorem for Steiner ncycles. Instead of using the inversion method, we computed the Gröbner bases or resultants for the equations of inscribed or circumscribed circles. As a result, we deduced several relations that could be called the Descartes circle theorem for n ≥ 4. We succeeded in computing the defining polynomials of circumradii with degrees 4, 24, and 48, for n = 4, 5, and 6, respectively.  ISBN  9783642406713/pbk 
URL 
http://link.springer.com/chapter/10.1007%2F9783642406720_4 
Language  English  Pages  4858  Publisher  Berlin: Springer  Year  2013  Edition  0  Translation 
No  Refereed 
No 
