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TitleExtending the descartes circle theorem for Steiner $n$-cycles.
Author(s) Shuichi Moritsugu
TypeBook, Chapter in Book, Conference Proceeding
AbstractThis paper describes the extension of the Descartes circle theorem for Steiner n-cycles. 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.
ISBN978-3-642-40671-3/pbk
URL http://link.springer.com/chapter/10.1007%2F978-3-642-40672-0_4
LanguageEnglish
Pages48--58
PublisherBerlin: Springer
Year2013
Edition0
Translation No
Refereed No
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