Abstract
This 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.
This work was supported by a Grant-in-Aid for Scientific Research (22500004) from the Japan Society for the Promotion of Science (JSPS).
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Moritsugu, S. (2013). Extending the Descartes Circle Theorem for Steiner n-Cycles. In: Ida, T., Fleuriot, J. (eds) Automated Deduction in Geometry. ADG 2012. Lecture Notes in Computer Science(), vol 7993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40672-0_4
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DOI: https://doi.org/10.1007/978-3-642-40672-0_4
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