On miquel's five-circle theorem

Authors:
Hongbo Li;Ronghua Xu;Ning Zhang
Affiliations:
Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China;Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China;Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China
Venue:
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
Year:
2004

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Abstract

Miquel's Five-Circle Theorem is difficult to prove algebraically. In this paper, the details of the first algebraic proof of this theorem is provided. The proof is based on conformal geometric algebra and its accompanying invariant algebra called null bracket algebra, and is the outcome of the powerful computational techniques of null bracket algebra embodying the novel idea breefs.