Cited By
View all- Li HWang D(2007)A recipe for symbolic geometric computingProceedings of the 2007 international symposium on Symbolic and algebraic computation10.1145/1277548.1277584(261-268)Online publication date: 29-Jul-2007
On miquel's five-circle theorem
Authors: 
Hongbo Li, Ronghua Xu, Ning ZhangAuthors Info & Claims
Pages 217 - 228
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.
References
[1]
S. Chou, X. Gao and J. Zhang. Machine Proof in Geometry, World Scientific, Singapore, 1994.
[2]
D. Hestenes, G. Sobczyk. Clifford Algebra to Geometric Calculus, Kluwer, Dordrecht, 1984.
[3]
H. Li, D. Hestenes, A. Rockwood. Generalized Homogeneous Coordinates for Computational Geometry. In: Geometric Computing with Clifford Algebras, G. Sommer (ed.), pp. 27-60, Springer, Heidelberg, 2001.
[4]
H. Li. Automated Theorem Proving in the Homogeneous Model with Clifford Bracket Algebra. In: Applications of Geometric Algebra in Computer Science and Engineering, L. Dorst et al. (eds.), pp. 69-78, Birkhauser, Boston, 2002.
[5]
H. Li. Clifford Expansions and Summations. MM Research Preprints 21: 112-154, 2002.
[6]
H. Li. Clifford Algebras and Geometric Computation. In: Geometric Computation, F. Chen and D. Wang (eds.), World Scientific, Singapore, pp. 221-247, 2004.
[7]
H. Li. Automated Geometric Theorem Proving, Clifford Bracket Algebra and Clifford Expansions. In: Trends in Mathematics: Advances in Analysis and Geometry, Birkhauser, Basel, pp. 345-363, 2004.
[8]
H. Li. Algebraic Representation, Elimination and Expansion in Automated Geometric Theorem Proving. In: Automated Deduction in Geometry, F. Winkler (ed.), Springer, Berlin, Heidelberg, pp. 106-123, 2004.
[9]
H. Li. Symbolic Computation in the Homogeneous Geometric Model with Clifford Algebra. In: Proc. ISSAC 2004, J. Gutierrez (ed.), ACM Press, pp. 221-228, 2004.
[10]
H. Li, Y. Wu. Automated Short Proof Generation in Projective Geometry with Cayley and Bracket Algebras I. Incidence Geometry. J. Symb. Comput. 36(5): 717-762, 2003.
[11]
H. Li, Y. Wu. Automated Short Proof Generation in Projective Geometry with Cayley and Bracket Algebras II. Conic Geometry. J. Symb. Comput. 36(5): 763- 809, 2003.
[12]
B. Sturmfels. Algorithms in Invariant Theory. Springer, Wien, 1993.
- On miquel's five-circle theorem
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Published: 19 May 2004
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Cited By
View all- Li HWang D(2007)A recipe for symbolic geometric computingProceedings of the 2007 international symposium on Symbolic and algebraic computation10.1145/1277548.1277584(261-268)Online publication date: 29-Jul-2007