Automated Geometry Reasoning
Automated Geometry Reasoning: Area Method

S.C. Chou, X.S. Gao, and J.Z. Zhang,
Machine Proofs in Geometry, World Scientific, Singapore, 1994.

S.C. Chou, X.S. Gao, and J.Z. Zhang,
A Deductive Database Approach To Automated Geometry Theorem
Proving and Discovering,
Journal Automated Reasoning, 25(3), 219246, 2000.

S.C. Chou, X.S. Gao, and J.Z. Zhang,
Automated Generation of of Readable Proofs with Geometric Invariants,
I. Multiple and Shortest Proof Generation,
Journal of Automated Reasoning, 17, 325347, 1996.

S.C. Chou, X.S. Gao, and J.Z. Zhang,
Automated Generation of of Readable Proofs with Geometric Invariants,
II. Proving Theorems with FullAngles,
Journal of Automated Reasoning, 17, 349370, 1996.

S.C. Chou, X.S. Gao, J.Z. Zhang,
Automated Production of Traditional Proofs in Solid Geometry,
Journal of Automated Reasoning,
14, p.257291, 1995.

S.C. Chou, X.S. Gao, and J. Z. Zhang,
``Automated Production of Traditional Proofs for Theorems in Euclidean Geometry,
Part I. The Hilbert Intersection Point Theorems'',
Annals of Mathematics and Artificial Intelligence,
13, (1995), p.109137.

L. Yang, X.S. Gao, S. C. Chou, and Z. J. Zhang,
Automated Proving and Discovering of Theorems in NonEuclidean
Geometries, in: Automated Deduction in Geometry\/ (D.\ Wang, ed.),
LNAI 1360, SpringerVerlag, Berlin Heidelberg, 1998,
pp. 171188.

S.C. Chou, X.S. Gao, J.Z. Zhang,
``Automated Geometry Theorem Proving
by Vector Calculation'', Proceedings of ISSAC93, 284291.
Automated Geometry Reasoning: Algebraic Method

S.C. Chou and X.S. Gao,
RittWu's Decomposition Algorithm and Geometry
Theorem Proving in Proceedings of CADE10, Lecture Notes
in Artificial Intelligence 449, SpringerVerlag, 1990, 207220.

S.C. Chou and X.S. Gao,
Methods for Mechanical Geometry Formula
Deriving in Proceedings of ISSAC'90 , Japan, ACM Press, August 1990, 265270.
 X.S. Gao and D.K. Wang,
On the Automatic Derivation of a Set of Geometric Formulae,
Journal of Geometry, vol. 53, p.7988, 1995.

S.C. Chou, X.S. Gao, N.M. Mcphee, and S. C. Chou,
``Mechanically Proving Geometry Theorems Using a
Combination of Wu's Method and Collins' Method'',
in Proceedings of CADE12, Nancy, France, June 1994, 222236.

S.C. Chou, X.S. Gao, and D.S. Arnon,
``On the Mechanical Proof of Geometry Theorems Involving Inequalities''
Advances in Computing Research, 1992, Vol. 6, 139181.
An international journal.

S.C. Chou and X.S. Gao,
Proving Geometry Statements of Constructive Type,
in Proceedings of CADE11, Lecture Notes in Computer
Science, Vol. 607, 2034, SpringerVerlag, 1992.

X.S. Gao, Transcendental Functions and Mechanical
Theorem Proving in Elementary Geometries,
Journal of Automated Reasoning, 6:403417, 1990,
Kluwer Academic Publishers.
Automated Geometry Reasoning: Differential Geometry

S. C. Chou and X.S. Gao,
Automated Reasoning in Differential Geometry and Mechanics: Part I.
An Improved Version of RittWu's Decomposition Algorithm
,
Journal of Automated Reasoning, 10: 161172, 1993.

S. C. Chou and X.S. Gao,
Automated Reasoning in Differential Geometry and Mechanics: Part
II. Mechanical Theorem Proving,
Journal of Automated Reasoning, 10: 173189, 1993.

SC Chou and XS Gao,
Automated Reasoning in Differential Geometry and
Mechanics Using the Characteristic Set Method; Part III Mechanical Formula
Derivation, in Proceedings of the IFIP International Workshop
on Automated Reasoning, Elsevier Science Publishers (NorthHolland),
Beijing, p112, 1992.

S. C. Chou and X.S. Gao,
Automated Reasoning in Differential Geometry and Mechanics:
Part IV, Bertrand Curves
,
Journal of Sys. and Math., vol. 6, p.186192, 1993.