Geometry Expert (GEX)
Geometry Expert (GEX) is a software system for automated geometry theorem provingdiscovering
and geometric constraint solving.
 GEX is a powerful computer program for
geometric reasoning. Within its domain, it invites comparison with
the best of human geometry provers. It implements most of the
effective methods for geometric reasoning introduced in the past
twenty years, including the deductive base method, Wu's method, the
area method, the Groebner basis method, the vector method, and the
fullangle method. With these methods, users may automated prove
geometry theorems, to discover new properties of theorems, and
to generate readable proofs for many geometry theorems.
 A variant of GEX: MMP also implements several state of the art methods
for geometric constraint solving, that is, the user can input the geometric
properties satisfied by a geometric diagram, and the software will automatically
generate a constructive way to draw the diagram.
Geometric constraint solving is a key property of socalled intelligent computeraided design (CAD).
 GEX is also a dynamic geometry software, and can be used to build dynamic visual
models to assist teaching and learning of various mathematical
concepts.
By dynamic visual models, we mean models built by computer
softwares that can be changed dynamically.
With GEX, we can build four classes of dynamic visual models:
geometric transformations, loci generation, diagrams of functions,
and loci generation.
Documents and Softwares

An introductory paper for GEX can be obtained
here

An experimental Windows version of GEX, with a set of examples,
can be obtained
here
Java Geometry Expert
Java GEX is an internet based version of Geometry Expert.
MMP/Geometer
MMP/Geometer is
a new Chinese version of GEX with ability of automated geometric diagram construction.
References for Automated Geometry Reasoning

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 of Automated Reasoning, 25(3), 219246, 2000.

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

S.C. Chou, X.S. Gao, and J.Z. Zhang,
Automated Generation of Readable Proofs with Geometric Invariants,
II. Proving Theorems with FullAngles,
Journal of of Automated Reasoning, 17, 349370, 1996.
References for Geometric Constraint Solving
 X.S. Gao, D. Lei, Q. Liao, and G. Zhang,
Generalized Stewart Platforms and their Direct Kinematics,
IEEE Trans. Robotics, vol 21, 141151, 2005.
 X.S. Gao, Q. Lin, and G. Zhang,
A Ctree Decomposition Algorithm
for 2D and 3D Geometric Constraint Solving,
ComputerAided Design, 38(1), 113, 2006.

X.S. Gao, C.M. Hoffmann and W. Yang,
Solving spatial basic geometric constraint configurations with locus intersection,
Computer Aided Design, 111122, 36(2), 2004.

J. Ge, S.C. Chou and X.S. Gao,
Geometric Constraint Satisfaction Using Optimization Methods,
Computer Aided Design, 31(14), 867879, 2000.

X.S. Gao and S. C. Chou,
Solving Geometric Constraint Systems,
I. A Global Propagation Approach,
Computer Aided Design,
Vol. 30, No. 1, 4754, 1998.

X.S. Gao and S. C. Chou,
Solving Geometric Constraint Systems,
II. A Symbolic Computational Approach,
Computer Aided Design,
Vol. 30, No.2, 115122, 1998.
Using GEX for Mathematics Instruction
 X.S. Gao, J.Z. Zhang, and S.C. Chou, Geometry Expert (in Chinese) , Nine Chapters, Taipei, 1998.

X. S. Gao, C.C. Zhu, and Y. Huang,
Building Dynamic Mathematical Models with Geometry Expert,
I. Geometric Transformations, Functions and Plane Curves,
Proceedings of the Third Asian Technology Conference in Mathematics,
eds W.C. Yang, pp. 216224, Springer, 1998.

X.S. Gao, C.C. Zhu, and Y. Huang,
Building Dynamic Mathematical Models with Geometry Expert, II. Linkages,
Proc. of the Third Asian Symposium on Computer
Mathematics, eds Z. B. Li, pp. 1522, LanZhou University Press, 1998.

X.S. Gao,
Building Dynamic Mathematical Models with Geometry Expert,
III. A Geometry Deductive Database
Proc. Of ATCM'99, 153162, 1999, ATCM Inc., USA (Best paper Award of ATCM'99).