Skip to main content
SpringerLink
Log in

MMP/Geometer – A Software Package for Automated Geometric Reasoning

  • Conference paper
Book cover Automated Deduction in Geometry (ADG 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2930))

Included in the following conference series:

Abstract

We introduce a software package, MMP/Geometer, developed by us to automate some of the basic geometric activities including geometric theorem proving, geometric theorem discovering, and geometric diagram generation. As a theorem prover, MMP/Geometer implements Wu’s method for Euclidean and differential geometries, the area method and the geometric deductive database method. With these methods, we can not only prove difficult geometric theorems but also discover new theorems and generate short and readable proofs. As a geometric diagram editor, MMP/Geometer is an intelligent dynamic geometric software tool which may be used to input and manipulate geometric diagrams conveniently and interactively by combining the idea of dynamic geometry and methods of automated diagram generation.

This work was supported by a National Key Basic Research Project (NO. G19980306) and by a USA NSF grant CCR-0201253.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aubry, P., Lazard, D., Moreno Maza, M.: On the Theories of Triangular Sets. J. of Symbolic Computation 28, 45–124 (1999)

    Article  MathSciNet  Google Scholar 

  2. Chou, S.C.: Mechanical Geometry Theorem Proving. D.Reidel Publishing Company, Dordrecht (1988)

    MATH  Google Scholar 

  3. Chou, S.C., Gao, X.S.: Ritt-Wu’s Decomposition Algorithm and Geometry Theorem Proving. In: Stickel, M.E. (ed.) CADE 1990. LNCS, vol. 449, pp. 207–220. Springer, Heidelberg (1990)

    Google Scholar 

  4. Chou, S.C., Gao, X.S.: Mechanical Formula Derivation in Elementary Geometries. In: Proc. ISSAC 1990, pp. 265–270. ACM Press, New York (1990)

    Chapter  Google Scholar 

  5. Chou, S.C., Gao, X.S.: Proving Constructive Geometry Statements. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 20–34. Springer, Heidelberg (1992)

    Google Scholar 

  6. Chou, S.C., Gao, X.S.: Automated Reasoning in Differential Geometry and Mechanics: Part II. Mechanical Theorem Proving. J. of Automated Reasoning 10, 173–189 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chou, S.C., Gao, X.S.: Automated Reasoning in Geometry. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 709–749. Elsevier, Amsterdam (2001)

    Google Scholar 

  8. Chou, S.C., Gao, X.S., Zhang, J.Z.: Machine Proofs in Geometry. World Scientific, Singapore (1994)

    MATH  Google Scholar 

  9. Chou, S.C., Gao, X.S., Zhang, J.Z.: A Deductive Database Approach To Automated Geometry Theorem Proving and Discovering. J. Automated Reasoning 25, 219–246 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  10. Davis, P.J.: The Rise, Fall, and Possible Transfiguration of Triangle Geometry: A Mini-history. The American Mathematical Monthly 102, 204–214 (1993)

    Article  Google Scholar 

  11. Gao, X.S., Huang, L., Jiang, K.: A Hybrid Method for Solving Geometric Constraint Problems. In: Richter-Gebert, J., Wang, D. (eds.) ADG 2000. LNCS (LNAI), vol. 2061, pp. 16–25. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  12. Gao, X.S., Wang, D.K., Qiu, Z., Yang, H., Lin, D.: MMP: A Mathematics- Mechanization Platform - a Progress Report, Preprints, MMRC, Academ, ia Sinica (April 2002), http://www.mmrc.iss.ac.cn/~mmsoft/

  13. Gao, X.S., Zhang, J.Z., Chou, S.C.: Geometry Expert. Nine Chapter Pub., Taipai (1998) (in Chinese)

    Google Scholar 

  14. Gao, X.S., Zhang, G.: Geometric Constraint Solving via C-tree Decomposition. In: Proc. of ACM SM 2003, Seattle, June 2003. ACM Press, New York (2003)

    Google Scholar 

  15. Gao, X.S., Hoffmann, C.M., Yang, W.: Solving Basic Gometric Constraint Configurations with Locus Intersection. In: Proc. ACM SM 2002, Saarbruecken Germany, pp. 95–104. ACM Press, New York (2002)

    Google Scholar 

  16. Gao, X.-S., Zhu, C., Chou, S.-C., Ge, J.-X.: Automated Generation of Kempe Linkages for Algebraic Curves and Surfaces. Mechanism and Machine Theory 36(9), 1019–1033 (2002)

    Article  Google Scholar 

  17. Ge, J., Chou, S.C., Gao, X.S.: Geometric Constraint Satisfaction Using Optimization Methods. Computer Aided Design 31(14), 867–879 (2000)

    Article  Google Scholar 

  18. Gelernter, H.: Realization of a Geometry-theorem Proving Machine. In: Feigenbaum, E.A., Feldman, J. (eds.) Comput. and Thought, pp. 134–152. Mcgraw Hill, New York (1963)

    Google Scholar 

  19. Heydon, A., Nelson, G.: The Juno-2 Constraint-Based Drawing Editor. SRC Research Report 131a (1994)

    Google Scholar 

  20. Hoffmann, C.: Geometric Constraint Solving in R2 and R3. In: Du, Z., Huang, F. (eds.) Computing in Euclidean Geometry, pp. 266–298. World Scientific, Singapore (1995)

    Google Scholar 

  21. Hong, H., Wang, D., Winkler, F.: Short Description of Existing Provers. Ann. Math. Artif. Intell. 13, 195–202 (1995)

    Article  Google Scholar 

  22. Jakiw, N.: Geometer’s Sketchpad, User Guide and Reference Manual. Key Curriculum Press, Berkeley (1994)

    Google Scholar 

  23. Laborde, J.M.: GABRI Geometry II, Texas Instruments, Dallas (1994)

    Google Scholar 

  24. Latheam, R.S., Middleditch, A.E.: Connectivity Analysis: a Tool for Processing Geometric Constraints. Computer Aided Design 28(11), 917–928 (1994)

    Article  Google Scholar 

  25. Lazard, D.: A New method for Solving Algebraic Systems of Positive Dimension. Discrete Appl. Math. 33, 147–160 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  26. Kalkbrener, M.: A Generalized Euclidean Algorithm for Computing Triangular Representations of Algebraic Varieties. J. Symb. Comput. 15, 143–167 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  27. Kapur, D., Wan, H.K.: Refutational Proofs of Geometry Theorems via Characteristic Set Computation. In: Proc. of ISSAC 1990, pp. 277–284. ACM Press, New York (1990)

    Chapter  Google Scholar 

  28. Richter-Gebert, J., Kortenkamp, U.H.: The Interactive Geometry Software Cinderalla. Springer, Berlin (1999)

    Google Scholar 

  29. Owen, J.: Algebraic Solution for Geometry from Dimensional Constraints. In: ACM Symp. Found of Solid Modeling, pp. 397–407. ACM Press, Austin (1991)

    Google Scholar 

  30. Wang, D.: Elimination Methods. Springer, Berlin (2000)

    Google Scholar 

  31. Wang, D.: Geother: A Geometry Theorem Prover. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. Lecture Notes in Computer Science(LNAI), vol. 1104, pp. 166–170. Springer, Heidelberg (1996)

    Google Scholar 

  32. Wang, D.K.: Polynomial Equations Solving and Mechanical Geometric Theorem Proving. Ph.D Thesis, Inst. of Sys. Sci., Academia Sinica (1993)

    Google Scholar 

  33. Wu, W.T.: Basic Principles of Mechanical Theorem Proving in Geometries. Science Press, Beijing (1984) (in chinese); English Version, Springer-Verlag, Berlin (1994)

    Google Scholar 

  34. Wu, W.T.: A Mechanization Method of Geometry and its Applications I. Distances, Areas, and Volumes. J. Sys. Sci. and Math. Scis. 6, 204–216 (1986)

    MATH  Google Scholar 

  35. Wu, W.T.: A Constructive Theory of Differential Algebraic Geometry. In: LNM, vol. 1255, pp. 173–189. Springer, Berlin (1987)

    Google Scholar 

  36. Wu, W.T.: Mathematics Mechanization. Science Press/Kluwer, Beijing (2000)

    MATH  Google Scholar 

  37. Yang, L., Zhang, J., Hou, X.R.: Nonlinear Algebraic Equation System and Automated Theorem Proving. Shanghai Sci. and Tech. Education Publ. House, Shanghai (1996) [in Chinese]

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Mathematics Mechanization Institute of System Science, AMSS, Academia Sinica, Beijing, 100080, China

    Xiao-Shan Gao & Qiang Lin

Authors
  1. Xiao-Shan Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qiang Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Institute for Symbolic Computation (RISC), J. Kepler University, Altenbergerstr. 69, A-4040, Linz, Austria

    Franz Winkler

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gao, XS., Lin, Q. (2004). MMP/Geometer – A Software Package for Automated Geometric Reasoning. In: Winkler, F. (eds) Automated Deduction in Geometry. ADG 2002. Lecture Notes in Computer Science(), vol 2930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24616-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24616-9_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20927-0

  • Online ISBN: 978-3-540-24616-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation