Towards an Electronic Geometry Textbook

  • Xiaoyu Chen
  • Dongming Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4869)


This paper proposes a system in the form of a textbook for managing geometric knowledge dynamically, effectively, and interactively. Such a system, called an Electronic Geometry Textbook, can be viewed or printed as a traditional textbook and run as dynamic software on computer. The knowledge in the textbook is being formalized by using standard formal languages and may be processed by software modules developed for geometric computing and reasoning, diagram generation, and visualization. The textbook can be generated automatically by organizing and presenting the textbook data according to some specifications. The system allows the user to manipulate (query, modify, restructure, etc.) the textbook with automated consistency checking. We present the main ideas on the design of the electronic geometry textbook, explain the features of the system, propose five phases of creating and managing the geometric knowledge in the textbook, discuss the involved tasks and some of the fundamental research problems in each phase, and report our progress and experiments on a preliminary implementation of the system.


Software Module Geometric Statement Atomic Formula Traditional Textbook Geometric Knowledge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    ActiveMath Home,
  2. 2.
    Allen, S., Bickford, M., Constable, R., Eaton, R., Kreitz, C., Lorigo, L.: FDL: A Prototype Formal Digital Library. Cornell University, USA (2002), Available at
  3. 3.
    Asperti, A., Padovani, L., Coen, C.S., Schena, I.: HELM and the Semantic Math-Web. In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152, pp. 58–74. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Caprotti, O., Carlisle, D.: OpenMath and MathML: Semantic Mark Up for Mathematics. ACM, New York (1999), ACM Crossroads, Google Scholar
  5. 5.
    Cinderella Home,
  6. 6.
    Coxeter, H.S.M., Greitzer, S.L.: Geometry Revisited. The Mathematical Association of America, Washington, DC (1967)zbMATHGoogle Scholar
  7. 7.
    Janic̆ić, P.: GCLC — A Tool for Constructive Euclidean Geometry and More than That. In: Iglesias, A., Takayama, N. (eds.) ICMS 2006. LNCS, vol. 4151, pp. 58–73. Springer, Heidelberg (2006)Google Scholar
  8. 8.
    Kohlhase, M.: OMDoc: An Infrastructure for OpenMath Content Dictionary Information. ACM SIGSAM Bulletin 34(2), 43–48 (2000)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Kohlhase, M., Franke, A.: MBase: Representing Knowledge and Context for the Integration of Mathematical Software Systems. J. Symb. Comput. 23(4), 365–402 (2001)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Liang, T., Wang, D.: Towards a Geometric-Object-Oriented Language. In: Hong, H., Wang, D. (eds.) ADG 2004. LNCS (LNAI), vol. 3763, pp. 130–155. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Lozier, D.W.: NIST Digital Library of Mathematical Functions. Ann. Math. Artif. Intell. 38(1-3), 105–119 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Piroi, F., Buchberger, B.: An Environment for Building Mathematical Knowledge Libraries. In: Windsteiger, W., Benzmueller, C. (eds.) Proceedings of the Workshop on Computer-Supported Mathematical Theory Development, Cork, Ireland, pp. 19–29 (2004)Google Scholar
  13. 13.
    Quaresma, P., Janic̆ić, P.: GeoThms — Geometry Framework. Technical Report 2006/002, Centre for Informatics and Systems, University of Coimbra (2006)Google Scholar
  14. 14.
    Trybulec, A., et al.: The Mizar System. Available and developed at the University of Warsaw, Poland, at
  15. 15.
    Wang, D.: GEOTHER 1.1: Handling and Proving Geometric Theorems Automatically. In: Winkler, F. (ed.) ADG 2002. LNCS (LNAI), vol. 2930, pp. 194–215. Springer, Heidelberg (2004)Google Scholar
  16. 16.
    W3C Math Home: What is MathML?,
  17. 17.
    Zeilberger, D.: Plane Geometry: An Elementary Textbook by Shalosh B. Ekhad, XIV (circa 2050), downloaded from the future by Doron Zeilberger. Available from:

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Xiaoyu Chen
    • 1
  • Dongming Wang
    • 1
    • 2
  1. 1.LMIB – School of Science, Beihang University, Beijing 100083China
  2. 2.Laboratoire d’Informatique de Paris 6, Université Pierre et Marie Curie – CNRS, 104 avenue du Président Kennedy, F-75016 ParisFrance

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