What Is a Line ?

  • Dominique Michelucci
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6877)


The playground is the projective complex plane. The article shows that usual, naive, lines are not all lines. From naive lines (level 0), Pappus geometry creates new geometric objects (circles or conics) which can also be considered as (level 1) lines, in the sense that they fulfil Pappus axioms for lines. But Pappus theory also applies to these new lines. A formalization of Pappus geometry should enable to automatize these generalizations of lines.


Intersection Point Common Point Generalize Line Common Line Dynamic Geometry Software 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Coxeter, H.: Projective geometry. Springer, Heidelberg (1987)zbMATHGoogle Scholar
  2. 2.
    Henle, M.: Modern Geometries: Non-Euclidean, Projective, and Discrete, 2nd edn. Prentice Hall (2001)Google Scholar
  3. 3.
    Michelucci, D.: Isometry group, words and proofs of geometric theorems. In: SAC 2008: Proceedings of the 2008 ACM Symposium on Applied Computing, pp. 1821–1825. ACM, New York (2008)CrossRefGoogle Scholar
  4. 4.
    Michelucci, D., Schreck, P.: Incidence constraints: a combinatorial approach. Int. J. Comput. Geometry Appl. 16(5-6), 443–460 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Richter-Gebert, J., Sturmfels, B., Theobald, T.: First steps in tropical geometry (2003)Google Scholar
  6. 6.
    Richter-Gebert, J.: Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry. Springer, Heidelberg (2011)CrossRefzbMATHGoogle Scholar
  7. 7.
    Gao, X.s.: Search methods revisited. In: Mathematics Mechanization and Application, ch. 10, pp. 253–272. Academic Press (2000)Google Scholar
  8. 8.
    Stahl, S.: The Poincaré Half-Plane. Jones and Bartlett Books in Mathematics (1993)Google Scholar
  9. 9.
    Wen-Tsün, W.: Mechanical Theorem Proving in Geometries - Basic Principles. Texts and monographs in symbolic computation. Springer, Heidelberg (1994)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dominique Michelucci
    • 1
  1. 1.Dijon University, LE2I, CNRS 5158France

Personalised recommendations