Skip to main content
Springer Nature Link
Log in

Plane Euclidean Reasoning

  • Conference paper
  • First Online:
Automated Deduction in Geometry (ADG 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1669))

Included in the following conference series:

Abstract

An automatic reasoning system for plane Euclidean geometry should handle the wide variety of geometric concepts: points, vectors, angles, triangles, rectangles, circles, lines, parallelism, perpendicularity, area, orientation, inside and outside, similitudes, isometries, sine, cosine, .... It should be able to construct and transform geometric objects, to compute geometric quantities and to prove geometric theorems. It should be able to call upon geometric knowledge transparently when it is needed. In this paper a type of ring generated by points and numbers is presented which may provide a formal basis for reasoning systems that meet these requirements. The claim is that this simple algebraic structure embodies all the concepts and properties that are investigated in the many different theories of the Euclidean plane.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Fearnley-Sander, D.: Affine Geometry and Exterior Algebra. Houston Math. J. 6 (1980), 53–58

    Google Scholar 

  2. Fearnly-Sander, D.: A Royal Road to Geometry. Math. Mag. 53 (1980), 259–268

    Article  MathSciNet  Google Scholar 

  3. Fearnley-Sander, D.: Plane Euclidean Geometry. Technical Report 161, Department of Mathematics, University of Tasmania, 1981. 109

    Google Scholar 

  4. Fearnley-Sander, D. and Stokes, T.: Area in Grassmann Geometry. In: Wang, D. (ed.): Automated Deduction in Geometry. Lecture Notes in Artificial Intelligence, Vol. 1360. Springer-Verlag, Berlin Heidelberg New York 1998 141–170 101

    Google Scholar 

  5. Forder, H. G.: The Calculus of Extension. Cambridge, 1941 110

    Google Scholar 

  6. Hestenes, D., and Sobczyk, G.: Clifford Algebra to Geometric Calculus. Reidel, 1984 110

    Google Scholar 

  7. Jacobson, N.: Basic Algebra II. Freeman, San Francisco, 1980 110

    MATH  Google Scholar 

  8. Porteous, I. R.: Topological Geometry. Cambridge, 1981 110

    Google Scholar 

  9. Wang, D.: Clifford Algebraic Calculus for Geometric Reasoning with Applications to Computer Vision. In: Wang, D. (ed.): Automated Deduction in Geometry. Lecture Notes in Artificial Intelligence, Vol. 1360. Springer-Verlag, Berlin Heidelberg New York 1998 115–140 109

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Tasmania, GPO Box 252-37, Hobart, Tasmania, 7001, Australia

    Desmond Fearnley-Sander

Authors
  1. Desmond Fearnley-Sander
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fearnley-Sander, D. (1999). Plane Euclidean Reasoning. In: Automated Deduction in Geometry. ADG 1998. Lecture Notes in Computer Science(), vol 1669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47997-X_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-47997-X_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66672-1

  • Online ISBN: 978-3-540-47997-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics