Skip to main content
Log in

An exercise in an interactive geometrical research

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

We describe how an interactive research with a computer led to a new, simple proof of the classical Mascheroni-Mohr theorem concerning constructions with a compass alone. We then discuss the difficult problem which will face any attempt to attack this theorem using an independent theorem prover.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Avron, Theorems on strong constructibility with a compass alone, J. Geometry 30(1987) 28–35.

    Google Scholar 

  2. A. Avron, On strict strong constructibility with a compass alone, J. Geometry 38(1990)12–15.

    Google Scholar 

  3. L. Mascheroni,La Geometria del Compass (Pavia V, 1797).

  4. G. Mohr,Euclidnes Danichs (Amsterdam, 1672).

  5. A. Borodin, R. Fagin, J.E. Hopcroft and M. Tompa, Decreasing the nesting depth of expressions involving square roots, J. Symbolic Comput. 1(1985)169–188.

    Google Scholar 

  6. R. Zippel, Simplification of expressions involving radicals, J. Symbolic Comput. 1(1985)189–210.

    Google Scholar 

  7. W. Bibel, Methods of automated reasoning, in:Fundamentals of Artificial Intelligence — An Advanced Course, ed. W. Bibel and Ph. Jorrand (Springer, Berlin, 1986).

    Google Scholar 

  8. H. Eves,A Survey of Geometry, revised ed. (Allyn and Bacon, 1972).

  9. H. Gelernter, J.R. Hansen and D.W. Loveland, Empirical explorations of the geometry theorem proving machines, in:Computer and Thought, ed. E.A. Feigenbaum and J. Feldman (McGraw-Hill, New York, 1963).

    Google Scholar 

  10. E. Rich and K. Knight,Artificial Intelligence, 2nd ed. (McGraw-Hill, New York, 1991).

    Google Scholar 

  11. J.S. Boyer and A. Moore,A Computational Logic (Academic Press, 1979).

  12. P.B. Andrews et al., Automating higher order logics, in:Automated Theorem Proving: After 25 Years, ed. W.W. Bledsoe and D. Loveland [Contemp. Math. Series 19 (Amer. Math. Soc., 1984)].

  13. N. Immerman, Languages which capture complexity classes, in:15th Symp. on Theory of Computing (Association for Computing Machinery, 1983) pp. 347–354.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Avron, A. An exercise in an interactive geometrical research. Ann Math Artif Intell 9, 239–252 (1993). https://doi.org/10.1007/BF01530934

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01530934

Keywords

Navigation