Skip to main content
Log in

Spiral surfaces enveloped by one-parametric sets of spheres

  • Published:
Journal of Geometry Aims and scope Submit manuscript

Abstract

In this paper, we study cyclic surfaces in E 3 generated by spiral motions of a circle. We find the representation of cyclic spiral surfaces in E 3 which are envelopes of one-parametric set of spheres. Finally, we give an example.

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.

Similar content being viewed by others

References

  1. Abdel-All N.H., Hamdoon F.M.: Cyclic surfaces in E 5 generated by equiform motions. J. Geom. 79, 1–11 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bottema O., Roth B.: Theoretical Kinematics. Dover, New York (1990)

    MATH  Google Scholar 

  3. Enneper A.: Die zyclischen Flächen. Z. Math. Phys. 14, 393–421 (1869)

    Google Scholar 

  4. López R.: Cyclic surfaces of constant Gauss curvature. Houston J. Math. 27, 799–805 (2001)

    MATH  MathSciNet  Google Scholar 

  5. Peternell M., Pottmann H.: Computing rational parametrization of canal surfaces. J. Symb. Comput. 23, 255–266 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  6. Schröcker H.P.: Das Erzeugnis dreier projektiv gekoppelter Kegelschnitte. Proceedings Süddt. Differentialgeometrie-Kolloquium 25, 79–94 (2001) Institute for Geometry, TU Wien

    Google Scholar 

  7. Wunderlich, W.: Darstellende Geometrie, Band 2. B. I. Hochschultaschenbücher, Bibliographisches Institut Mannheim, Wien, Zürich (1967)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fathy M. Hamdoon.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hamdoon, F.M. Spiral surfaces enveloped by one-parametric sets of spheres. J. Geom. 98, 51–58 (2010). https://doi.org/10.1007/s00022-010-0052-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00022-010-0052-0

Mathematics Subject Classification (2010)

Keywords

Navigation