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On the constructibility of the axes of an ellipsoid: the construction of Chasles in practice

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Abstract

In this paper we discuss Chasles’s construction on ellipsoid to draw the semi-axes from a complete system of conjugate diameters. We prove that there is such situation when the construction is not planar (the needed points cannot be constructed with compasses and ruler) and give some others in which the construction is planar.

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References

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Authors and Affiliations

  1. Department of Geometry, Budapest University of Technology and Economics, 1521, Budapest, Hungary

    Ákos G. Horváth & István Prok

Authors
  1. Ákos G. Horváth
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  2. István Prok
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Correspondence to Ákos G. Horváth.

Additional information

Dedicated to the memory of the teaching of Descriptive Geometry in BME Faculty of Mechanical Engineering.

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Horváth, Á.G., Prok, I. On the constructibility of the axes of an ellipsoid: the construction of Chasles in practice. J. Geom. 109, 29 (2018). https://doi.org/10.1007/s00022-018-0437-z

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  • DOI: https://doi.org/10.1007/s00022-018-0437-z

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