Automatic determination of envelopes and other derived curves within a graphic environment

  • Authors:

  • Francisco Botana;José L. Valcarce

  • Affiliations:

  • Department of Applied Mathematics I, University of Vigo, 36005 Pontevedra, Spain;IES Pontepedriña, 15701 Santiago de Compostela, Spain

  • Venue:
  • Mathematics and Computers in Simulation - Special issue: Applications of computer algebra in science, engineering, simulation and special software
  • Year:
  • 2004

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Abstract

Dynamic geometry programs provide environments where accurate construction of geometric configurations can be done. Nevertheless, intrinsic limitations in their standard development technology mostly produce objects that are equationally unknown and so can not be further used in constructions. In this paper, we pursue the development of a geometric system that uses in the background the symbolic capabilities of two computer algebra systems, CoCoA and Mathematica. The cooperation between the geometric and symbolic modules of the software is illustrated by the computation of plane envelopes and other derived curves. These curves are described both graphically and analytically. Since the equations of these curves are known, the system allows the construction of new elements depending on them.