Details:

Title	Automatic determination of envelopes and other derived curves within a graphic environment
Author(s)	Francisco Botana, Jose L. Valcarce
Type	Article in Journal
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.
Keywords	Groebner bases, caustics, dynamic geometry, envelopes, pedals, symbolic computing, symbolic-numeric interface
Length	11
ISSN	0378-4754
File
URL	dx.doi.org/10.1016/j.matcom.2004.05.004
Language	English
Journal	Mathematics and Computers in Simulation
Volume	67
Number	1-2
Pages	3-13
Publisher	Elsevier Science Publishers B. V.
Address	Amsterdam, The Netherlands, The Netherlands
Year	2004
Translation	No
Refereed	No