Computing envelopes in dynamic geometry environments
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We review the behavior of some popular dynamic geometry software when computing envelopes, relating the diverse methods implemented in these programs with the various definitions of envelope. Special attention is given to the new GeoGebra 5.0 version, that incorporates a mathematically rigorous approach for envelope computations. Furthermore, a discussion on the role, in this context, of the cooperation between GeoGebra and a recent parametric polynomial solving algorithm is detailed. This approach seems to yield accurate results, allowing for the first time sound computations of envelopes of families of plane curves in interactive environments.
KeywordsAutomated deduction in geometry Envelope computation Dynamic geometry
Mathematics Subject Classification (2010)Primary 68T15 Secondary 68W30
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- 1.List of interactive geometry software: Available at http://en.wikipedia.org/wiki/List_of_interactive_geometry_software (2013)
- 2.EUKLID DynaGeo Forum: Available at http://www.dynageo.de/discus/messages/14/232.html?1076183239 (2014)
- 3.Dana-Picard, Th., Zehavi, N.: Revival of a classical topic in differential geometry: envelopes of parameterized families of curves and surfaces. In: Martínez–Moro, E., Kotsireas, I. (eds.) Applications of Computer Algebra ACA 2015 Booklet of Abstracts, pp 53–56, Kalamata (2015)Google Scholar
- 9.Botana, F., Recio, T.: A propósito de la envolvente de una familia de elipses. Bol. Soc. Puig–Adam 95, 15–30 (2013)Google Scholar
- 11.Botana, F., Recio, T.: Some issues on the automatic computation of plane envelopes in interactive environments. Math. Comp. Simul. doi: 10.1016/j.matcom.2014.05.011
- 12.Curve definitions: Available at http://www-history.mcs.st-andrews.ac.uk/history/Curves/Definitions2.html#Envelope (2014)
- 13.Envelope: Available at http://xahlee.info/SpecialPlaneCurves_dir/Envelope_dir/envelope.html (2014)
- 14.Envelope_(mathematics): Available at https://en.wikipedia.org/wiki/Envelope_mathematics (2015)
- 16.GeoGebra User Forum: Available at http://www.geogebra.org/forum/viewtopic.php?f=2&t=20103 (2011)