Computing envelopes in dynamic geometry environments

  • Francisco BotanaEmail author
  • Tomas Recio


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.


Automated deduction in geometry Envelope computation Dynamic geometry 

Mathematics Subject Classification (2010)

Primary 68T15 Secondary 68W30 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Depto. de Matemática Aplicada IUniversidad de VigoPontevedraSpain
  2. 2.Depto. de Matemáticas, Estadística y ComputaciónUniversidad de CantabriaSantanderSpain

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