Thierry Dana-Picard: Plane curves - revival of classical topics in an ICT rich environment

Přednáška významného izraelského matematika a odborníka na využití digitálních technologií ve výuce matematiky

Přednášející:
Thierry Dana-Picard
Jerusalem College of Technology
http://en.wikipedia.org/wiki/Noah_Dana-Picard

Anotace přednášky:
Along the time, classical topics disappeared from the math curriculum, no matter if we deal with students in mathematics, in engineering, or pre-service mathematics teachers.
The usage of Computer Algebra Systems (CAS) and other kinds of Information and Communication Technology (ICT) enable to revive such classical topics, bypassing some of the theoretical problems. A CAS provides generally efficient tools for solving nonlinear systems of equations, for graphing, etc. Other ICTs yield a broad environment enabling various directions for study and enquiry.
We present how the usage of technology enabled us to revive two topics in Differential Geometry:
1. Isoptic curves of plane curves; this yields a pathway from conic sections to toric sections. Here new results have been derived.
2. Envelopes of 1-parameter families of plane curves (Back to 1962, René Thom complained about the disappearance of envelopes of 1-parameter families of curves, resp. surfaces).
In both cases, systems of polynomial equations have to be solved using algorithms based on Gröbner bases.

Joint work with N. Zehavi and G. Mann