From conic sections to toric sections: experiments with Computer Algebra System leading to curriculum changes

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• Professor Thierry Dana-Picard, President of Jerusalem College of Technology, Israel
• Wednesday 22 May 2013, 12:30-13:30
• GS1, Donald McIntyre Building, Faculty of Education, 184 Hills Road, Cambridge.

If you have a question about this talk, please contact Ann Waterman.

We present a unified point of view on conics, the invariant of the study being the angle under which a given conic is viewed. The geometric locus of points from which a given ellipse or hyperbola is viewed under a fixed angle θ (θ -isoptic curve of the conic) is a quartic named spiric curve. We show how to characterize the number of components of the θ -isoptic curve and reconstruct it as a toric section. This work has been done in parallel to a course on Analytic Geometry for in-service teachers in Israel. At the beginning, not all of them had a strong CAS literacy, but they underwent an interesting instrumental genesis. As far as we are concerned by improving the regular curriculum, the work shows how the usage of a Computer Algebra System enables the teacher to enrich the curriculum by the means of a revival of classical topics in mathematics.

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• GS1, Donald McIntyre Building, Faculty of Education, 184 Hills Road, Cambridge

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