Automated algebraic calculation of interactively constructed geometric figures — a didactic analysis

Heinz Schumann

Heinz Schumann University of Education, Weingarten, Germany

Keywords: planimetry, automated calculation, interactive dynamic geometry systems

Abstract

Ordinary interactive dynamic geometry systems (IDGS) cannot generally show, how a measurable property of an interactively constructed geometric figure depends on the determining variables of that figure. With a certain method of “Automated Deduction in Geometry” (ADG), implemented in Geometry Expressions (abbreviated GX, homepage: http://www.geometryexpressions.com/), it is now possible to calculate such a dependency as an algebraic expression consisting of the determining variables. We explain this facility by selected examples, which represent the usage of this tool and evaluate its application in classroom. keywords planimetry, automated calculation, interactive dynamic geometry systems.

Author Biography

Heinz Schumann, University of Education, Weingarten, Germany

Prof. Dr. habil., Faculty II, Mathematics,
University of Education Weingarten D-88250
Weingarten Germany

References

1. Schumann, H. (2013). Automatisierte algebraische Berechnungen an geometrischen Figuren. Beitr¨ age zum Mathematikunterricht 2013. Jahrestagung der Gesellschaft fur Didaktik der Mathematik 4.3.2013 ¨- 8.3.2013 Munster, 930 ¨ –933.
2. Todd, Ph. H. (2009). Looking Forward to Interactive Symbolic Geometry. In Craine, T. V.; Rubinstein, R. (Eds.): Understanding Geometry for a Changing World. 71st Yearbook. Reston, VA: The National Council of Teachers of Mathematics, Inc., 349–365.