THE GREENHOUSE PROBLEM AND THALES' THEOREM

In this paper we discuss new possibilities and limitations of using the CAS graphics calculator, e. g. ClassPad II, in the education of our students. A growing number of international studies has shown that a Computer Algebra System (CAS)-based instruction has the potential to positively affect the teaching and learning of mathematics at various levels of the education system. Let us illustrate the use of a CAS software applied to an optimization problem, adapted from Cohen et al (1991). In this problem students are asked to optimize the usable floor space of the greenhouse that their parents are building adjacent to their house. The floor space in the greenhouse is only considered usable if both parents can stand up in it. The roof of the greenhouse is the sloped glass of a given fixed size. Various mathematical models are presented and evaluated. Different areas of mathematics are used: a family of straight lines with parameters or the envelope of this family of curves or right-angled triangles in the Thales circle. key words: optimization problem, word problem, various mathematical models, family of straight lines with parameters, the envelope of a family of curves, right-angled triangles in a Thales' circle.

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