Finding and Proving New Geometry Theorems in Regular Polygons with Dynamic Geometry and Automated Reasoning Tools

We report, through different examples, the current development in GeoGebra, a widespread Dynamic Geometry software, of geometric automated reasoning tools by means of computational algebraic geometry algorithms. Then we introduce and analyze the case of the degeneracy conditions that so often arise in the automated deduction in geometry context, proposing two different ways for dealing with them. One is working with the saturation of the hypotheses ideal with respect to the ring of geometrically independent variables, as a way to globally handle the statement over all non-degenerate components. The second is considering the reformulation of the given hypotheses ideal—considering the independent variables as invertible parameters—and developing and exploiting the specific properties of this zero-dimensional case to analyze individually the truth of the statement over the different non-degenerate components.

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The Area of the Disk in Middle School Grade by GeoGebra.

International Journal of Emerging Technologies in Learning (iJET) ◽

10.3991/ijet.v12i11.6834 ◽

2017 ◽

Vol 12 (11) ◽

pp. 28 ◽

Cited By ~ 2

Author(s):

David Lognoli

Keyword(s):

Middle School ◽

Sampling Methods ◽

Teaching Strategy ◽

Dynamic Geometry ◽

Dynamic Geometry Software ◽

Regular Polygons ◽

School Grade ◽

Level Of Knowledge ◽

Multimedia Environments ◽

Dynamic Software

The visualization and exploration of mathematical objects and concepts in multimedia environments can facilitate learning. Geometry is particularly involved with the growing use of software in teaching. GeoGebra is a dynamic geometry system that increases the level of knowledge and skills in mathematics. Use of GeoGebra permits to complete and extend a teaching strategy based on manipulative activities. The area of a disk in the Middle School, i.e. Grades 7-8 offers the opportunity to a large use of geometry dynamic software. This paper proposes, as example of combining between manipulative activating and dynamic geometry software, the use GeoGebra to permit the visualization of three different approaches to the area of a disk. First is based on the limit of the area of inscribed regular polygons, second on dynamical morphing of the disk in a triangle and third on sampling methods.

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