Linking geometry and algebra with GeoGebra

GeoGebra is a software package and is so named because it combines geometry and algebra as equal mathematical partners in its representations. At one level, GeoGebra can be as a dynamic geometry system like other, commercially available, software. But this is only part of the story. Another window (the algebra part of GeoGebra) provides an insight into the relationship between the geometric aspects of figures and their algebraic representations. Here each equation or set of coordinates can be edited in the algebra window and the figure instantly changes. What is more, an equation (or a function) can be typed into the space at the foot of the GeoGebra interface and the corresponding geometric representation will appear in the geometry window. Perhaps utilising GeoGebra could inspire a change from regular forms of enrichment/ extension activity to things that need high level thinking, and things that pupils may find themselves wanting to follow-up outside school lessons

Automatic Deduction in Dynamic Geometry using Sage

We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer algebra system Sage, corresponding to two different ways of coding a geometric construction. In one worksheet, diagrams constructed with the open source dynamic geometry system GeoGebra are accepted. In this worksheet, Groebner bases are used to either compute the equation of a geometric locus in the case of a locus construction or to determine the truth of a general geometric statement included in the GeoGebra construction as a boolean variable. In the second worksheet, locus constructions coded using the common file format for dynamic geometry developed by the Intergeo project are accepted for computation. The prototype and several examples are provided for testing. Moreover, a third Sage worksheet is presented in which a novel algorithm to eliminate extraneous parts in symbolically computed loci has been implemented. The algorithm, based on a recent work on the Groebner cover of parametric systems, identifies degenerate components and extraneous adherence points in loci, both natural byproducts of general polynomial algebraic methods. Detailed examples are discussed.Comment: In Proceedings THedu'11, arXiv:1202.453

Learning Media Development Approach with a Rectangle Problem Posing Based Geogebra

This study aims to develop learning media quadrilateral with problem posing approach based GeoGebra. 8 teachers from three different schools have stated that this media can be used to teach the nature - the nature of the quadrilateral. After the learning is done using this media, this media can facilitate students in asking about the nature - the nature of wake quadrilateral, facilitating students to learn the relationship between the type - the type of wake rectangles that have the same properties, and provides the opportunity for teachers in the evaluation of mathematical communication current students ask and write