With the growth in interest in geometrical ideas it is important to be clear about the nature of geometrical reasoning and how it develops. This paper provides an overview of three theoretical frameworks for the learning of geometrical reasoning: the van Hiele model of thinking in geometry, Fischbein’s theory of figural concepts, and Duval’s cognitive model of geometrical reasoning. Each of the...

GeoThms is a web-based framework for exploring geometrical knowledge that integrates Dynamic Geometry Software (DGS), Automatic Theorem Provers (ATP), and a repository of geometrical constructions, figures and proofs. The GeoThms users can easily use/browse through existing geometrical content and build new contents. In this paper we describe GeoThms functionalities, focusing on the interface s...

SIMULGEO is a geometrical software developed for the position monitoring system of the CMS detector at the LHC accelerator. This software is capable to model opto-geometrical systems including error propagation and geometrical reconstruction. Thanks to a special description method, any opto-geometrical system can easily be described and analysed. This report explains how to use SIMULGEO, descri...

In this paper a geometric calculator is presented. A language of geometrical expressions, that are evaluated by the calculator, and the design and implementation of its interpreter is also presented. Geometrical expressions correspond to abstract data-types that can be defined dynamically through composition operations. Diagrams can be represented by a set of geometrical expressions, and the ge...