Towards an electronic geometry textbook

Abstract

This paper proposes a system in the form of a textbook for managing geometric knowledge dynamically, effectively, and interactively. Such a system, called an Electronic Geometry Textbook, can be viewed or printed as a traditional textbook and run as dynamic software on computer. The knowledge in the textbook is being formalized by using standard formal languages and may be processed by software modules developed for geometric computing and reasoning, diagram generation, and visualization. The textbook can be generated automatically by organizing and presenting the textbook data according to some specifications. The system allows the user to manipulate (query, modify, restructure, etc.) the textbook with automated consistency checking. We present the main ideas on the design of the electronic geometry textbook, explain the features of the system, propose five phases of creating and managing the geometric knowledge in the textbook, discuss the involved tasks and some of the fundamental research problems in each phase, and report our progress and experiments on a preliminary implementation of the system. © Springer-Verlag Berlin Heidelberg 2007.