Management of geometric knowledge in textbooks

This paper describes Geometric Knowledge Management, explains its main topics and research challenges, and introduces several methods and techniques for geometric knowledge representation, encapsulation, organization, communication, and processing. The proposed methods and techniques make use of general methodologies developed in Mathematical Knowledge Management and take into account the special features of geometry. They are applied to the design and implementation of a system, called an Electronic Geometry Textbook, for representing and managing (plane Euclidean) geometric knowledge in the form of dynamic textbooks. The system may be used to assist users in constructing, maintaining, and sharing geometry textbooks or documents at a detailed granularity, and it is capable of automatically checking the consistency of the presentation structure and the completeness and redundancy of the contents of the constructed textbooks. It also interfaces with external geometry software for automated theorem proving and dynamic diagram drawing.