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Towards an electronic geometry textbook. (English) Zbl 1195.68091
Botana, Francisco (ed.) et al., Automated deduction in geometry. 6th international workshop, ADG 2006, Pontevedra, Spain, August 31–September 2, 2006. Revised papers. Berlin: Springer (ISBN 978-3-540-77355-9/pbk). Lecture Notes in Computer Science 4869. Lecture Notes in Artificial Intelligence, 1-23 (2007).
Summary: 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 a computer. The knowledge in the textbook is 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.
For the entire collection see [Zbl 1132.68006].
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
51-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry
51-04 Software, source code, etc. for problems pertaining to geometry
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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