Automated Deduction in Geometry: 6th International Workshop, by Francisco Botana, Tomas Recio

By Francisco Botana, Tomas Recio

This ebook constitutes the completely refereed post-proceedings of the sixth foreign Workshop on computerized Deduction in Geometry, ADG 2006, held at Pontevedra, Spain, in August/September 2006 as a satellite tv for pc occasion of the foreign Congress of Mathematicians, ICM 2006.

The thirteen revised complete papers awarded have been rigorously chosen from the submissions made as a result of a decision for papers - in the scope of ADG - almost immediately after the assembly. The papers convey the vigorous number of themes and strategies and the present applicability of automatic deduction in geometry to diverse branches of arithmetic and to different sciences and technologies.

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Additional info for Automated Deduction in Geometry: 6th International Workshop, ADG 2006, Pontevedra, Spain, August 31-September 2, 2006, Revised Papers

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If we attempt to construct a point X as the intersection of the lines p and q (by adding the command intersec X p q at the end of the code given in Figure 1), we will get the following message: Error 14: Run-time error: Bad definition. Can not determine intersection. (Line: 18, position: 10) File not processed. , for these three particular points, the lines p and q are parallel.

The proof of this second ingredient is based on the first ingredient. We note that the edge coherence condition is a Dehn invariant type condition. With the original Dehn invariant, all the edges are line segments, which are all locally congruent. This helps to explains why the Dehn invariant, which is a single invariant for polyhedra, must be expanded to a collection of conditions for general quadratic regions. We have a separate condition for each congruence type of curve. 7 Remove Nonplanar Intersections We are ready to give details of the algorithm.

Proceedings of the Workshop on Computer-Supported Mathematical Theory Development, Cork, Ireland, pp. 19–29 (2004) 13. : GeoThms — Geometry Framework. Technical Report 2006/002, Centre for Informatics and Systems, University of Coimbra (2006) 14. : The Mizar System. pl/system/ 15. 1: Handling and Proving Geometric Theorems Automatically. In: Winkler, F. ) ADG 2002. LNCS (LNAI), vol. 2930, pp. 194–215. Springer, Heidelberg (2004) 16. org/Math/ 17. : Plane Geometry: An Elementary Textbook by Shalosh B.

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