Results 1  10
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14
Geometric applications of the GrassmannCayley algebra, in: Handbook of Discrete and
 Computational Geometry, 881–892, CRC Press Ser. Discrete Math. Appl., CRC, Boca
, 1997
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An Application of Automatic Theorem Proving in Computer Vision
 IN AUTOMATED DEDUCTION IN GEOMETRY
, 1998
"... Getting accurate construction of tridimensional CAD models is a field of great importance: with the increasing complexity of the models that modeling tools can manage nowadays, it becomes more and more necessary to construct geometrically accurate descriptions. Maybe the most promising technique, ..."
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Cited by 8 (0 self)
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Getting accurate construction of tridimensional CAD models is a field of great importance: with the increasing complexity of the models that modeling tools can manage nowadays, it becomes more and more necessary to construct geometrically accurate descriptions. Maybe the most promising technique, because of its full generality, is the use of automatic geometric tools: these can be used for checking the geometrical coherency and discovering geometrical properties of the model. In this paper, we describe an automatic method for constructing the model of a given geometrical configuration and for discovering the theorems of this configuration. This approach motivated by 3D modeling problems is based on characteristic set techniques and generic polynomials in the bracket algebra.
Using automatic theorem proving to improve the usability of geometry software
 IN: MATHEMATICAL USER INTERFACES
, 2004
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Automated Geometric Reasoning: Dixon Resultants, Gröbner Bases, and Characteristic Sets
 Automated Deduction in Geometry, volume 1360 of Lecture
, 1996
"... Three different methods for automated geometry theorem proving  a generalized version of Dixon resultants, Grobner bases and characteristic sets  are reviewed. The main focus is, however, on the use of the generalized Dixon resultant formulation for solving geometric problems and determining geo ..."
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Three different methods for automated geometry theorem proving  a generalized version of Dixon resultants, Grobner bases and characteristic sets  are reviewed. The main focus is, however, on the use of the generalized Dixon resultant formulation for solving geometric problems and determining geometric quantities.
Geometry and Education in the Internet Age
 In EDMEDIA World Conference on Educational Multimedia, Hypermedia and Telecommunications. 790–799
, 1998
"... Interactive Geometry is a major tool in modern geometry education and various software tools are available. We discuss the requirements of such tools and how they can be fulfilled. We also explain how a geometry tool can benefit from the Internet and present Cinderella's Café, which is an inter ..."
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Cited by 5 (3 self)
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Interactive Geometry is a major tool in modern geometry education and various software tools are available. We discuss the requirements of such tools and how they can be fulfilled. We also explain how a geometry tool can benefit from the Internet and present Cinderella's Café, which is an internetaware geometry tool with a high mathematical background.
Formalizing Projective Plane Geometry in Coq
, 2008
"... We investigate how projective plane geometry can be formalized in a proof assistant such as Coq. Such a formalization increases the reliability of textbook proofs whose details and particular cases are often overlooked and left to the reader as exercises. Projective plane geometry is described thro ..."
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We investigate how projective plane geometry can be formalized in a proof assistant such as Coq. Such a formalization increases the reliability of textbook proofs whose details and particular cases are often overlooked and left to the reader as exercises. Projective plane geometry is described through two different axiom systems which are formally proved equivalent. Usual properties such as decidability of equality of points (and lines) are then proved in a constructive way. The duality principle as well as formal models of projective plane geometry are then studied and implemented in Coq. Finally, we formally prove in Coq that Desargues’ property is independent of the axioms of projective plane geometry.
Automated Theorem Proving in the Homogeneous Model with Clifford Bracket Algebra
 IN: APPLICATIONS OF GEOMETRIC ALGEBRA IN COMPUTER SCIENCE AND ENGINEERING
, 2002
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Algebraic Representation, Elimination and Expansion in Automated Geometric Theorem Proving
 In: Automated Deduction in Geometry
, 2004
"... Abstract. Cayley algebra and bracket algebra are important approaches to invariant computing in projective and affine geometries, but there are some difficulties in doing algebraic computation. In this paper we show how the principle “breefs ” – bracketoriented representation, elimination and expan ..."
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Abstract. Cayley algebra and bracket algebra are important approaches to invariant computing in projective and affine geometries, but there are some difficulties in doing algebraic computation. In this paper we show how the principle “breefs ” – bracketoriented representation, elimination and expansion for factored and shortest results, can significantly simply algebraic computations. We present several typical examples on conics and make detailed discussions on the procedure of applying the principle to automated geometric theorem proving.
Automated Proofs using Bracket Algebra with Cinderella and OpenMath
"... This paper describes the results of a project intended to make it possible to put forward geometrical theorems by pointing and clicking, and then obtain a proof for that theorem automatically. This goal was achieved by adding various options to Cinderella [1], a computer program with which one can c ..."
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This paper describes the results of a project intended to make it possible to put forward geometrical theorems by pointing and clicking, and then obtain a proof for that theorem automatically. This goal was achieved by adding various options to Cinderella [1], a computer program with which one can create geometrical configurations. Its internal ‘Randomized prover ’ is able to discover theorems automatically. In the project the functionality was added to find proofs for these theorems with the aid of the computer algebra package GAP [9]. Communication between these two programs and the various steps in generating the proof is done by means of OpenMath [5, 7]. The proofs are represented by bracket calculations as proposed in [8].
Dynamic Projective Geometry
, 1999
"... The theme of this thesis is dynamic geometry, a new way of exploring classical geometry using interactive computer software. This kind of software allows the user to make geometric constructions on a computer's screen. The constructions might consist of points, lines and conics whose position ..."
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The theme of this thesis is dynamic geometry, a new way of exploring classical geometry using interactive computer software. This kind of software allows the user to make geometric constructions on a computer's screen. The constructions might consist of points, lines and conics whose positions have been constrained in various ways. The constraints, which may involve incidences, distances and angles, can be added and removed dynamically. For example, to force a line to always be incident on a point, the user would simply grab the line with the cursor and drop it onto the point. Any object whose position is not completely determined by the constraints can be grabbed and dragged around on the screen. The rest of the objects will then automatically selfadjust in order to keep the constraints satised. Dynamic geometry software is primarily used for teaching mathematics, but is useful in any situation where it is important to understand the geometric properties of a dynamic system. Over the last few years, a number of tools for dynamic geometry have been