Geometry Constructions Language

Janicic, Predrag

doi:10.1007/s10817-009-9135-8

Cited by 31 publications

(21 citation statements)

References 26 publications

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“…Currently export to natural language form (in English language, in LaTeX format), as well as export to the GCLC language are supported. For example, a generated construction for problem 32: Formal specification of generated 9 construction, along with its illustration, is generated automatically using geometrical language GCLC (Janičić, 2006(Janičić, , 2010Janičić & Quaresma, 2006). Beside construction, a specification of input to the provers integrated in GCLC tool can be generated.…”

Section: Methodsmentioning

confidence: 99%

ArgoTriCS – automated triangle construction solver

Marinković

2016

Journal of Experimental & Theoretical Artificial Intelligen

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In this paper, a method for automatically solving a class of straightedge-andcompass construction problems is proposed. These are the problems where the goal is to construct a triangle given three located points. The method is based on identifying and systematising geometric knowledge, a specific, restricted search and handling redundant or locus-dependent instances. The proposed method is implemented and the current implementation can solve a large number of triangle construction problems. To our knowledge this is the first systematic automated construction solver focused on solving problems from the corpus given. This is also the first approach that considers proving correctness of generated constructions (using external automated theorem provers). ARTICLE HISTORY

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Section: Methodsmentioning

confidence: 99%

ArgoTriCS – automated triangle construction solver

Marinković

2016

Journal of Experimental & Theoretical Artificial Intelligen

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“…GCLC 12 [29,32] is a tool for the visualisation of objects and notions of geometry and other fields of mathematics. The primary focus of the first versions of the GCLC was producing digital illustrations of Euclidean constructions in L A T E X form (hence the name "Geometry Constructions → L A T E X Converter"), but now it is more than that: GCLC can be used in mathematical education, for storing visual mathematical contents in textual form (as figure descriptions in the underlying language), and for studying automated reasoning methods for geometry.…”

Section: Gclcmentioning

confidence: 99%

“…A figure can be generated (in the Cartesian model of Euclidean plane) on the basis of an abstract description. The language of GCLC [32] consists of commands for basic definitions and constructions, transformations, symbolic calculations, flow control, drawing and printing (including commands for drawing parametric curves and surfaces, functions, graphs, and trees), automated theorem proving, etc. Libraries of GCLC procedures provide additional features, such as support for hyperbolic geometry.…”

Section: Gclcmentioning

confidence: 99%

The Area Method

2010

Self Cite

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The area method for Euclidean constructive geometry was proposed by Chou, Gao and Zhang in the early 1990's. The method can efficiently prove many non-trivial geometry theorems and is one of the most interesting and most successful methods for automated theorem proving in geometry. The method produces proofs that are often very concise and human-readable. In this paper, we provide a first complete presentation of the method. We provide both algorithmic and implementation details that were omitted in the original presentations. We also give a variant of Chou, Gao and Zhang's axiom system. Based on this axiom system, we proved formally all the lemmas needed by the method and its soundness using the Coq proof assistant. To our knowledge, apart from the original implementation by the authors who first proposed the method, there are only three implementations more. Although the basic idea of the method is simple, implementing it is a very challenging task because of a number of details that has to be dealt with. With the description of the method given in this paper, implementing the method should be still complex, but a straightforward task. In the paper we describe all these implementations and also some of their applications. 490 P. Janičić et al.

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“…Typical relations among elements are equivalence, congruence, perpendicularity, parallelism, coincident, membership(X is a part of Y), and their negations [7]. Part of the primitive geometric bases is raised in [2,[6][7]. In our framework, the primitive geometric bases include: …”

Section: Geometric Basismentioning

confidence: 99%

“…We define the geometric basis, which is similar to the concept of "construction". Reference [6] define some constructions. But we use different theorem provers.…”

Section: Introductionmentioning

confidence: 99%

A preliminary framework for geometric basis computing pattern

Wang

2010

2010 IEEE International Conference on Progress in Informatics and Computing

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Geometric problems are usually solved by algebraic methods, which narrows the capacity of geometry. We represent a preliminary framework for geometric basis computing pattern.The pattern is based on He's theory and solves the problems in the synthetic way. We define the geometric basis and use an axiomatic prover to generate a sequence of geometric bases.Computing is made according to the sequence. We also give an example to demonstration the feasibility of our approach.

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Geometry Constructions Language

Cited by 31 publications

References 26 publications

ArgoTriCS – automated triangle construction solver

ArgoTriCS – automated triangle construction solver

The Area Method

A preliminary framework for geometric basis computing pattern

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