ArgoTriCS – automated triangle construction solver

Marinković, Vesna

doi:10.1080/0952813x.2015.1132271

Cited by 11 publications

(8 citation statements)

References 22 publications

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“…For building a set of production rules for Wernick's points, we used our tool ArgoTriCS for automated solving of construction problems [22,24]. The tool, using its knowledge base (consisting of definitions, lemmas and construction primitives), can solve almost all solvable problems from Wernick's list, but here we are not interested in these solutions, but in production rules that the tool can yield.…”

Section: Production Rulesmentioning

confidence: 99%

Constructibility Classes for Triangle Location Problems

2016

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Straightedge-and-compass construction problems are well known for different reasons. One of them is the difficulty to prove that a problem is not constructible: it took about two millennia to prove that it is not possible in general to cut an angle into three equal parts by using only straightedge and compass. Today, such proofs rely on algebraic tools difficult to apprehend by high school student. On the other hand, the technique of problem reduction is often used in theory of computation to prove other kinds of impossibility. In this paper, we adapt the notion of reduction to geometric constructions in order to have geometric proofs for unconstructibility based on a set of problems known to be unconstructible. Geometric reductions can also be used with constructible problems: in this case, besides having constructibility, the reduction also yields a construction. To make the things concrete, we focus this study to a corpus of triangle location problems proposed by William Wernick in the eighties.

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Section: Production Rulesmentioning

confidence: 99%

Constructibility Classes for Triangle Location Problems

2016

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“…In further text, we rely on the notation used by Marinković [3]. We also assume the geometric knowledge presented in [3], as well as the set of elementary and compound construction steps used in that work.…”

Section: Ruler-and-compass Constructionsmentioning

confidence: 99%

Automation of Triangle Ruler-and-Compass Constructions Using Constraint Solvers

Banković

2024

Electron. Proc. Theor. Comput. Sci.

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In this paper, we present an approach to automated solving of triangle ruler-and-compass construction problems using finite-domain constraint solvers. The constraint model is described in the MiniZinc modeling language, and is based on the automated planning. The main benefit of using general constraint solvers for such purpose, instead of developing dedicated tools, is that we can rely on the efficient search that is already implemented within the solver, enabling us to focus on geometric aspects of the problem. We may also use the solver's built-in optimization capabilities to search for the shortest possible constructions. We evaluate our approach on 74 solvable problems from the Wernick's list, and compare it to the dedicated triangle construction solver ArgoTriCS. The results show that our approach is comparable to dedicated tools, while it requires much less effort to implement. Also, our model often finds shorter constructions, thanks to the optimization capabilities offered by the constraint solvers.

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“…Gulwani et al [6] formulated a logic and a programming language of geometry constructions and then applied methods for program synthesis to obtain RC-constructions. Marinković and Janičić [9,10] focused on triangle construction given its significant points. Their system ArgoTriCS is capable of solving 66 out of 74 solvable problems from Wernick's list.…”

Section: Related Workmentioning

confidence: 99%

“…ArgoTriCS is a PROLOG system that can solve geometry construction problems automatically, given some background geometrical knowledge [10]. It generates informal description of found construction in natural language (in English) and formal description in GCLC language [8], accompanied by a corresponding illustration.…”

Section: Argotricsmentioning

confidence: 99%

“…RC-constructions) have been intensively studied in mathematics and mathematical education since ancient Greeks, for now more than two and a half thousand years. Triangles are also a very nice polygon to develop and test artificial intelligence and automated reasoning tools, and systems that automatically solve RC-construction problems are actively being developed (e.g., ArgoTriCS [10]).…”

Section: Introductionmentioning

confidence: 99%

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On Automating Triangle Constructions in Absolute and Hyperbolic Geometry

Marinković

Šukilović

Marić

2021

Electron. Proc. Theor. Comput. Sci.

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We describe first steps towards a system for automated triangle constructions in absolute and hyperbolic geometry. We discuss key differences between constructions in Euclidean, absolute and hyperbolic geometry, compile a list of primitive constructions and lemmas used for constructions in absolute and hyperbolic geometry, build an automated system for solving construction problems and test it on a corpus of triangle-construction problems. We also provide an online compendium containing construction descriptions and illustrations. * This research is supported by the Serbian Ministry of Education, Science and Technological Development through the University of Belgrade, Faculty of Mathematics.1 Usually only a straightedge (ruler with no marks) is allowed.2 This notation will be used throughout the paper

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ArgoTriCS – automated triangle construction solver

Cited by 11 publications

References 22 publications

Constructibility Classes for Triangle Location Problems

Constructibility Classes for Triangle Location Problems

Automation of Triangle Ruler-and-Compass Constructions Using Constraint Solvers

On Automating Triangle Constructions in Absolute and Hyperbolic Geometry

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