Visually Dynamic Presentation of Proofs in Plane Geometry

Zheng, Yi; Chou, Shang-Ching; Gao, Xiao-Shan

doi:10.1007/s10817-009-9162-5

Cited by 23 publications

(9 citation statements)

References 28 publications

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“…(semi-)synthetic proof with a corresponding natural language rendering; 5. (semi-)synthetic proof with a corresponding natural language and visual renderings [35,36].…”

Section: Test Benchmentioning

confidence: 99%

Towards Ranking Geometric Automated Theorem Provers

Baeta

Quaresma

2019

Electron. Proc. Theor. Comput. Sci.

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The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers.The geometry automated deduction area differs from other areas by the strong connection between the axiomatic theories and its standard models. In many cases the geometric constructions are used to establish the theorems' statements, geometric constructions are, in some provers, used to conduct the proof, used as counter-examples to close some branches of the automatic proof. Synthetic geometry proofs are done using geometric properties, proofs that can have a visual counterpart in the supporting geometric construction.With the growing use of geometry automatic deduction tools as applications in other areas, e.g. in education, the need to evaluate them, using different criteria, is felt. Establishing a ranking among geometric automated theorem provers will be useful for the improvement of the current methods/implementations. Improvements could concern wider scope, better efficiency, proof readability and proof reliability.To achieve the goal of being able to compare geometric automated theorem provers a common test bench is needed: a common language to describe the geometric problems; a comprehensive repository of geometric problems and a set of quality measures.

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“…(semi-)synthetic proof with a corresponding natural language rendering; 5. (semi-)synthetic proof with a corresponding natural language and visual renderings [35,36].…”

Section: Test Benchmentioning

confidence: 99%

Towards Ranking Geometric Automated Theorem Provers

Baeta

Quaresma

2019

Electron. Proc. Theor. Comput. Sci.

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“…The study of proofs in education is important as can be seen by the many contributions in proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education [8]. A number of DGS already incorporates GATPs: GCLC incorporates four GATPs in it [11]; new versions of GeoGebra [10] already include a connection to GATPs allowing to give a formal answer to a given validation question [1]; Java Geometry Expert [26,27,28] incorporates several GATPs. Cinderella uses a technique called "randomised theorem checking", generating a large number of random examples, checking if the conjecture holds, establishing the truthfulness if the answer is yes for all examples generated [20].…”

Section: Clients and Servers Of Geometric Informationmentioning

confidence: 99%

Exchange of Geometric Information Between Applications

Quaresma

Santos

Baeta

2018

Electron. Proc. Theor. Comput. Sci.

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The Web Geometry Laboratory (WGL) is a collaborative and adaptive e-learning Web platform integrating a well known dynamic geometry system. Thousands of Geometric problems for Geometric Theorem Provers (TGTP) is a Web-based repository of geometric problems to support the testing and evaluation of geometric automated theorem proving systems.The users of these systems should be able to profit from each other. The TGTP corpus must be made available to the WGL user, allowing, in this way, the exploration of TGTP problems and their proofs. On the other direction TGTP could gain by the possibility of a wider users base submitting new problems.Such information exchange between clients (e.g. WGL) and servers (e.g. TGTP) raises many issues: geometric search-someone, working in a geometric problem, must be able to ask for more information regarding that construction; levels of geometric knowledge and interest-the problems in the servers must be classified in such a way that, in response to a client query, only the problems in the user's level and/or interest are returned; different aims of each tool-e.g. WGL is about secondary school geometry, TGTP is about formal proofs in semi-analytic and algebraic proof methods, not a perfect match indeed; localisation issues, e.g. a Portuguese user obliged to make the query and process the answer in English; technical issues-many technical issues need to be addressed to make this exchange of geometric information possible and useful.Instead of a giant (difficult to maintain) tool, trying to cover all, the interconnection of specialised tools seems much more promising. The challenges to make that connection work are many and difficult, but, it is the authors impression, not insurmountable.

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“…Such methods include the area method, the full-angle method, the bracket algebra method, methods based on Clifford algebra, axiom-based deductive methods, and diagrammatic reasoning methods (see [2,6,21] and references therein). Some dynamic geometry software systems have implemented specialized methods (e.g., randomized proving methods in Cinderella [14]) to prove theorems for constructed diagrams, or interfaces with geometric theorem provers for generating proofs diagrammatically [23,26] and exploring knowledge in repositories of geometric constructions and proofs [19]. A web-based library of problems in geometry is being created for testing and evaluating methods and tools of automated theorem proving [18].…”

Section: Other Related Workmentioning

confidence: 99%

Automated generation of geometric theorems from images of diagrams

Chen

Song

Wang

2014

Ann Math Artif Intell

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We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to mine basic geometric relations. Candidate propositions are generated from the retrieved information by using six strategies and geometric theorems are obtained from the candidates via algebraic computation. Experiments with a preliminary implementation illustrate the effectiveness and efficiency of the proposed approach for generating nontrivial theorems from images of diagrams. This work demonstrates the feasibility of automated discovery of profound geometric knowledge from simple image data and has potential applications in geometric knowledge management and education.

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Visually Dynamic Presentation of Proofs in Plane Geometry

Cited by 23 publications

References 28 publications

Towards Ranking Geometric Automated Theorem Provers

Towards Ranking Geometric Automated Theorem Provers

Exchange of Geometric Information Between Applications

Automated generation of geometric theorems from images of diagrams

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