Solving Shaded Area Problems by Constructing Equations

Feng, Zihan; Yu, Xinguo; Li, Qilin; Sun, Hao

doi:10.1007/978-981-16-7527-0_8

Cited by 1 publication

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Despite its strengths, the method falls short in terms of the interpretability of solutions, which is a crucial aspect of APGD-solving tasks. Alvin et al's approach called GeoShader [13] and Feng et al's approach [14] are both tailored to tackle shaded area problems, formalizing and solving such tasks efficiently. Despite their effectiveness for this specific problem type, these methods exhibit limitations in their applicability, as they are primarily designed to solve shaded area problems.…”

Section: Methods Of Solving Apgdsmentioning

confidence: 99%

“…For GCP-SS, the Geometry3K dataset [10] is used, containing 3,002 problems. Regarding the SAP-PS dataset, 120 problems are collected from various versions of primary school math textbooks, while for SAP-SS, Feng's dataset [14] containing 192 problems is utilized. All problem texts have been translated into English.…”

Section: Datasets and Evaluation Metricsmentioning

confidence: 99%

“…FengAlg [14] is a method specifically designed for solving shaded area problems. It focuses on constructing equations to generate readable solutions, addressing the challenges associated with the diverse expressions of such problems and the complex relationships between shaded areas and other areas.…”

Section: Inter-gpsmentioning

confidence: 99%

“…For shaded area problems, the symbolic solver from Feng's method [14] is selected, which also takes the geometric relations obtained by PROPOSED as input. This solver is specifically designed to address the challenges associated with computing shaded areas in geometric diagrams.…”

Section: Implementation Detailsmentioning

confidence: 99%

See 3 more Smart Citations

Solving Algebraic Problems with Geometry Diagrams Using Syntax-Semantics Diagram Understanding

Huang,

Yu,

Niu

et al. 2023

CMC

View full text Add to dashboard Cite

Solving Algebraic Problems with Geometry Diagrams (APGDs) poses a significant challenge in artificial intelligence due to the complex and diverse geometric relations among geometric objects. Problems typically involve both textual descriptions and geometry diagrams, requiring a joint understanding of these modalities. Although considerable progress has been made in solving math word problems, research on solving APGDs still cannot discover implicit geometry knowledge for solving APGDs, which limits their ability to effectively solve problems. In this study, a systematic and modular three-phase scheme is proposed to design an algorithm for solving APGDs that involve textual and diagrammatic information. The three-phase scheme begins with the application of the statetransformer paradigm, modeling the problem-solving process and effectively representing the intermediate states and transformations during the process. Next, a generalized APGD-solving approach is introduced to effectively extract geometric knowledge from the problem's textual descriptions and diagrams. Finally, a specific algorithm is designed focusing on diagram understanding, which utilizes the vectorized syntax-semantics model to extract basic geometric relations from the diagram. A method for generating derived relations, which are essential for solving APGDs, is also introduced. Experiments on real-world datasets, including geometry calculation problems and shaded area problems, demonstrate that the proposed diagram understanding method significantly improves problem-solving accuracy compared to methods relying solely on simple diagram parsing.

show abstract

Section: Methods Of Solving Apgdsmentioning

confidence: 99%

Section: Datasets and Evaluation Metricsmentioning

confidence: 99%

Section: Inter-gpsmentioning

confidence: 99%

Section: Implementation Detailsmentioning

confidence: 99%

See 2 more Smart Citations