Towards Automated Discovery of Geometrical Theorems in GeoGebra
- URL: http://arxiv.org/abs/2007.12447v1
- Date: Fri, 24 Jul 2020 10:59:39 GMT
- Title: Towards Automated Discovery of Geometrical Theorems in GeoGebra
- Authors: Zolt\'an Kov\'acs and Jonathan H. Yu
- Abstract summary: We describe a prototype of a new experimental GeoGebra command and tool Discover that analyzes geometric figures for salient patterns, properties, and theorems.
The paper focuses on the mathematical background of the implementation, as well as methods to avoid explosion when storing the interesting properties of a geometric figure.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We describe a prototype of a new experimental GeoGebra command and tool
Discover that analyzes geometric figures for salient patterns, properties, and
theorems. This tool is a basic implementation of automated discovery in
elementary planar geometry. The paper focuses on the mathematical background of
the implementation, as well as methods to avoid combinatorial explosion when
storing the interesting properties of a geometric figure.
Related papers
- Geometry of Lightning Self-Attention: Identifiability and Dimension [2.9816332334719773]
We study the identifiability of deep attention by providing a description of the generic fibers of the parametrization for an arbitrary number of layers.
For a single-layer model, we characterize the singular and boundary points.
Finally, we formulate a conjectural extension of our results to normalized self-attention networks, prove it for a single layer, and numerically verify it in the deep case.
arXiv Detail & Related papers (2024-08-30T12:00:36Z) - AutoGeo: Automating Geometric Image Dataset Creation for Enhanced Geometry Understanding [18.223835101407637]
This paper introduces AutoGeo, a novel approach for automatically generating mathematical geometric images.
By leveraging precisely defined geometric clauses, AutoGeo-100k contains a wide variety of geometric shapes.
Experimental results indicate significant improvements in the model's ability in handling geometric images.
arXiv Detail & Related papers (2024-08-28T14:49:26Z) - A Survey of Geometric Graph Neural Networks: Data Structures, Models and
Applications [67.33002207179923]
This paper presents a survey of data structures, models, and applications related to geometric GNNs.
We provide a unified view of existing models from the geometric message passing perspective.
We also summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation.
arXiv Detail & Related papers (2024-03-01T12:13:04Z) - Adaptive Surface Normal Constraint for Geometric Estimation from Monocular Images [56.86175251327466]
We introduce a novel approach to learn geometries such as depth and surface normal from images while incorporating geometric context.
Our approach extracts geometric context that encodes the geometric variations present in the input image and correlates depth estimation with geometric constraints.
Our method unifies depth and surface normal estimations within a cohesive framework, which enables the generation of high-quality 3D geometry from images.
arXiv Detail & Related papers (2024-02-08T17:57:59Z) - A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems [87.30652640973317]
Recent advances in computational modelling of atomic systems represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space.
Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation.
This paper provides a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems.
arXiv Detail & Related papers (2023-12-12T18:44:19Z) - Exploring Data Geometry for Continual Learning [64.4358878435983]
We study continual learning from a novel perspective by exploring data geometry for the non-stationary stream of data.
Our method dynamically expands the geometry of the underlying space to match growing geometric structures induced by new data.
Experiments show that our method achieves better performance than baseline methods designed in Euclidean space.
arXiv Detail & Related papers (2023-04-08T06:35:25Z) - Plane Geometry Diagram Parsing [29.921409628478152]
We propose a powerful diagram based on deep learning and graph reasoning.
A modified instance segmentation method is proposed to extract geometric primitives.
The graph neural network (GNN) is leveraged to realize relation parsing and primitive classification.
arXiv Detail & Related papers (2022-05-19T07:47:01Z) - A singular Riemannian geometry approach to Deep Neural Networks I.
Theoretical foundations [77.86290991564829]
Deep Neural Networks are widely used for solving complex problems in several scientific areas, such as speech recognition, machine translation, image analysis.
We study a particular sequence of maps between manifold, with the last manifold of the sequence equipped with a Riemannian metric.
We investigate the theoretical properties of the maps of such sequence, eventually we focus on the case of maps between implementing neural networks of practical interest.
arXiv Detail & Related papers (2021-12-17T11:43:30Z) - Inter-GPS: Interpretable Geometry Problem Solving with Formal Language
and Symbolic Reasoning [123.06420835072225]
We construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language.
We propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem solver (Inter-GPS)
Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step.
arXiv Detail & Related papers (2021-05-10T07:46:55Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.