Related papers: Automatic Synthesis of Geometry Problems for an In…
Intelligent tutoring systems have long enabled automated immediate feedback on student work when it is presented in a tightly structured format and when problems are very constrained, but reliably assessing free-form mathematical reasoning…
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…
Plane Geometry Diagram Synthesis has been a crucial task in computer graphics, with applications ranging from educational tools to AI-driven mathematical reasoning. Traditionally, we rely on manual tools (e.g., Matplotlib and GeoGebra) to…
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…
Multimodal Large Language Models (MLLMs) have significantly advanced vision-language understanding. However, even state-of-the-art models struggle with geometric reasoning, revealing a critical bottleneck: the extreme scarcity of…
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
The introduction of automated deduction systems in secondary schools face several bottlenecks. Beyond the problems related with the curricula and the teachers, the dissonance between the outcomes of the geometry automated theorem provers…
The task of generating natural images from 3D scenes has been a long standing goal in computer graphics. On the other hand, recent developments in deep neural networks allow for trainable models that can produce natural-looking images with…
The area of geometry with its very strong and appealing visual contents and its also strong and appealing connection between the visual content and its formal specification, is an area where computational tools can enhance, in a significant…
Humans have long relied on visual aids like sketches and diagrams to support reasoning and problem-solving. Visual tools, like auxiliary lines in geometry or graphs in calculus, are essential for understanding complex ideas. However, many…
Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of vectors is introduced in such a way that it encodes the famous…
Constructive-deductive method for plane Euclidean geometry is proposed and formalized within Coq Proof Assistant. This method includes both postulates that describe elementary constructions by idealized geometric tools (pencil, straightedge…
Semi-supervised 3D object detection, aiming to explore unlabeled data for boosting 3D object detectors, has emerged as an active research area in recent years. Some previous methods have shown substantial improvements by either employing…
Many problems in Euclidean geometry, arising in computational design and fabrication, amount to a system of constraints, which is challenging to solve. We suggest a new general approach to the solution, which is to start with analogous…
Geometry Problem Solving (GPS), which is a classic and challenging math problem, has attracted much attention in recent years. It requires a solver to comprehensively understand both text and diagram, master essential geometry knowledge,…
Mathematics olympiads are prestigious competitions, with problem proposing and solving highly honored. Building artificial intelligence that proposes and solves olympiads presents an unresolved challenge in automated theorem discovery and…
Multimodal geometry reasoning requires models to jointly understand visual diagrams and perform structured symbolic inference, yet current vision--language models struggle with complex geometric constructions due to limited training data…
Generative Artificial Intelligence (GenAI) has emerged as a valuable assistant in many fields such as marketing, finance, project management, and education. In education, many GenAI tools have been developed to aid teachers in preparing…
Powerful sentence encoders trained for multiple languages are on the rise. These systems are capable of embedding a wide range of linguistic properties into vector representations. While explicit probing tasks can be used to verify the…
We consider the task of automated theorem proving, a key AI task. Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning. To address this…