# Beyond Lines and Circles: Unveiling the Geometric Reasoning Gap in Large Language Models

arXiv: https://arxiv.org/abs/2402.03877 · HTML: https://mlsanity.com/paper/2402.03877/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 9 of its 70 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 9 of 9)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Social Simulacra: Creating Populated Prototypes for Social Computing Systems](https://mlsanity.com/paper/2208.04024/) (2022)
- [RoleLLM: Benchmarking, Eliciting, and Enhancing Role-Playing Abilities of Large Language Models](https://mlsanity.com/paper/2310.00746/) (2023)
- [Progressive-Hint Prompting Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2304.09797/) (2023)

## Built on by (most cited first, 11 of 11)

- [Agentic Reasoning and Tool Integration for LLMs via Reinforcement Learning](https://mlsanity.com/paper/2505.01441/) (2025)
- [Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2](https://mlsanity.com/paper/2502.03544/) (2025)
- [OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization](https://mlsanity.com/paper/2506.18880/) (2025)
- [How Far are VLMs from Visual Spatial Intelligence? A Benchmark-Driven Perspective](https://mlsanity.com/paper/2509.18905/) (2025)
- [Position: Multimodal Large Language Models Can Significantly Advance Scientific Reasoning](https://mlsanity.com/paper/2502.02871/) (2025)
- [The CLRS-Text Algorithmic Reasoning Language Benchmark](https://mlsanity.com/paper/2406.04229/) (2024)
- [Towards Geometry Problem Solving in the Large Model Era: A Survey](https://mlsanity.com/paper/2506.02690/) (2025)
- [Decoupling the components of geometric understanding in Vision Language Models](https://mlsanity.com/paper/2503.03840/) (2025)
- [GeoTikzBridge: Advancing Multimodal Code Generation for Geometric Perception and Reasoning](https://mlsanity.com/paper/2603.22687/) (2026)
- [Reasoning-Intensive Regression](https://mlsanity.com/paper/2508.21762/) (2025)
- [Language Models Refine Mechanical Linkage Designs Through Symbolic Reflection and Modular Optimisation](https://mlsanity.com/paper/2604.27962/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) demonstrate ever-increasing abilities in mathematical and algorithmic tasks, yet their geometric reasoning skills are underexplored. We investigate LLMs' abilities in constructive geometric problem-solving one of the most fundamental steps in the development of human mathematical reasoning. Our work reveals notable challenges that the state-of-the-art LLMs face in this domain despite many successes in similar areas. LLMs exhibit biases in target variable selection and struggle with 2D spatial relationships, often misrepresenting and hallucinating objects and their placements. To this end, we introduce a framework that formulates an LLMs-based multi-agents system that enhances their existing reasoning potential by conducting an internal dialogue. This work underscores LLMs' current limitations in geometric reasoning and improves geometric reasoning capabilities through self-correction, collaboration, and diverse role specializations.