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.

大型语言模型（LLMs）在数学和算法任务中展现日益增长的能力，但它们的几何推理技能尚未被充分探索。我们研究了 LLMs 在构造性几何问题求解上的能力，这是人类数学推理发展中最基本的一步。我们的工作揭示了当前 LLMs 面临的显著挑战，尽管在类似领域取得了很多成功。LLMs 在目标变量选择上存在偏见，并且在二维空间关系方面遇到困难，常常误代和产生对象及其放置的幻觉。为此，我们介绍了一个基于 LLMs 的多智能体系统框架，通过进行内部对话来增强它们现有的推理潜力。这项工作突出了 LLMs 在几何推理中目前的局限性，并通过自我纠正、协作和多样化角色专业化来改善几何推理能力。