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.

翻译：大型语言模型（LLMs）在数学和算法任务中展现出日益增强的能力，但其几何推理技能仍未得到充分探索。我们研究了LLMs在构造性几何问题求解中的能力——这是人类数学推理发展中最基础的步骤之一。我们的工作揭示了当前最先进的LLMs在该领域面临的显著挑战，尽管它们在类似领域取得了诸多成功。LLMs在目标变量选择上表现出偏差，并难以处理二维空间关系，常常错误表征甚至幻觉化物体及其位置。为此，我们提出一个框架，构建基于LLMs的多智能体系统，通过内部对话增强其现有推理潜力。本研究强调了LLMs当前在几何推理中的局限性，并通过自我修正、协作及多样化角色专长提升了其几何推理能力。