迈向最小包围球及相关问题的数学基础
Towards the mathematical foundation of the minimum enclosing ball and related problems
AI总结：
本文为d维欧几里得空间中的最小包围球问题构建了数学基础与理论框架，基于若干包围与划分定理，推导出集合外接半径、内切半径、直径与宽度间的界限与关系，并指出其作为基石对非欧几何发展的深刻影响。
摘要：
本文为最小包围球问题的数学基础提供了理论背景。该问题涉及确定包围d维欧几里得空间中给定有界集的最小半径的唯一球面。由于这类问题在科学技术的各个领域有大量应用，对若干与最小包围球问题相似或相关问题的研究受到了极大推动。所提出的理论框架基于若干包围（覆盖）与划分（聚类）定理，并给出了集合外接半径、内切半径、直径与宽度之间的界限和关系。这些包围与划分定理被视为该领域的基石，深刻影响了对其他空间和非欧几何的发展与推广。
英文摘要：
Theoretical background is provided towards the mathematical foundation of the minimum enclosing ball problem. This problem concerns the determination of the unique spherical surface of smallest radius enclosing a given bounded set in the d-dimensional Euclidean space. The study of several problems that are similar or related to the minimum enclosing ball problem has received a considerable impetus from the large amount of applications of these problems in various fields of science and technology. The proposed theoretical framework is based on several enclosing (covering) and partitioning (clustering) theorems and provides among others bounds and relations between the circumradius, inradius, diameter and width of a set. These enclosing and partitioning theorems are considered as cornerstones in the field that strongly influencing developments and generalizations to other spaces and non-Euclidean geometries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
