Cubical Geometry

立方几何

• 批准号: 238946-2013
• 负责人: Wise, Daniel
• 金额: $ 2.77万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=547147
• 关键词: Cubical; Geometry

Mathematics is the study of patterns. The most fundamental and elementary type of pattern is a symmetry. There are finite `groups' of symmetries, such as the group consisting of the 48 distinct symmetries of a cube, and there are also infinite groups of symmetries such as the group of symmetries of the tiling of the Euclidean plane by squares. While finite groups of symmetries can be understood quite well, some infinite groups are so complex that they are provably impossible to understand. Nevertheless, many important problems in geometry and topology can be reduced to understanding the infinite group of symmetries of some infinite geometric object.

数学是对模式的研究。图案的最基本和基本类型是对称性。存在有限的对称“群”，例如由立方体的 48 个不同对称组成的群，并且也存在无限的对称群，例如由正方形平铺欧几里得平面的对称群。虽然有限对称群可以很好地理解，但一些无限对称群是如此复杂，以至于它们被证明是不可能理解的。然而，几何和拓扑中的许多重要问题可以简化为理解某些无限几何对象的无限对称群。