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.

数学是研究模式的。最基本和最基本的图案类型是对称性。有有限的对称性“群”，例如由立方体的48个不同对称性组成的群，也有无限的对称性群，例如用正方形平铺欧几里得平面的对称性群。虽然有限群的对称性可以很好地理解，但一些无限群是如此复杂，以至于可以证明它们不可能理解。然而，几何学和拓扑学中的许多重要问题都可以归结为理解某个无限几何对象的无限对称群。