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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=594205
• 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。最基本、最基本的图案类型是对称。有有限的对称“群”，如由立方体的48个不同对称组成的群，也有无限的对称群，如欧几里得平面的平方平铺的对称群。虽然对称的有限群可以很好地理解，但一些无限群是如此复杂，以至于它们显然是不可能理解的。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些无限几何对象的无限对称组。