图 书 馆
你能用相同的瓷砖铺飞机吗？Can you pave the plane with identical tiles? |
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| 课程网址: | http://videolectures.net/FPSAC2019_zong_identical_tiles/ |
| 主讲教师: | Chuánmíng Zōng |
| 开课单位: | 天津大学 |
| 开课时间: | 2019-07-19 |
| 课程语种: | 英语 |
| 中文简介: |  每个人都知道，相同的正三角形或正方形可以平铺整个平面。许多人知道相同的正六边形也可以正确地平铺平面。实际上，即使蜜蜂也知道并使用这个事实！还有其他可以平铺欧几里得平面的凸域吗？当然，它们的清单很长！查找列表并显示列表的完整性是一个独特的数学戏剧，它持续了一个多世纪，而且列表的完整性被错误地宣布了一次！到目前为止，该列表由三角形，四边形，十五种五边形和三种六边形组成。 2017年，Michael Rao宣布了一份清单完整的计算机证明。同时，祁琦和宗传明在欧几里得平面上的多个平铺中发现了一系列意外发现。例如，除了平行四边形和中心对称的六边形外，没有其他凸形域可以在平面中形成任何两，三或四折的平铺图块。但是，有八种八边形和一种八边形可以形成不平凡的五折平铺图块。此外，当且仅当凸畴可以形成五重晶格平铺时，才能形成该平面的五倍平铺平铺。在本次演讲中，我们将报告这些进展。 |
| 课程简介: | Everybody knows that identical regular triangles or squares can tile the whole plane. Many people know that identical regular hexagons can tile the plane properly as well. In fact, even the bees know and use this fact! Is there any other convex domain which can tile the Euclidean plane? Of course, there is a long list of them! To find the list and to show the completeness of the list is a unique drama in mathematics, which has lasted for more than one century and the completeness of the list has been mistakenly announced not only once! Up to now, the list consists of triangles, quadrilaterals, fifteen types of pentagons, and three types of hexagons. In 2017, Michael Rao announced a computer proof for the completeness of the list. Meanwhile, Qi Yang and Chuanming Zong made a series of unexpected discoveries in multiple tilings in the Euclidean plane. For examples, besides parallelograms and centrally symmetric hexagons, there is no other convex domain which can form any two-, three- or four-fold translative tiling in the plane. However, there are two types of octagons and one type of decagons which can form nontrivial five-fold translative tilings. Furthermore, a convex domain can form a five-fold translative tiling of the plane if and only if it can form a five-fold lattice tiling. In this talk we will report these progresses. |
| 关 键 词: | 欧几里得平面; 数学戏剧; 平铺图块 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2020-11-29：cjy |
| 最后编审: | 2020-11-29：cjy |
| 阅读次数: | 39 |