图 书 馆
你能用相同的瓷砖铺设飞机吗？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。很多人都知道相同的正六边形也可以正确地平铺平面。事实上，即使是蜜蜂也知道并使用这个事实！是否有任何其他凸域可以平铺欧几里得平面？当然，他们的名单很长！查找列表并显示列表的完整性是数学上的一出独特的戏剧，持续了一个多世纪，并且列表的完整性被错误地宣布了不止一次！截至目前，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 宣布了列表完整性的计算机证明。与此同时，齐扬和传明宗在欧氏平面的多重平铺中，有了一系列意想不到的发现。例如，除了平行四边形和中心对称六边形之外，没有其他凸域可以在平面内形成任何二、三或四折平移平铺。然而，有两种类型的八边形和一种类型的十边形可以形成非平凡的五折平移平铺。此外，凸域可以形成平面的五重平移平铺，当且仅当它可以形成五重格子平铺。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: | 凸域; 欧几里得平面; 五重格子 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2021-06-04：yumf |
| 最后编审: | 2021-06-04：yumf |
| 阅读次数: | 39 |