【手を動かしてまなぶ】結晶・文様と平面結晶群【原隆先生『手を動かしてまなぶ　群論』特別講義《後編》】

Why not enjoy modern mathematics in your spare time? This is a special video from the "Learning by Doing" series. Video appearance: Professor Takashi Hara (Associate Professor, Department of Mathematics, Faculty of Liberal Arts, Tsuda University) Video shooting and editing: Yobinori Yasu Book editing: Kume Taro (Shokabo Planning and Editorial Department) ■ Takashi Hara, "Learning Group Theory by Doing" (Shokabo) https://www.shokabo.co.jp/mybooks/ISB... ■ Links to materials related to this video Classification of patterns into 17 types (Archived by Professor Tsuboi Shun on the Urabe Tosuke Laboratory webpage) https://www.ms.u-tokyo.ac.jp/~tsuboi/... ■ Message from the Book Editor "We asked Professor Hara to discuss topics related to 'Learning Group Theory Through Hands-on Activities,' in a way that even beginners would find insightful." However, Professor Hara's suggestions were completely unexpected. One topic was the marriage laws of minority groups.    • 【手を動かしてまなぶ】少数民族の婚姻法則に潜む群論【原隆先生『手を動かしてまなぶ　群...   The other was the group theory underlying crystals and patterns. Initially, we planned to film only one of these topics. However, both topics were equally compelling! We decided to film both. If you watch Professor Hara's message at the end of this video, you will understand exactly why we study group theory. -------------------------------------------- [Video Table of Contents] 00:00 Professor Hara Takashi (again) appears 00:24 Symmetry of Plane Figures - Dihedral Groups of Order 10 01:59 What are Plane Crystal Groups and Pattern Groups? 03:52 Examples: Seigaiha, Kumi-kikko, Shippo-tsunagi 08:20 Symmetries have "names" 09:40 There are 17 types of Plane Crystal Groups 11:26 One idea for proof - Classifying quotient set spaces 13:00 Considering subgroups consisting of translations within Plane Crystal Groups 15:08 Orbital Manifolds, named by mathematician Thurston 18:05 Discrete Infinite Groups are compatible with geometry [Reference: "Learning Group Theory by Doing" p.155 Nielsen-Schreier Theorem] 19:34 Penrose Tiling 22:27 Discovery of Einstein Tiles (around 2023) 25:23 Summary — Why Study Group Theory? 29:03 Epilogue -------------------------------------------- ■ Professor Takashi Hara's Profile Associate Professor, Department of Mathematics, Faculty of Liberal Arts, Tsuda University PhD in Mathematical Sciences, University of Tokyo Specializes in number theory and arithmetic geometry (especially non-commutative Iwasawa theory) Born in Hyogo Prefecture in 1983 Graduated from Azabu High School (private) in 2002 Graduated from the Department of Mathematics, Faculty of Science, University of Tokyo in 2006 Completed the doctoral program in Mathematical Sciences, Graduate School of Mathematical Sciences, University of Tokyo in 2011 Assistant Professor, Department of Mathematics, Faculty of Future Science, Tokyo Denki University in 2014 Associate Professor, Department of Mathematics, Faculty of Liberal Arts, Tsuda University in 2019 ■ Shokabo, a publisher of natural science books Shokabo primarily publishes textbooks and reference books in mathematics, physics, chemistry, and biology for universities, junior colleges, and technical colleges. We aim to create high-quality books that will be appreciated by our readers. Shokabo Official Website https://www.shokabo.co.jp/ Shokabo Editorial Department Official X (formerly Twitter) https://x.com/shokabo_editors?s=20