论文标题
2D Rubik的形状的完整性
The Completeness of 2D Rubik's Shapes
论文作者
论文摘要
Erno Rubik于1974年发明了Rubik的立方体，他对玩具会带来的令人难以置信的受欢迎程度和数学迷人不知道。通过对立方体数学特性的多年研究，引入了Rubik的立方体组，以代表一个人可以在立方体上执行的所有可能的动作。在本文中，我们定义了一个平面的类似物，该平面类似物是我们配音rubik的正方形的，并证明了Rubik的正方形是完整的，因为鉴于任何两种配置，都有一系列动作，将一个移动变化为另一个。魔方没有此属性。然后，我们将Rubik正方形的概念抽象成魔术片的形状，并在此更一般的环境中分析完整性。
The Rubik's cube was invented in 1974 by Erno Rubik, who had no idea of the incredible popularity and mathematical fascinations his toy would bring. Through the years of study on the mathematical properties of the cube, the Rubik's Cube group was introduced to represent all possible moves one could perform on the cube. In this paper, we define a planar analogue to the Rubik's cube, which we dub the Rubik's Square, and prove that the Rubik's square is complete in the sense that given any two configurations there is a sequence of moves which changes one to the other. The Rubik's cube does not have this property. We then abstract the concept of the Rubik's Square to a Rubik's Shape and analyse the completeness in this more general setting.
