论文标题
立方体上的最短路径
Shortest Paths on Cubes
论文作者
论文摘要
1903年，著名的拼图制造商亨利·达德尼（Henry Dudeney）出版了《蜘蛛和蝇拼》，该拼图要求沿着正方形面孔的两个点（源和目标）之间的正方形棱镜表面的最短路径，令人惊讶地表明，最短的路径遍历了五个脸。 Dudeney的来源和目标点具有非常对称的位置。在本文中，我们允许源和目标点在相对面的内部任何地方，但现在要求方形棱镜成为立方体。在这种情况下，我们发现，根据源和目标位置，最短的路径可以穿越三到四个面，并且我们研究导致四面溶液的条件，并估算获得最短四面路径的概率。我们利用数值计算，基本几何形状和转换的组合，我们称之为立方体的角移动图，
In 1903, noted puzzle-maker Henry Dudeney published The Spider and the Fly puzzle, which asks for the shortest path along the surfaces of a square prism between two points (source and target) located on the square faces, and surprisingly showed that the shortest path traverses five faces. Dudeney's source and target points had very symmetrical locations; in this article, we allow the source and target points to be anywhere in the interior of opposite faces, but now require the square prism to be a cube. In this context, we find that, depending on source and target locations, a shortest path can traverse either three or four faces, and we investigate the conditions that lead to four-face solutions and estimate the probability of getting a four-face shortest path. We utilize a combination of numerical calculations, elementary geometry, and transformations we call corner moves of cube unfolding diagrams,
