立方体上的最短路径
Shortest Paths on Cubes
摘要：
1903年，着名的谜题制作者亨利·杜德尼（Henry Dudeney）出版了蜘蛛和苍蝇谜题，要求在正方形面上的两个点（源点和目标点）之间沿着正方形棱柱表面的最短路径，令人惊讶的是，最短路径穿过五个面。Dudeney的源点和目标点的位置非常对称;在本文中，我们允许源点和目标点位于相对面内部的任何位置，但现在要求正方形棱柱是立方体。在这种情况下，我们发现，根据源和目标的位置，最短路径可以穿过三个或四个面，我们调查的条件，导致四面的解决方案和估计的概率得到四面最短路径。我们利用组合的数值计算，初等几何，和变换，我们称之为角移动的立方体展开图，
英文摘要：
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,
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
