蚂蚁之旅
Ant Journey
题目详情
一只蚂蚁坐在单位立方体的一个角落，希望走到离它最远的角落。蚂蚁为了达到目标必须行进的最短距离是多少？请注意，蚂蚁必须始终与表面接触并且不能飞行。
An ant sits at one corner of a unit cube, wishing to travel to the corner farthest from it. What is the minimal distance the ant must travel to achieve its goal? Note that the ant must always be in contact with a surface and cannot fly.
解析
为了解决这个问题，想象一下你将 3D 立方体展平为二维表面。立方体看起来如下：
$\def\arraystretch{1.5} \begin{array}{c:c:c} && \ \hdashline &&\ \hdashline && \end{array}$
从立方体的任意角到距它最远的角的路径是一条直线。该路径是边长为 1 和 2 的三角形的斜边。因此最长路径的长度为
Original Explanation
To solve this question imagine that you flattened the 3D cube to a two-dimensional surface. The cube would look as follows:
$\def\arraystretch{1.5} \begin{array}{c:c:c} & & \ \hdashline & & \ \hdashline & & \end{array}$
The path from any corner of the cube to the corner furthest from it is a straight line. The path is the hypotenuse of a triangle with side lengths of 1 and 2. Thus the length of the longest path is