Mathematics
Mathematics
Problem
A room is 6 m long, 4 m wide and 3 m high. Find the shortest length of a rope that can connect one lower corner of the room to the opposite upper corner.Intuitive explanation
The key is to imagine "unfolding" the room like a box—flattening it into a 2D net—so that the two corners lie on a plane where you can draw a straight line between them. The shortest path is that straight line, which you'll find using the Pythagorean theorem once you've chosen the right unfolding. Different ways of unfolding give different distances; you need to check a few and pick the smallest.
Intuitive explanation
The key is to imagine "unfolding" the room like a box—flattening it into a 2D net—so that the two corners lie on a plane where you can draw a straight line between them. The shortest path is that straight line, which you'll find using the Pythagorean theorem once you've chosen the right unfolding. Different ways of unfolding give different distances; you need to check a few and pick the smallest.