A spider is sitting in the middle of one of the smallest walls in my living room, and a fly is resting by the side of the window on the opposite wall, \(\quantity{2}{m}\) above the floor and \(\quantity{0.5}{m}\) from the adjacent wall.

The room is \(\quantity{8}{m}\) long, \(\quantity{4}{m}\) wide and \(\quantity{3}{m}\) high.

What is the shortest distance the spider could crawl to reach the fly?

Do check your numerical answer before you look at the full solution to this problem!

The shortest possible distance is \(\quantity{10.44}{m}\) (to the nearest centimetre).

If your answer is \(\quantity{10.51}{m}\) or \(\quantity{10.61}{m}\), then have a look at Suggestion 4.

What is the shortest path between two points in the same plane?

Can you apply the same sort of reasoning to find some potential candidates for the shortest distance between the spider and the fly for this problem?

Can you think of any way of “flattening” the room to make the shortest distance between the spider and the fly easier to compute?

What different ways can you find to “flatten” the room? Do all of them give the same “shortest distance”?

You have probably “flattened” the room in one of these ways:

This gives two good nets for the room. But can you find a way of combining these nets to get an even better net?