The spider and the fly
A great classical...
Usually they are in a parallelepipedic room, see The ant
Here they walk on an (empty) glass.
The fly is gently sipping the remaining drops inside the glass.
The spider is outside, and want the shortest path to catch her,
just walking on the glass.
Of course, the spider can walk "under" the glass.
And also the spider must obviously go through the edge in order to walk down inside the glass !
Let's say, the diameter of the glass is 6cm, the height is 8cm.
The fly is inside, at 1cm from the edge.
The spider, outside, at 2cm from edge and diametrally opposite to the fly.
Same question, but the glass is a cone with diameter 6cm and height 4cm.
The fly is still inside at 1cm from the edge (along the glass, not in altitude).
The spider, fully opposite, outside and at 2cm from the edge.
Distances from fly or spider to the edge still being along the glass,
hence curved (along a circle arc).