Y by goodbear, Adventure10, Mango247
Let be a connected region in the plane. Suppose that the cop is a segment of length and the robber is a segment of length .
The cop starts inside (so we assume that a segment of length fits somewhere inside ), as does the robber. Based on , , , and the initial positions, does the cop catch the robber if both use optimal play?
A good place to start might be regions where all sides are parallel to the coordinate axes.
How does the result change if the cop and robber are circles or squares instead of segments?
What if the game is played inside connected regions in space?
The cop starts inside (so we assume that a segment of length fits somewhere inside ), as does the robber. Based on , , , and the initial positions, does the cop catch the robber if both use optimal play?
A good place to start might be regions where all sides are parallel to the coordinate axes.
How does the result change if the cop and robber are circles or squares instead of segments?
What if the game is played inside connected regions in space?