They pace because they live in a concrete hellhole that is undoubtedly past its prime. The good news is that some zoos are beginning to plant this new-fangled substance called "grass" in their polar bear exhibits, although Detroit's "Arctic Ring of Life" (built in 2001) is still the #1 habitat of its kind in North America.
Detroit's one is amazing but a closer zoo with a fine new exhibit is Philadelphia, they should take over these two until a new exhibit has been completed.
It's so sad to watch pacing bears in places like this. It's my abiding memory (as a child) of London Zoo in the 70s where the bear exhibits looked very similar.
@ Geomorph, your statement is ironic because the male polar bear came from the Detroit Zoo. However, I think he was only here for a couple of years before he died.