Can a panorama be square?

River, originally uploaded by jiihaa.

I took several photos of this river view, from a bridge, trying out different compositions. None was really good. Then I decided to try out PTGui to join together two horizontal photos into a larger square one. Although this isn't perfect either, it is better than the others.

This was a case where the 24 mm wide lens of the Panasonic LX3 was not enough to capture the view as needed. Even wider lens would have been nice to have. Or a square aspect ratio in the camera in addition to the existing 4:3, 3:2 and 16:9.