Jheri sent this bit from Copenhagen Cycle Chic on Pedersen bikes.
I've only seen a few and have never riden one. A design by a Dane living in England, the idea was to concentrate on a comfortable riding experience. The original company went out of business, but in the late 70s they began to reappear. A bit more detail as well as framesizing for the interested here. And of course the wikipedia entry...
I suspect you would want to try one, but there would be a good chance you could go for a long time before seeing another in most areas.
(the photo is from the wikipedia entry and is of an example made in 1910)