Brandon Kohn wrote:
I think failing to compile would be the most reasonable. I cannot think of any reasonable use-case where one would want the area of a point, or a line. I suspect the most often encountered case would be that the user has made a logic-error. The same applies to volume (or any integral quantity which is a function of dimension). I would suggest that area would require a 2D concept and that the shape of the object be at minimum a 2-simplex (triangle.. possibly degenerate).
Shapes, volumes, etc. are sets of points. Various sets have a null area. This is perfectly valid and is not a logic error. Points (a point is just a set of points which one element) and lines have zero area, this is common knowledge. This is even stated in the definition on "area" on wikipedia, for example.