What is the surface area of Norway?

Answer 1

That would depend on the precision of the instrument that you measure it with. Theoretically, the area of Norway is infinite.

Not so. Because of the fractal nature of a coastline the length of a coastline may be calculated to be infinite, but this infinity can not be extended to an area. The proof is simple.

Construct a rectangle 3,000 km long by 1,000 km wide. This will have an area of 3,000,000 km2. The whole of Norway will fit inside the rectangle, therefore the area of Norway is less than 3,000,000 km2 and is not infinite.

By joining pairs of points on the rectangle while taking care never to cross the coastline you can lower the upper bound to a great extent. By adding more and more lines that do not cross the coastline you can measure the upper bound to the area with as much precision as you like.

If you construct a geometrical area small enough to be contained inside the country, you can then run the process described above in reverse; this will give a lower bound to the area. As you draw more and more lines the upper and lower bounds to the area get closer and closer together.

Once the uncertainty is measured in a few mal spread over all of Norway, the question of attainable precision becomes an exercise in nit-picking.