77. THE SPAIN – PORTUGAL BORDER

The graceful Algarve Bridge marks one of the border crossings between the countries of Spain and Portugal. The border between these two countries is of relatively recent mathematical interest. A Spanish encyclopedia claimed that the length of the border is 616 miles, while a Portuguese encyclopedia gave the figure of 758 miles. How do we explain this very large difference? Was someone guilty of sloppy work? And if so, who? In fact, it is not possible to give any meaningful determination of the length of most borders. For, measured length is determined by counting up the lengths of certain small measured line segments. And the smaller these line segments, the longer the length!

You might think of measuring the length of a stretch of coast line. Do you measure around the rocks? the pebbles? the grains of sand? We do seem to have a problem here!



http://en.wikipedia.org/wiki/How_Long_Is_the_Coast_of_Britain
%3F_Statistical_Self-Similarity_and_Fractional_Dimension