Students' Contributions: The Coastline Paradox (by 9B Angela Tien)

A coastline paradox is an observation based on intuition that landmasses/coastlines are not measured accurately. This proposition was first contemplated by L. F. Richardson (1881-1953). He thought that determining the length of a country’s coastline does not have a well defined length. In fact, he stated that the answer to the length of a coastline depends entirely upon the method used to measure it. Since landmasses can be shrunk down to any possible scale, there is no minimum scale. Any scale can be dwindled into a scale so incredibly small in measurements that it is almost impossible to measure. Therefore Richardson introduced a practical cogitation.

The order of the units being used to measure is the cogitation that Richardson has acknowledged. He affirmed that certain coastlines which are measured in miles, have measurements that ignored small variations less than a mile. Since the fjord is made up of many of the small variations, the scale of a fjord would be far from precise. When one use a ruler of a smaller length, the length of the actual border of the landmass increases. While, longer rulers diminish the more accurate length of the border, Richardson concluded that the smaller the units the border is measures in, the longer (precise) the border is.

Coastline paradoxes are also fractals. A fractal is an object or quantity that displays self-similarity (See textbook p. 590-591 --Mr. Ip). The curves of the coastline of a landmass would be similar to that of a Koch Snowflake. It is said that these curves have a dimension of either 1 or 2. Because the whole purpose of scales is to have the same measurement of the actual border as the scale, both would be a fractal since they’re similar.

It is impossible to actually measure the most precise length of any border because some even consider measuring atoms as well.