Wikipedia:Reference desk/Archives/Mathematics/2015 January 20

= January 20 =

What is % of world coastline represent?
This wikipedia page (List_of_countries_by_length_of_coastline) says that Coast/area ratio(m/km²) of the world is 7.80. How would this be represented in percentage??

What % of the world is coastline?201.78.192.174 (talk) 11:57, 20 January 2015 (UTC)
 * The units are at the top of the column; m/(km^2). -- Q Chris (talk) 12:14, 20 January 2015 (UTC)
 * Which means that you can't represent it as a percentage. A percentage is a ratio of two quantities of the same type.  Rojomoke (talk) 12:52, 20 January 2015 (UTC)
 * You could just change the meters to km. Or not??201.78.192.174 (talk) 12:56, 20 January 2015 (UTC)


 * It's not a percentage, or cannot be converted into one, as you're comparing two things, length in metres and area in square kilometres. To make it a percentage you can add an extra dimension.


 * E.g. assume the coast is 100m wide, so it has an area length * 100m. Taking the ratio of 7.8, that's 7.8 metres [per sq km]. So for every square km (1 000 000 sq m) there's 7.8 x 100 = 780 sq m. This gives


 * 780 / 1 000 000 = 0.00078 = 0.078%
 * -- JohnBlackburne wordsdeeds 12:57, 20 January 2015 (UTC)
 * But inst X squared km, just X * X km?201.78.192.174 (talk) 13:05, 20 January 2015 (UTC)


 * No, X square km is an area of X squares 1km by 1km. On the other hand, X km squared is an area measure of a square X km by X km, which makes X2 square kilometers. --CiaPan (talk) 13:57, 20 January 2015 (UTC)


 * Note that the length of the coastline is always indeterminate, as each coastline has a different length, depending on how closely it is examined. See coastline paradox.  Therefore, the ratio of that number to any other is also meaningless. StuRat (talk) 14:44, 20 January 2015 (UTC)


 * Since this is the Maths desk I should probably point out that dimensional analysis is (i.e. "you cannot compare km to km2") is not necessarily the right concept here, but measure theory is. The (2d) measure of a one dimensional object (like the coastline) is zero, so the ratio mu(costline)/mu(all land) is zero. I.e. coastline is 0% of all land. Now as StuRat has pointed out people argue that the costline has length (i.e. 1d measure) infinity. In this setup the coastline is really a fractal, that is it has (or can be assigned) a dimension d, with 1<d<2. Googling gives estimates of the dimension of coastlines between d=1.25 and d=1.5 (Norway). In any case the 2-d measure of a 1.5-dimensional object is still zero, so the result remains that the coastline is 0% of all land. 86.177.229.70 (talk) 23:55, 20 January 2015 (UTC)


 * If the coastline length were well defined, we could say that the ratio of land area to coastline is N km. For an intuitive sense of what this means, imagine a planet that has the same land area and the same coastline length, but where all the land is in strips running around lines of latitude; the ratio is half the average width of the strips. —Tamfang (talk) 08:48, 21 January 2015 (UTC)