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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
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)reply
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)reply
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)reply
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)reply
Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a
transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the
current reference desk pages.
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
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)reply
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)reply
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)reply
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)reply