How Long Is the Coastline of Great Britain?

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‘Only truly ‘accurate’ measure of the length of the coastline — any coastline — shows that it is almost infinitely long.’[1]
The coastline of Great Britain is difficult to measure because of the methods of measuring them. This report will attempt to find the length of Britain’s coastline using two different methods and discuss the advantages and disadvantages of each method.
One method that gives a brief outline of a coastline’s length would be looking at maps of various scales. The result of this would be smaller scale maps resulting in shorter coastline lengths and larger scale maps, longer coastline lengths. This is called the coastline paradox: a term founded by English mathematician Lewis Fry Richardson and means that the larger the scale of map used, the longer the measured coastline length is. This is because the greater a map is enlarged, the finer the details captured of a place’s border. The results would be the same if measuring a coastline physically but also the idea that tides are constantly changing and waves are breaking so the point of where sea meets land is unclear also makes physically measuring a coastline difficult.
Coastlines are considered to be fractals. A fractal is an image that contains self-similarity which is described as something that is exactly or similar to a part of itself [5]. They usually have complex detail at every scale and are difficult to measure when in the shape of a coastline therefore a fractal’s dimension should be found. This would outline whether a fractal’s length is at least finite, infinite or zero. The problem being that a fractal’s dimension is never a whole number however a method known as the box dimension helps solve this. The method consist...

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...e scale at which you measure it [6]. Or in other words the coastline is infinitely long.

Works Cited

[1][6] Darkes, G., 2008. The British Cartographic Society. How long is the UK coastline?.http://www.cartography.org.uk/default.asp?contentID=749. Accessed: 21/04/14.
[2] Fractalfoundation.org, 2014. Fractal Foundation Online Course - Chapter 1 - FRACTALS IN NATURE. http://fractalfoundation.org/OFC/OFC-10-4.html. Accessed 21/04/14.
[3] Lippman, D. and Rasmussen, M., 2014. Active Textbook | Sample Textbook 3. Activetextbook.com. http://www.activetextbook.com/active_textbooks/563#page. Accessed 21/04/14.
[4] Wikipedia, 2014. Minkowski–Bouligand dimension. http://en.wikipedia.org/wiki/Minkowski-Bouligand_dimension. Accessed 21/04/14.
[5] Wikipedia. Self-similarity. http://en.wikipedia.org/wiki/self-similarity. Accessed: 21/04/2014.
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