Topic > How Long Is Britain's Coastline? - 962

'Only a truly 'accurate' measurement of the length of the coastline - any coastline - shows that it is almost infinitely long.'[1]Britain's coastline is difficult to measure due to methods to measure them. This report will attempt to find the length of the British coastline using two different methods and will discuss the advantages and disadvantages of each method. One method that provides a brief description of the length of a coast would be to examine maps of various scales. The result would be smaller scale maps leading to shorter coast lengths and larger scale maps, longer coast lengths. This is called the coastline paradox: a term founded by English mathematician Lewis Fry Richardson and means that the larger the map scale used, the longer the coastline is measured. This is because the more a map is zoomed in, the finer the details of a place's boundary will be captured. The results would be the same if you physically measured a coastline, but the idea that tides are constantly changing and waves are breaking, so where the sea meets the land is unclear, also makes physically measuring a coastline difficult. Coasts are considered fractals. A fractal is an image containing self-similarity that is described as something that is exactly or similar to a part of itself [5]. They usually have complex details at each scale and are difficult to measure when shaped like a coast, so finding the dimension of a fractal is necessary. This would delineate whether the length of a fractal is at least finite, infinite, or zero. The problem is that the dimension of a fractal is never an integer, however a method known as box dimension helps solve this problem. The method consists... in the middle of the paper... in the scale on which you measure it [6]. Or in other words the coast is infinitely long. Works Cited[1] [6] Darkes, G., 2008. The British Cartographic Society. How long is the coastline of the UK? http://www.cartography.org.uk/default.asp?contentID=749. Accessed: 04/21/14.[2] Fractalfoundation.org, 2014. Online course on the Fractal Foundation - Chapter 1 - FRACTALS IN NATURE. http://fractalfoundation.org/OFC/OFC-10-4.html. Accessed 04/21/14.[3] Lippman, D. and Rasmussen, M., 2014. Active Textbook | Sample textbook 3. Activetextbook.com. http://www.activetextbook.com/active_textbooks/563#page. Accessed 04/21/14.[4] Wikipedia, 2014. Minkowski-Bouligand dimension. http://en.wikipedia.org/wiki/Minkowski-Bouligand_dimension. Accessed 04/21/14.[5] Wikipedia. Self-similarity. http://en.wikipedia.org/wiki/self-similarity. Logged in: 21/04/2014.