‘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.
coast (as shown in pictures 1 & 2). The area of sea is subject to the
See Location Map of the coastline being studied from Herne Bay to Reculver.
While relaxing on the beach with Mrs. Ratignolle, the sight of the endless ocean brings back memories from Edna's childhood. She suddenly recalls a summer day in Kentucky and "a meadow that seemed as big as the ocean to the very little girl...and I felt as if I must walk on forever without coming to th...
Gull, John. The Oxford Illustrated History of Brittan. Great Brittan: Butler & Tanner Ltd, Frome, Somerset., 1984. Print.
United States v. Smiley, et al.. (n.d) retrieved February 17 2014, from NOAA Coastal Services Center Web Site: http://www.csc.noaa.gov/data/Documents/OceanLawSearch/U.S.v.Smiley_CaseSummary_PDF.pdf
Increased sea levels can give way to a variety of problems: rapid coastal erosion, shoreline change, loss of natural protective barriers, saltwater intrusion into aquifers and surface water, changes in tidal prisms (volume of water in an inlet between high tide and low tide), and rising water tables ("Climate Change and Impacts of Sea Level Rise"). Ventura County is facing many issues with rapid coastal erosion and loss of natural protective barriers. Beach Erosion Authority for Clean Oceans and Nourishment (BEACON) conducted a study to evaluate the conditions of different beaches along the Ventura County coast (Barlow, "Coastal Erosion Problems Highlighted in New Study"). Port Hueneme’s western beaches (picture to the left) are losing three to five inches per month due to sea level rise pushing beaches farther back.
Noggle, C. A., Dean, R. S., & Horton, A. M. (Eds.). (2012) The Encyclopedia of
Ed. Jay P. Pederson, Ph.D. 4th ed. of the book. New York: St. James Press, 1996. Goldfarb, Sheldon.
Rhys, Jean, and Judith L. Raiskin. "Wide Sargasso Sea." Wide Saragossa Sea: Backgrounds, Criticism. New York: W.W. Norton, 1998. 3-112. Print.
In being characterized with fractional dimensions, Fractals are considered to be a new division of math and art, which is perhaps why the common man recognizes them as nice-looking and appealing pictures that are valuable as background on computer screens and art patterns. But they are more meaningfully understood by way of the recognition that many of nature’s physical systems and a lot of human works of art are not standard geometry forms. Fractal geometry enables infinite methods of relating, evaluating and forecasting these kinds of natural phenomena. Simply said it’s a never ending pattern that repeats itself at different scales again and again. Thinking in patterns refers to fractals as “the approach to study roughness in both pure mathematics and in mathematical sciences of the real world (Novak 1).” Roughness is the idea that mathematics can measure obscure geometric patterns. This includes nature (turbulence, clusters of statistical physics, broken solids, art, finance, noises, and many more every day encounters). The issue that arises from the concept is whether it is possible to classify the entire world by making use of mathematical equations.
Ed. Lee A. Jacobus, Ph.D. 3rd ed. of the year. Boston: Bedford Books, 1996. 672-709. 2.
This followed from the work of Willebrord Snell in 1615–17, who showed how a point could be located from the angles subtended from three known points, but measured at the new unknown point rather than the previously fixed points, a problem calledresectioning. Surveying error is minimized if a mesh of triangles at the largest appropriate scale is established first. Points inside the triangles can all then be accurately located with reference to it. Such triangulation methods were used for accurate large-scale land surveying.
Statistic images and landscapes, or know as fractal landscapes, and the way that this component works is that these statistic images...
When the output was what is now called a fractal, no one called it artificial... Fractals suddenly broadened the realm in which understanding can be based on a plain physical basis. (McGuire, Foreword by Benoit Mandelbrot) A fractal is a geometric shape that is complex and detailed at every level of magnification, as well as self-similar. Self-similarity is something looking the same over all ranges of scale, meaning a small portion of a fractal can be viewed as a microcosm of the larger fractal. One of the simplest examples of a fractal is the snowflake.