form of the Hausdorff dimension, later the fractal dimension. Rearranging the expression yields where Fε−D must be the number of units ε required to obtain L. The broken line measuring a coast does not extend in one direction nor does it represent an area, but is intermediate between the two and can be thought of as a band of width 2ε. D is its fractal dimension, ranging between 1 and 2 (and typically less than 1.5). More broken coastlines have greater D, and therefore L is longer for the same ε. D is approximately 1.02 for the coastline of South Africa, and approximately 1.25 for the west coast of Great Britain. For lake shorelines, the typical value of D is 1.28. Mandelbrot showed that D is independent of ε. See also Alaska boundary dispute – Alaskan and Canadian claims to the Alaskan Panhandle differed greatly, based on competing interpretations of the ambiguous phrase setting the border at "a line parallel to the windings of the coast", applied to the fjord-dense region. Fractal dimension Gabriel's Horn, a geometric figure with infinite surface area but finite volume "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", a paper by Benoît Mandelbrot Paradox of the heap Zeno's paradoxes References Citations Sources Post, David G., and Michael Eisen. "How Long is the Coastline of Law? Thoughts on the Fractal Nature of Legal Systems". Journal of Legal Studies XXIX(1), January 2000. External links "Coastlines" at Fractal Geometry (ed. Michael Frame, Benoit Mandelbrot, and Nial Neger; maintained for Math 190a at Yale University) The Atlas of Canada – Coastline and Shoreline NOAA GeoZone Blog on Digital Coast What Is The Coastline Paradox? – YouTube video by Veritasium The Coastline Paradox Explained – YouTube video by RealLifeLore Paradoxes Coasts Cartography Topography Fractals Coastal geography Problems in spatial analysis