Coastline paradox


Coastline paradox
An example of the coastline paradox. If the coastline of Great Britain is measured using fractal units 100 km (62 mi) long, then the length of the coastline is approximately 2,800 km (1,700 mi). With 50 km (31 mi) units, the total length is approximately 3,400 km (2,100 mi), approximately 600 km (370 mi) longer.

The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. This results from the fractal-like properties of coastlines.[1][2] It was first observed by Lewis Fry Richardson.

More concretely, the length of the coastline depends on the method used to measure it. Since a landmass has features at all scales, from hundreds of kilometers in size to tiny fractions of a millimeter and below, there is no obvious limit to the size of the smallest feature that should not be measured around, and hence no single well-defined perimeter to the landmass. Various approximations exist when specific assumptions are made about minimum feature size.

For practical considerations, an appropriate choice of minimum feature size is on the order of the units being used to measure. If a coastline is measured in kilometers, then small variations much smaller than one kilometer are easily ignored. To measure the coastline in centimeters, tiny variations of the size of centimeters must be considered. However, at scales on the order of centimeters various arbitrary and non-fractal assumptions must be made, such as where an estuary joins the sea, or where in a broad tidal flat the coastline measurements ought to be taken.

Extreme cases of the coastline paradox include the fjord-heavy coastlines of Norway, Chile and the Pacific Northwest of North America. From the southern tip of Vancouver Island northwards to the southern tip of the Alaska Panhandle, the convolutions of the coastline of the Canadian province of British Columbia make it over 10% of the entire Canadian coastline—25,725 km (15,985 mi) vs 243,042 km (151,019 mi)[clarification needed] over a linear distance of only 965 km (600 mi), including the maze of islands of the Arctic archipelago.[3]

See also

Notes

  1. ^ Weisstein, Eric W., "Coastline Paradox" from MathWorld.
  2. ^ Mandelbrot, Benoit (1983). The Fractal Geometry of Nature. W.H. Freeman and Co.. 25–33. ISBN 978-0-7167-1186-5. 
  3. ^ Sebert, L.M., and M. R. Munro. 1972. Dimensions and Areas of Maps of the National Topographic System of Canada. Technical Report 72-1. Ottawa: Department of Energy, Mines and Resources, Surveys and Mapping Branch.

External links


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Coastline of the United Kingdom — For the problem in fractal geometry, see How Long Is the Coast of Britain?. Bedruthan Steps, North Cornwall, A spectacular section of the UK coastline, managed by the National Trust. The coastline of the United Kingdom is long in comparison to… …   Wikipedia

  • Sorites paradox — The Sorites paradox ( σωρός ( sōros ) being Greek for heap and σωρίτης ( sōritēs ) the adjective) is a paradox that arises from vague predicates. The paradox of the heap is an example of this paradox which arises when one considers a heap of sand …   Wikipedia

  • List of U.S. states by coastline — This is a list of U.S. states having an ocean coastline, ranked by coastline length. The data was retrieved from a CRS Report for Congress [ [http://www.fas.org/sgp/crs/misc/RS21729.pdf] CRS Report for Congress] using data from U.S. Department of …   Wikipedia

  • Artemis Fowl: The Time Paradox — The Time Paradox redirects here. For the time travel paradox, see Temporal paradox. Artemis Fowl and the Time Paradox   …   Wikipedia

  • List of paradoxes — This is a list of paradoxes, grouped thematically. Note that many of the listed paradoxes have a clear resolution see Quine s Classification of Paradoxes.Logical, non mathematical* Paradox of entailment: Inconsistent premises always make an… …   Wikipedia

  • Список парадоксов — …   Википедия

  • List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia

  • Great Lakes — This article is about the Great Lakes of North America. For the region, see Great Lakes region (North America). For other uses of this term, see Great Lakes (disambiguation). A rare cloudless satellite view of the entire Great Lakes region, April …   Wikipedia

  • Coral reef — Marine habitats Biodiversity of a coral reef Lit …   Wikipedia

  • United States — a republic in the N Western Hemisphere comprising 48 conterminous states, the District of Columbia, and Alaska in North America, and Hawaii in the N Pacific. 267,954,767; conterminous United States, 3,022,387 sq. mi. (7,827,982 sq. km); with… …   Universalium


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.