As all fans of fractal geometries
know, St. Benoit Mandelbrot
wrote a seminal paper in 1967
which appeared in Science
under the title "How long is the
coast of Britain? Statistical
Self-similarity and Fractional
Dimension". Undaunted by the
problem that the length of a
coastline depends on the scale
of the measurement, there have
been more or less accepted
estimates of coastlines
published. Since the length of
the coastline of a landlocked
country is zero (Uzbekistan,
despite being doubly landlocked
is also just zero) a contrived
measure is formed by dividing
coast line by area. Well into the
sixteenth century
mathematicians since
Archimedes and probably well
before had struggled with four
problems. For a general curve,
what is the tangent at a point;
what is the area under the
curve, what is the length of a
curve and what are the
minimum and maximum.
know, St. Benoit Mandelbrot
wrote a seminal paper in 1967
which appeared in Science
under the title "How long is the
coast of Britain? Statistical
Self-similarity and Fractional
Dimension". Undaunted by the
problem that the length of a
coastline depends on the scale
of the measurement, there have
been more or less accepted
estimates of coastlines
published. Since the length of
the coastline of a landlocked
country is zero (Uzbekistan,
despite being doubly landlocked
is also just zero) a contrived
measure is formed by dividing
coast line by area. Well into the
sixteenth century
mathematicians since
Archimedes and probably well
before had struggled with four
problems. For a general curve,
what is the tangent at a point;
what is the area under the
curve, what is the length of a
curve and what are the
minimum and maximum.
Except for gain or loss of territory, there is little a country can do
about its ratio. Nor does the ratio really indicate potential
economic damage from a tsunami.
about its ratio. Nor does the ratio really indicate potential
economic damage from a tsunami.