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Beyond its application to distance comparison, squared Euclidean distance is of central importance in statistics, where it is used in the method of least squares, a standard method of fitting statistical estimates to data by minimizing the average of the squared distances between observed and estimated values, [17] and as the simplest form of ...
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...
To keep the projection conformal, the projection increases the displayed distance between lines of latitude (north–south distances) in proportion; thus a square is shown as a square everywhere on the chart, but a square on the Arctic Circle appears much bigger than a square of the same size at the equator.
A nautical mile is a unit of length used in air, marine, and space navigation, and for the definition of territorial waters. [2] [3] [4] Historically, it was defined as the meridian arc length corresponding to one minute ( 1 / 60 of a degree) of latitude at the equator, so that Earth's polar circumference is very near to 21,600 nautical miles (that is 60 minutes × 360 degrees).
Empirical evidence suggests that the smaller the increment of measurement, the longer the measured length becomes. If one were to measure a stretch of coastline with a yardstick, one would get a shorter result than if the same stretch were measured with a 1-foot (30 cm) ruler. This is because one would be laying the ruler along a more ...
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In addition to coastline lengths, this is the source of the land area used to calculate the "coast/area ratio" for both TWF and WRI (see below) coastline measurement. This ratio measures how many metres of coastline correspond to every square kilometer of land area. The ratio illustrates the ease of accessibility to the country's coast from ...