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The distributions of a wide variety of physical, biological, and human-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, [2] cloud sizes, [3] the foraging pattern of various species, [4] the sizes of activity patterns of neuronal populations, [5] the frequencies of words in most languages ...
Old decimal balance scale A drawing to illustrate a design with two-point support of the platform. A decimal balance or decimal scale is a balance scale which uses the lever in which the arm for weights is 10 times longer than the arm for weighted objects, so that much lighter weights may be used to weigh heavy object. [1]
Examples include temperature scales with the Celsius scale, which has two defined points (the freezing and boiling point of water at specific conditions) and then separated into 100 intervals, date when measured from an arbitrary epoch (such as AD), location in Cartesian coordinates, and direction measured in degrees from true or magnetic north.
Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. On the number line, the distance between two points is the unit length if and only if the difference of the represented numbers equals 1. Other choices are possible.
It is a convenient unit for long-term measurements. For example, oceans appeared on Earth after 4 GY, life is detectable at 5 GY, and multicellular organisms first appeared at 15 GY. The age of the Earth is estimated at 20 GY. [74] This use of GY is not to be confused with Gyr for gigayear or Gy for Gray (unit).
A graphical or bar scale. A map would also usually give its scale numerically ("1:50,000", for instance, means that one cm on the map represents 50,000cm of real space, which is 500 meters) A bar scale with the nominal scale expressed as "1:600 000", meaning 1 cm on the map corresponds to 600,000 cm=6 km on the ground.
For any point x in a metric space M and any real number r > 0, the open ball of radius r around x is defined to be the set of points that are strictly less than distance r from x: = {: (,) <}. This is a natural way to define a set of points that are relatively close to x .
For example, both the old Celsius scale and Fahrenheit scale were originally based on the linear expansion of a narrow mercury column within a limited range of temperature, [4] each using different reference points and scale increments. Different empirical scales may not be compatible with each other, except for small regions of temperature ...