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In geometry, visibility is a mathematical abstraction of the real-life notion of visibility.. Given a set of obstacles in the Euclidean space, two points in the space are said to be visible to each other, if the line segment that joins them does not intersect any obstacles.
The international definition of fog is a visibility of less than 1 km (3,300 ft); mist is a visibility of between 1 km (0.62 mi) and 2 km (1.2 mi) and haze from 2 km (1.2 mi) to 5 km (3.1 mi). Fog and mist are generally assumed to be composed principally of water droplets, haze and smoke can be of smaller particle size.
Early in World War II, target range and bearing measurements were taken over a period of time and plotted manually on a chart. [14] The speed and course of the target could be computed using the distance the target traveled over an interval of time. During the latter part of World War II, the speed of the target could be measured using radar data.
For example, for an observer B with a height of h B =1.70 m standing on the ground, the horizon is D B =4.65 km away. For a tower with a height of h L =100 m, the horizon distance is D L =35.7 km. Thus an observer on a beach can see the top of the tower as long as it is not more than D BL =40.35 km away.
Image distance in a spherical mirror + = () Subscripts 1 and 2 refer to initial and final optical media respectively. These ratios are sometimes also used, following simply from other definitions of refractive index, wave phase velocity, and the luminal speed equation:
A difference of 1.0 in magnitude corresponds to the brightness ratio of , or about 2.512. For example, a magnitude 2.0 star is 2.512 times as bright as a magnitude 3.0 star, 6.31 times as magnitude 4.0, and 100 times magnitude 7.0.
A trivial example. In mathematics, the mountain climbing problem is a mathematical problem that considers a two-dimensional mountain range (represented as a continuous function), and asks whether it is possible for two mountain climbers starting at sea level on the left and right sides of the mountain to meet at the summit, while maintaining equal altitudes at all times.
Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined to be the sum of the absolute differences of their respective Cartesian coordinates, a distance function (or metric) called the taxicab distance, Manhattan distance, or city block distance.
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