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Therefore in sketch c we see that using the principle of similar triangles, given that each triangle has identical angles, the sides will be in proportion: x the distance to the object in proportion to x', the height set on the vertical scale of the hypsometer, and h the height of the object above the observers eye-line in proportion to h', the ...
Since the rod is stationary in K 0, the distance between the marks is the proper length of the rod regardless of the time lapse between the two markings. On the other hand, it is not the proper distance between the marking events if the marks are not made simultaneously in K 0."
Length measurement, distance measurement, or range measurement (ranging) all refer to the many ways in which length, distance, or range can be measured. The most commonly used approaches are the rulers, followed by transit-time methods and the interferometer methods based upon the speed of light. Surveying is one ancient use of measuring long ...
The top mark is at 1,500 mm and the lower is at 1,345 mm; the distance between those two marks is 155 mm, yielding a distance to the rod of 15.5 m. Optical levelling , also known as spirit levelling and differential levelling , employs an optical level , which consists of a precision telescope with crosshairs and stadia marks .
Various terms for the length of a fixed object are used, and these include height, which is vertical length or vertical extent, width, breadth, and depth. Height is used when there is a base from which vertical measurements can be taken. Width and breadth usually refer to a shorter dimension than length. Depth is used for the measure of a third ...
A fast but expensive way to measure large areas is with a helicopter, using a GPS to record the location of the helicopter and a laser scanner to measure the ground. To increase precision, surveyors place beacons on the ground (about 20 km (12 mi) apart). This method reaches precisions between 5–40 cm (depending on flight height). [12]
This is because the travel time between any two points for a non-relativistic moving particle will just be the proper distance (that is, the comoving distance measured using the scale factor of the universe at the time of the trip rather than the scale factor "now") between those points divided by the velocity of the particle.
Wasserstein metrics measure the distance between two measures on the same metric space. The Wasserstein distance between two measures is, roughly speaking, the cost of transporting one to the other. The set of all m by n matrices over some field is a metric space with respect to the rank distance (,) = ().
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